Rozprawy doktorskie na temat „Mechanical Waveguides”

Thesis (Ph. D.)--Joint Program in Oceanography/Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), February 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 163-170).
Much of the recent research in ocean acoustics has focused on developing methods to exploit the effects that the sea surface and seafloor have on acoustic propagation. Many of those methods require detailed knowledge of the acoustic properties of the seafloor and the sound speed profile (SSP), which limits their applicability. The range-frequency waveguide invariant describes striations that often appear in plots of acoustic intensity versus range and frequency. These range-frequency striations have properties that depend strongly on the frequency of the acoustic source and on distance between the acoustic source and receiver, but that depend mildly on the SSP and seafloor properties. Because of this dependence, the waveguide invariant can be utilized for applications such as passive and active sonar, time-reversal mirrors, and array processing, even when the SSP or the seafloor properties are not well known. This thesis develops a framework for understanding and calculating the waveguide invariant, and uses that framework to develop signal processing techniques for the waveguide invariant. A method for passively estimating the range from an acoustic source to a receiver is developed, and tested on experimental data. Heuristics are developed to estimate the minimum source bandwidth and minimum horizontal aperture required for range estimation. A semi-analytic formula for the waveguide invariant is derived using WKB approximation along with a normal mode description of the acoustic field in a rangeindependent waveguide. This formula is applicable to waveguides with arbitrary SSPs, and reveals precisely how the SSP and the seafloor reflection coefficient affect the value of the waveguide invariant. Previous research has shown that the waveguide invariant range-frequency striations can be observed using a single hydrophone or a horizontal line array (HLA) of hydrophones. This thesis shows that traditional array processing techniques are sometimes inadequate for the purpose of observing range-frequency striations using a HLA. Array processing techniques designed specifically for observing range-frequency striations are developed and demonstrated. Finally, a relationship between the waveguide invariant and wavenumber integrations is derived, which may be useful for studying range-frequency striations in elastic environments such as ice-covered waveguides.
by Kevin L. Cockrell.
Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.
Includes bibliographical references (p. 165-175).
When an acoustic field propagates through a multimodal waveguide, the effect of variations in medium properties induced by 3D random inhomogeneities accumulates by multiple forward scattering over range. This causes significant random fluctuations in the received field and greatly affects underwater acoustic sensing and communication systems, such as Ocean Acoustic Waveguide Remote Sensing(OAWRS). In order to characterize this effect, analytical expressions are derived for the mean, variance and temporal covariance of the acoustic field forward propagated through an ocean waveguide containing internal waves, fish shoals, wind-generated bubble clouds and krill. These expressions account for the accumulated effects of multiple forward scattering through temporally and spatially varying scatter function densities of the 3D inhomogeneities. In order to quantify the statistics of the scatter function densities, physical models and statistical descriptions of these inhomogeneities are developed.Acoustic field transmission through internal waves in both continental shelf and deep ocean waveguides is investigated. Stratified ocean models are used to describe physical and statistical internal waves properties. Simulations for a typical continental-shelf environment show that when the standard deviation of the internal wave displacement exceeds the acoustic wavelength, the acoustic forward field becomes so randomized that the expected total intensity is dominated by the variance field and lacks a the coherent interference structure beyond moderate ranges. This leads to an effectively saturated field that decays monotonically. It is found that 3D scattering effects become pronounced when the acoustic Fresnel width exceeds the cross-range coherence length of the internal waves. This leads to frequency and range-dependent power losses in the forward field that explains some of the attenuation observed in acoustic transmission through typical continental shelf and deep ocean waveguides.
(cont.) A general analytical expression is derived for the temporal coherence of an acoustic signal propagating through an ocean waveguide with random 3D inhomogeneities.Advance knowledge of this coherence time scale is often essential in the design of ocean acoustic experiments and subsequent data analysis. This is because it determines the number of fluctuations in a given measurement period and the time window within which the coherent processing techniques essential to ocean acoustic data reduction and analysis can be applied. The analytic approach is found to explain the time scale of acoustic field fluctuations observed both at mega meters ranges in the deep ocean, as well as at kilometer ranges in continental shelf environments. The acoustic time scale is found to be much shorter than the coherence time scale of ocean internal waves. This is shown to be a consequence of multiple forward scattering of the acoustic waves through the internal waves. Analytical expressions are derived for the attenuation and dispersion of the acoustic field forward propagated through fish shoals and wind-generated bubble clouds in an ocean waveguide. It is found that at swim bladder resonance, fish shoals may sometimes lead to measurable attenuation in the forward field. The attenuation at off-resonant OAWRS frequencies, however, is typically negligible as shown both by the present theory and experimental data. The modeled attenuation due to random wind-generated bubble clouds is found to be highly sensitive to the choice of cutoff radius, which determines whether resonant bubbles are included in the bubble spectra. It is also found that bubble clouds generated under high wind speeds lead to additional dispersion and attention of the transmitted signal. These expected distortions can significantly degrade standard coherent processing techniques in ocean acoustics, such as the match filter, if not taken into account.
(cont.) Antarctic krill play a key role in the marine food chain as the primary source of sustenance for many species of whales, seals, birds, squid and fish. This makes knowledge of the distribution and abundance of krill essential to ecological research in the southern oceans. It is shown that swarms of Antarctic krill with typical packing densities can be instantaneously imaged by OAWRS over thousands of square kilometers in both deep and shallow water environments given properly designed experiments.
by Tianrun Chen.
Ph.D.

Harsh environment acoustic emission and ultrasonic wave sensing applications often benefit from placing the sensor in a remote and more benign physical location by using waveguides to transmit elastic waves between the structural location under test and the transducer. Waveguides are normally designed to have high fidelity over broad frequency ranges to minimize distortion - often difficult to achieve in practice. This thesis reports on an examination of using nonlinear ball chain waveguides for the transmission of acoustic emission and ultrasonic waves for the monitoring of thermal protection systems undergoing severe heat loading, leading to ablation and similar processes. Experiments test the nonlinear propagation of solitary, harmonic and mixed harmonic elastic waves through a copper tube filled with steel and elastomer balls and various other waveguides. Triangulation of pencil lead breaks occurs on a steel plate. Data are collected concerning the usage of linear waveguides and a water-cooled linear waveguide. Data are collected from a second water-cooled waveguide monitoring Atmospheric Reentry Materials in UVM's Inductively-Coupled Plasma Torch Facility. The motion of the particles in the dimer waveguides is linearly modeled with a three ball and spring chain model and the results are compared per particle. A theoretical nonlinear model is presented which is capable of exactly modeling the motion of the dimer chains. The shape of the waveform propagating through the dimer chain is modeled in a sonic vacuum. Mechanical pulses of varying time widths and amplitudes are launched into one end of the ball chain waveguide and observed at the other end in both time and frequency domains. Similarly, harmonic and mixed harmonic mechanical loads are applied to one end of the waveguide. Balls of different materials are analyzed and discriminated into categories. A copper tube packed with six steel particles, nine steel or marble particles and a longer copper tube packed with 17 steel particles are studied with a frequency sweep. The deformation experienced by a single steel particle in the dimer chain is approximated. Steel ball waveguides and steel rods are fitted with piezoelectric sensors to monitor the force at different points inside the waveguide during testing. The corresponding frequency responses, including intermodulation products, are compared based on amplitude and preloads. A nonlinear mechanical model describes the motion of the dimer chains in a vacuum. Based on the results of these studies it is anticipated that a nonlinear waveguide will be designed, built, and tested as a possible replacement for the high-fidelity waveguides presently being used in an Inductively Coupled Plasma Torch facility for high heat flux thermal protection system testing. The design is intended to accentuate acoustic emission signals of interest, while suppressing other forms of elastic wave noise.

Series impedances, including source and transfer impedances, are commonly used to model a variety of noise sources and noise treatment elements in duct systems. Particle velocity is assumed to be constant on the plane where the series impedances are defined. The research reported herein details investigations into measuring source and transfer impedance. Especially, the measurement and prediction of the transfer impedance of micro-perforated panel (MPP) absorbers is considered. A wave decomposition method for measuring source impedance and source strength was developed that was purely based on acoustic concepts instead of the equivalent circuit analysis. The method developed is a two-load method. However, it is not necessary to know the impedances of either load a priori. The selection of proper loads was investigated via an error analysis, and the results suggested that it was best to choose one resistive and one reactive load. In addition, a novel type of perforated element was investigated. MPP absorbers are metal or plastic panels with sub-millimeter size holes or slits. In the past, Maa's equation has been used to characterize their performance. However, Maa's equation is only valid for circular perforations. In this research, an inverse method using a nonlinear least square data fitting algorithm was developed to estimate effective parameters that could be used in Maa's theory. This inverse approach was also used to aid in understanding the effect of dust and fluid contamination on the performance of MPP absorbers. In addition, an approach to enhance the attenuation of MPP absorbers by partitioning the backing cavity was investigated experimentally and numerically. Results indicated that partitioning improved the attenuating of grazing sound waves. The effect of modifying both the source and transfer impedances on the system response was also studied using the Moebius transformation. It was demonstrated that the Moebius transformation is a mathematical tool that can be employed to aid in determining and understanding the impact of acoustic impedance modifications on a vibro-acoustic system.

Use of Slotted Waveguide Antenna Stiffened Structures (SWASS) in future commercial and military aircraft calls for the development of an airworthiness certification procedure. The first step of this procedure is to provide a computationally low-cost method for modeling waveguide antenna arrays on the scale of an aircraft skin panel using a multi-fidelity model. Weather detection radar for the Northrop Grumman X-47 unmanned air system is considered as a case study. COMSOL Multiphysics is used for creating high-fidelity waveguide models that are imported into the MATLAB Phased Array Toolbox for large-scale array calculations using a superposition method. Verification test cases show that this method is viable for relatively accurate modeling of large SWASS arrays with low computational effort. Additionally, realistic material properties for carbon fiber reinforced plastic (CFRP) are used to create a more accurate model. Optimization is performed on a 12-slot CFRP waveguide to determine the waveguide dimensions for the maximum far-field gain and separately for the maximum critical buckling load. Using the two separate optima as utopia points, a multi-objective optimization for the peak far-field gain and critical buckling load is performed, to obtain a balance between EM performance and structural strength. This optimized waveguide is then used to create a SWASS array of approximately the same size as an aircraft wing panel using the multi-fidelity modeling method that is proposed. This model is compared to a typical conventional weather radar system, and found to be well above the minimum mission requirements.
Master of Science

Microstructure manipulation is a fundamental process to the study of biology and medicine, as well as to advance micro- and nano-system applications. Manipulation of microstructures has been achieved through various microgripper devices developed recently, which lead to advances in micromachine assembly, and single cell manipulation, among others. Only two kinds of integrated feedback have been demonstrated so far, force sensing and optical binary feedback. As a result, the physical, mechanical, optical, and chemical information about the microstructure under study must be extracted from macroscopic instrumentation, such as confocal fluorescence microscopy and Raman spectroscopy. In this research work, novel Micro-Opto-Electro-Mechanical-System (MOEMS) microgrippers are presented. These devices utilize flexible optical waveguides as gripping arms, which provide the physical means for grasping a microobject, while simultaneously enabling light to be delivered and collected. This unique capability allows extensive optical characterization of the structure being held such as transmission, reflection, or fluorescence. The microgrippers require external actuation which was accomplished by two methods: initially with a micrometer screw, and later with a piezoelectric actuator. Thanks to a novel actuation mechanism, the “fishbone”, the gripping facets remain parallel within 1 degree. The design, simulation, fabrication, and characterization are systematically presented. The devices mechanical operation was verified by means of 3D finite element analysis simulations. Also, the optical performance and losses were simulated by the 3D-to-2D effective index (finite difference time domain FDTD) method as well as 3D Beam Propagation Method (3D-BPM). The microgrippers were designed to manipulate structures from submicron dimensions up to approximately 100 µm. The devices were implemented in SU-8 due to its suitable optical and mechanical properties. This work demonstrates two practical applications: the manipulation of single SKOV-3 human ovarian carcinoma cells, and the detection and identification of microparts tagged with a fluorescent “barcode” implemented with quantum dots. The novel devices presented open up new possibilities in the field of micromanipulation at the microscale, scalable to the nano-domain.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.
Includes bibliographical references (p. 211-225).
Methods are developed for passive source localization and environmental parameter estimation in seismo-acoustic waveguides by exploiting the dispersive behavior of guided wave propagation. The methods developed are applied to the terrestrial continental shelf environment and the Jovian icy satellite Europa. The thesis is composed of two parts. First, a method is derived for instantaneous source-range estimation in a horizontally-stratified ocean waveguide from passive beam-time intensity data obtained after conventional plane-wave beamforming of acoustic array measurements. The method is advantageous over existing source localization methods, since (1) no knowledge of the environment is required except that the received field should not be dominated by purely waterborne propagation, (2) range can be estimated in real time with little computational effort beyond plane-wave beamforming, and (3) array gain is fully exploited. Second, source range estimation and environmental parameter inversion using passive echo-sounding techniques are discussed and applied to Europa. We show that Europa's interior structure may be determined by seismo-acoustic echo sounding techniques by exploiting natural ice fracturing events or impacts as sources of opportunity.
(cont.) A single passive seismic sensor on Europa's surface may then be used to estimate the thickness of its ice shell and the depth of its subsurface ocean. To further understand the seismo-acoustic characteristics of natural sources on Europa, a fracture mechanics model is developed for the initiation and propagation of a crack through a porous ice layer of finite thickness under gravitational overburden. It is found that surface cracks generated in response to a tidally induced stress field may penetrate through the entire outer brittle layer if a subsurface ocean is present on Europa. While Europa's ice is likely highly porous and fractured, our current caculations show that porosity-induced scattering loss of ice-penetrating radar waves should not be significant.
by Sunwoong Lee.
Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 259-278).
Reported declines in the population of Atlantic cod have a potential to affect long-term ecological balance and the sustainability of the cod fishery along the US northeast coast. These assessments have led to severe fishing cuts over the past few years, have consequently threatened the centuries-old Atlantic cod fishery along the New England coast and put the livelihood of thousands of fishermen at risk. Amidst this fisheries crisis, calls by elected officials, environmental groups and fishing consortiums were made for an Ocean Acoustic Waveguide Remote Sensing (OAWRS) survey of the Gulf of Maine cod stock. Typically, cod stock assessments incorporate data collected from conventional acoustic and trawl line transect surveys that highly undersample the marine environment in space and time and lead to ambiguities in population estimates. The combination of conventional methods and OAWRS techniques, however, has been demonstrated to provide rapid and accurate fish stock assessments over ecosystem-scale areas for other species. In this thesis, the feasibility of accurately surveying cod stocks with OAWRS is theoretically assessed. These theoretical predictions are then experimentally verified by successfully sensing cod with OAWRS over ecosystem scales in the Nordic Seas. Following direct requests by Massachusetts state officials to determine if OAWRS could be used to detect and survey the reported waning cod populations in coastal New England waters, we obtained measurements of typical aggregation densities and occupancy depths of spawning cod in Ipswich Bay from conventional echosounder surveys conducted in Spring 2011. Cod length distributions were also measured from which we estimated the swimbladder resonance frequencies of local cod via a harmonic oscillator model that includes the effects of damping, the cod's swim bladder air volume at a given neutral buoyancy depth as well as changes to this volume for deviations from neutral buoyancy depth. The optimal frequency for OAWRS detection typically corresponds to that where the resonance peak is found. We showed that our theoretical estimates of cod swimbladder resonance matched very well with independent measurements of caged cod resonance from decades old Norwegian data. Using parabolic equation modeling of ocean waveguide propagation, the scattered level of typical spawning cod aggregations was estimated and compared with that from seafloor scattering, which is a typical limiting factor in long range active sensing. Seafloor scattering was estimated via a Rayleigh-Born approach we developed, where the magnitude squared of seafloor scattering amplitude was empirically determined from thousands of measurements made during major OAWRS experiments along the US Northeast coast. It was found that near cod swimbladder resonance (roughly 150-600 Hz), determined from the New England length and depth distribution data, OAWRS was capable of robustly detecting spawning cod aggregations from many tens of kilometers in range with high signal-to- noise ratios (SNRs) greater than 20 dB for typical spawning cod configurations in New England waters. Above the resonance frequency peak, it is possible to detect cod for typical shoaling densities because cod scattering reaches a plateau due to geometric scattering that is above the seafloor scattering trend for typical OAWRS frequencies. Well below the resonance peak, scattering from cod is expected to fall off rapidly and faster than seafloor scattering, and so provides important information about resonance behavior but can be difficult to probe given the very low frequencies involved. This theoretical feasibility study emphasized the need for a low frequency source that spans cod swimbladder resonance and helped demonstrate the potential for use of OAWRS for cod assessments over ecosystem scales. To confirm our theoretical predictions on the OAWRS detection of cod and other keystone fish species, we designed, prepared and conducted a major oceanographic experiment in the Nordic Seas in the Arctic in the winter (February-March) of 2014 using three major research vessels, the US RV Knorr, the Norwegian RV Johan Hjort and the Norwegian FV Artus. The Nordic Seas 2014 experiment was conducted in difficult gale and hurricane force weather conditions along most of Norway's western and northern coast. MIT's OAWRS Source, obtained through a NSF-Sloan MRI grant, spanned the 800-1600 Hz range, and the receiver was ONR's Five Octave Receiver Array (FORA). Unlike the declining trend of cod population in New England waters, cod population in the Nordic Seas has been thriving for many years and is currently at its healthiest recorded state. The experiment period was chosen such that it coincided with the peak spawning period of cod along the coastal Lofoten region in Norway where they congregate in high densities, as well as other keystone species that migrate from the ice-edge to spawn in some of the world's largest mass migrations. In planning, we determined likely spawning grounds for cod, and other keystone species such as capelin, herring, and haddock using historic survey data collected along the Norwegian coast. With our calibrated model of fish swimbladder resonance and historic length distribution data from Norway, swimbladder resonance frequencies and target strengths of these fish species were estimated. We also determined optimal OAWRS ship tracks for remote detection of these species above seafloor scattering using waveguide propagation modeling. While the OAWRS frequencies were greater than those expected for cod swimbladder resonance, cod shoals over ten kilometers in length were robustly detected and successfully imaged from tens of kilometer ranges during the experiment. This produced the first instantaneous images of a vast cod shoal. It also confirmed our predictions that OAWRS can be used to remotely sense and survey cod populations. Our theoretical predictions suggest that the use of lower OAWRS frequencies near cod swimbladder resonance would lead to greater dynamic range in population density estimates. The Nordic Seas experiment provided the first look revealing the entire horizontal morphology of vast cod, capelin, haddock and Norwegian herring shoals. This was done with instantaneous OAWRS imaging. The presence of multiple shoaling fish species during the Nordic Seas experiment provided us with a unique opportunity to study general shoaling behavior across species over ecosystem scales with OAWRS. For example, many pelagic and demersal fish species are known to undergo distant migrations for feeding, spawning and overwintering year after year. This suggests that migrating populations have an ability to efficiently sense their environment. By combining OAWRS estimates of fish scattering strength and population density obtained from simultaneous depth echo-sounding along line transects, areal population densities over entire shoals were determined. This enabled estimation of total shoal population, shoal aspect ratio, and shoal migration speed via cross correlation of population density over time. It was shown that across several species, as shoal population increased (tens of thousands to hundreds of millions of individuals), shoal aspect ratio also increased (roughly from one to ten). Single-celled organisms with higher aspect ratios have been shown to more efficiently and accurately detect chemical gradients at microscopic scales. The high-aspect ratio or elongated morphology of a large migrating fish shoal is consistent with the entire shoal serving the function of a biological antenna for efficient spatial and temporal sensing of mesoscale processes in the environment. We also studied the evolution of air resonance power efficiency in the violin and its ancestors. We collected historical data, including samples from roughly 500 classical Cremonese violins from the renowned workshops of Amati, Stradivari and Guarneri, to establish historic time series of key design traits. We determined the primary physical mechanisms governing radiated air resonance power in the violin and its ancestors and used this knowledge to explain the evolutionary trends we discovered.
by Ankita Deepak Jain.
Ph. D.

We study different phenomena associated with single-photon propagation in optical cavities coupled through optical fibers. We first address the issue of storing and delaying single-photon wavepackets in an array of microcavities. This has possible applications in developing reliable and efficient quantum repeaters that will be utilized in building long distance quantum networks. Second, we investigate a Hong-Ou-Mandel (HOM) type of interference between two photons that are produced in two coupled atom-cavity systems. The HOM effect in this setup can test the degree of indistinguishability between photons when they are stored inside cavities. This part of the dissertation also includes the study of entanglement between atoms, cavities and atom-cavity systems induced by the photons. Finally, we focus on single-photon interactions with a tiny movable mirror in the context of quantum optomechanics. We investigate how the mechanical motion of the mirror leaves its imprints on the optical spectrum of the photon This dissertation includes previously published and unpublished co-authored material.
10000-01-01

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 117-119).
In this thesis, we derive full theoretical expressions for the moments of the matched filtered scattered field due to volume inhomogeneities in an ocean waveguide and provide a computationally efficient time harmonic approximation to the matched filtered model. Following the approach developed by Galinde et al 16], the expressions are derived from first principles, by applying Green's theorem and the Born approximation. The scattered field and the total moment expressions are in terms of the fractional changes in the bottom compressibility and density, as well as the waveguide Green function and its gradients. The volume inhomogeneities are assumed to be statistically stationary, and assumed to be correlated in all three directions following a delta correlation function. Sound propagation in the ocean is modeled using the parabolic equation model and actual measurements of bathymetry and sound speed at the experimental locations. Monte Carlo simulations are used to account for the sound speed variability in the ocean waveguide due to internal waves or other sources of acoustic field randomization. The computationally efficient time-harmonic model is shown to provide a good approximation to the full broadband matched filtered model for a standard Pekeris waveguide. The time-harmonic model is then calibrated for ocean bottom reverberation at several frequencies in the 415-1325 Hz band, with data collected during the 2003 and 2006 ONR Geoclutter Experiments on the New Jersey continental shelf and on the northern flank of Georges Bank in the Gulf of Maine, respectively. The statistics for the inverted bottom parameters are summarized for all frequencies and experimental locations considered. The acoustically determined bottom parameters are shown to vary with approximately the wavelength cubed, suggesting that, by different frequencies selecting the scale of the acoustic inhomogeneities, the acoustic effects dominate over the geophysical effects.
by Anamaria Ignisca.
S.M.

The study makes use of a variation of the Finite-Difference Time-Domain (FDTD) method as first proposed by Yee to simulate electromagnetic field distribution and propagation in an open waveguide structure. In order to prove that this new method is valid, a reflection coefficient is calculated with simulation data and compared to measurements. The agreement between measurement and simulation data, while not exact, is enough to establish the veracity of the new method. This study contains a detailed discussion of the discrepancies which were observed. Also presented are colour images of the simulation which give the reader an idea as to the nature and level of detail of the information which can be obtained from the simulation.

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, February, 2021
Cataloged from the official PDF version of thesis.
Includes bibliographical references (pages 87-91).
In this thesis, we perform a spectral discrimination of fish shoals from background returns using statistical techniques. Classification of fish species requires an efficient and solid approach to distinguish fish scattering from seafloor returns. Neyman-Pearson Hypothesis Testing, Kullback-Leibler divergence, Matched Filter and discriminating based on the shape of the spectral dependence, methods originated from Detection theory, are applied in well documented cases from Gulf of Maine during spawning season to distinguish seafloor returns from fish scattering across frequency domain. The discrimination of fish shoals from seafloor returns is achieved by analyzing the absolute levels of scattered returns and the pattern of their frequency response. A generalization of the statistical techniques is developed that enables all frequencies to be tested at once, allowing the spectral discrimination and echolocation of fish shoals from regions dominated by background returns. Conclusions derived from statistical techniques are consistent with physical evidences, such as in situ echosounder measurements and frequency responses. Fish shoals are distinguished from background regions by evaluating the likelihood ratio test, matched filter and analyzing the slope of the frequency dependence of all pixels in an examined ocean acoustic waveguide remote sensing (OAWRS) image.
by Eleftherios Kaklamanis.
S.M.
S.M. Massachusetts Institute of Technology, Department of Mechanical Engineering

Photonics, the technological field that encompasses all aspects of light, has been rapidly growing and increasingly useful in uncovering fundamental truths about nature. It has helped detect gravitational waves, allowed for a direct measurement of the quantum wave function, and has helped realize the coldest temperatures in the universe. But photonics has also had an enormous impact on day-to-day life as well; it has enabled high capacity and/or high speed telecommunication, offered cancer treatment solutions, and has completely revolutionized display and scanning technology. All of these discoveries and applications have required a superb understanding of light, but also a high degree of control over the sometimes abstract properties of light. The work contained in this thesis explores two novel means of controlling and manipulating two different abstract properties of light. In Part I, the property under investigation is the polarization state of light – a property that is paramount to all light-matter interactions, and even some light-light interactions such as interference. Here, a liquid crystal on silicon spatial light modulator (LCOS-SLM)’s capabilities in manipulating the polarization state of light is theoretically examined and experimentally exploited, tested, and reported on. It is found through experimentation that, for an appropriate range of beam sizes and input polarizations, a single LCOS-SLM can be used to produce any light field with an arbitrary, spatially varying polarization profile. In Part II, the property under investigation loosely corresponds to light’s spatial degree of freedom – how light can move from one spot in space to another in a non-trivial manner. Here, control over light’s position through a waveguide array through the use of quantum geometric phase is theoretically examined, simulated, and experimentally designed. It is found through simulation that a threewaveguide array is capable of implementing two dimensional unitary transformations. The common theme between Part I and Part II is manipulating these properties of light to realize classes of general transformations. Moreover, if the light field is treated as a quantum state in the basis of either property under investigation, a two dimensional computational basis ensues. This is precisely the right cardinality for applications in quantum information.

Els forats negres acústics en mecànica (coneguts per les sigles ABHs, de l’anglès Acoustic Black Holes) solen estar formats per osques en bigues i plaques, el gruix de les quals decau segons una llei potencial. L’efecte de l’ABH és el d’alentir les velocitats de fase i de grup de les ones de flexió incidents de tal manera que, en teoria, faria falta un temps infinit perquè les ones arribessin al centre de l’ABH, si el gruix d’aquest últim fos exactament zero. Tanmateix, a la pràctica això no és possible tot i que es pot aconseguir una forta dissipació col·locant una capa de material esmorteïdor al centre de l’ABH, on es concentra la major part de l’energia de les ones. En els darrers anys, els ABHs no només s’han explotat com a mètode passiu per reduir vibracions estructurals i l’emissió corresponent de soroll, sinó que també s’ha explorat el seu potencial per altres aplicacions com la manipulació d’ones o la captació d’energia. Aquesta tesi té tres objectius principals. Així, doncs, després d'una introducció general als ABHs, el treball s’ha dividit en tres grans seccions. La primera aborda aplicacions dels ABHs en bigues rectes i plaques planes. Per començar, es proposa i s’analitza un voladís piezoelèctric amb un acabament d’ABH per capturar energia. A continuació es presenten ABHs en forma d’anell per tal d’aïllar punts d’excitació externs en plaques planes i així evitar la transmissió de vibracions. Finalment, es contemplen configuracions periòdiques de matrius d’ABHs per tal de col·limar feixos d'ones de flexió i concentrar la seva energia en zones predeterminades d’una placa. La segona part de la tesi proposa nous dissenys d’ABHs per a estructures amb curvatura. Aquestes són molt habituals en els sectors naval, aeronàutic i industrial, de manera que val la pena investigar si els ABH poden resultar alguns casos. La secció comença analitzant la inclusió d’ABHs en bigues circulars i es veu com això dona peu a l’aparició de fenòmens típics en sistemes periòdics. Acte seguit es proposa un ABH anular per reduir les vibracions en conductes cilíndrics. En concret, es tracten els casos d’un conducte simplement suportat amb un ABH anular, i el d’un conducte amb ABH, suports periòdics i rigidificadors. Per finalitzar la secció, s’investiguen els efectes dels ABH anulars en la radiació acústica del conducte tenint en compte el nivell de potència acústica, l’eficiència de radiació i la intensitat supersònica. La tercera part de la tesi és més curta que les anteriors i simula l’aïllament d'una placa amb múltiples ABHs, en el rang de mitja i alta freqüència. A tal efecte s’empra el mètode de l’anàlisi estadística de distribució modal d'energia (SmEdA: statistical modal energy distribution analysis). En aquesta secció, l’estructura amb ABHs ja no s’analitza com un element individual sinó que s’acobla a dues cavitats d’aire, formant part d’un sistema mecànic més complex. Al llarg de la tesi s’utilitza repetidament el mètode d’expansió gaussiana (GEM: Gaussian expansion method). Pel GEM entenem prendre funcions gaussianes com a base per resoldre equacions diferencials en derivades parcials en el marc del mètode de Rayleigh-Ritz. El GEM s’assembla molt als enfocaments d’ondetes, però ofereix alguns avantatges en el cas de condicions de contorn periòdiques. Al principi de la tesi s’exposa un breu repàs del GEM i, quan és necessari, s’aborda la seva reformulació per a un problema particular en el capítol corresponent.
Los agujeros negros acústicos en mecánica (conocidos por las siglas ABHs, del inglés Acoustic Black Holes) suelen estar formados por muescas en vigas y placas, el grueso de las cuales decae según una ley potencial. El efecto del ABH es el de ralentizar las velocidades de fase y de grupo de las ondas de flexión incidentes de tal modo que, en teoría, haría falta un tiempo infinito para que las ondas alcanzaran el centro del ABH, si el grueso de este último fuera exactamente cero. Sin embargo, en la práctica esto no es posible, aunque se puede conseguir una fuerte disipación colocando una capa de material amortiguador en el centro del ABH, donde se concentra la mayor parte de la energía de las ondas. En los últimos años, los ABHs no sólo se han explotado como método pasivo para reducir vibraciones estructurales y la consecuente emisión de ruido, sino que también se ha explorado su potencial para otras aplicaciones como la manipulación de ondas o la captación de energía. Esta tesis tiene tres objetivos principales. Así pues, tras una introducción general a los ABHs, el trabajo se ha dividido en tres grandes secciones. La primera aborda aplicaciones de los ABHs en vigas rectas y placas planas. Para empezar, se propone y analiza un voladizo piezoeléctrico con un acabado de ABH para capturar energía. A continuación, se presentan ABHs en forma de anillo para aislar puntos de excitación externos en placas planas y así evitar la transmisión de vibraciones. Finalmente, se contemplan configuraciones periódicas de matrices de ABHs para colimar haces de ondas de flexión y concentrar su energía en zonas predeterminadas de una placa. La segunda parte de la tesis propone nuevos diseños de ABHs para estructuras con curvatura. Estas son muy habituales en los sectores naval, aeronáutico e industrial, por lo que merece la pena investigar si los ABH pueden dar buenos resultados en algunos casos. La sección comienza analizando la inclusión de ABHs en vigas circulares y se ve como estos dan pie a la aparición de fenómenos típicos de sistemas periódicos. Seguidamente se propone un ABH anular para reducir las vibraciones en conductos cilíndricos. En concreto, se tratan los casos de un conducto simplemente soportado con un ABH anular, y el de un conducto con ABH, soportes periódicos y rigidificadores. Para finalizar la sección, se investigan los efectos de los ABH anulares en la radiación acústica del conducto teniendo en cuenta el nivel de potencia acústica, la eficiencia de radiación y la intensidad supersónica. La tercera parte de la tesis es más corta que las anteriores y simula el aislamiento de una placa con múltiples ABHs, en el rango de media y alta frecuencia. A tal efecto se emplea el método del análisis estadístico de distribución modal de energía (SmEdA: statistical modal energy distribution analysis). En esta sección, la estructura con ABHs ya no se analiza como un elemento individual, sino que se acopla a dos cavidades de aire formando parte de un sistema mecánico más complejo. A lo largo de la tesis se utiliza repetidamente el método de expansión gaussiana (GEM: Gaussian expansión method). Por GEM entendemos tomar funciones gaussianas como base para resolver ecuaciones diferenciales en derivadas parciales en el marco del método de Rayleigh-Ritz. El GEM se parece mucho a los enfoques de ondículas, pero ofrece algunas ventajas en el caso de condiciones de contorno periódicas. Al principio de la tesis se expone un breve repaso del GEM y, cuando es necesario, se aborda su reformulación para un problema particular en el capítulo correspondiente.
Acoustic black holes (ABHs) in mechanics usually consist of geometrical indentations on beams and plates having a power-law decreasing thickness profile. An ABH slows down the phase and group velocity of incident flexural waves in such a way that, ideally, it would take an infinite amount of time for them to reach the ABH center, if the latter had an exact zero thickness. Though this is not possible in practice, strong wave dissipation can be achieved by placing a damping layer at the central region of the ABH, where most vibration energy concentrates. In recent years, ABHs have been not only exploited as a passive means for structural vibration and noise reduction, but its potential for other applications like wave manipulation or energy harvesting have been also explored. The objective of this thesis is threefold. Therefore, after an initial overview the work is divided into three main parts. The first one deals with ABH applications on straight beams and flat plates. To start with, an ABH piezoelectric bimorph cantilever for energy harvesting is proposed and analyzed. Then, ring-shaped ABH indentations are suggested as a means of isolating external excitation points in flat plates and prevent vibration transmission. Finally, periodic ABH array configurations are contemplated to collimate flexural wave beams and focus energy at desired plate locations. The second part of the thesis proposes new ABH designs for curved structures. The latter are very common in the naval, aeronautical and industrial sectors so it is worth investigating if ABHs could function for them. The section starts analyzing the embedding of ABHs on circular beams and how this results in the appearance of typical phenomena of periodic systems. After that, an annular ABH is proposed to reduce vibrations in cylindrical shells. The cases of a simply supported shell with an annular ABH indentation and of a periodic simply supported ABH shell with stiffeners are considered. To finish the section, the effects of annular ABHs on sound radiation are investigated in terms of sound power level, radiation efficiency and supersonic intensity. The third part of the thesis is shorter than the previous ones and is devoted to analyzing the transmission loss of a plate with multiple ABH indentations, in the mid-high frequency range. Statistical modal energy distribution analysis is used for that purpose. Here, the ABH plate is not taken as an individual structure but coupled to two air cavities, thus being part of a more complex mechanical system. Throughout the thesis repeated use is made of the Gaussian expansion method (GEM). The GEM refers to taking Gaussian functions as the basis for solving partial differential equations in the framework of the Rayleigh-Ritz method. The GEM closely resembles wavelet approaches but offers some advantages in the case of periodic boundary conditions. A brief overview of the GEM is exposed at the beginning of the thesis and, when necessary, its reformulation for a particular problem is tackled in its corresponding chapter.

Orientador: Luiz Carlos Kretly
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: O propósito deste trabalho é, a partir dos conceitos de linhas de transmissão, teoria de filtros e o conhecimento pioneiro deste grupo acerca das chaves MEMS de RF, propor duas aplicações reais baseadas nesta estrutura singular: um deslocador de fase e um filtro sintonizável na faixa de 0,1-35GHz e banda Ku (12,4-18GHz) respectivamente. Uma abordagem puramente eletromecânica é realizada na etapa inicial, observando a tensão de ativação da chave para diferentes formas estruturais, desmistificando a histerese mecânica, fenômeno intrínseco a este tipo de dispositivo. Na segunda fase do trabalho é feito um detalhamento do comportamento eletromagnético da chave MEMS, explorando fortemente a extração dos parâmetros elétricos e sua inserção em outros circuitos. Por fim, a implementação do filtro sintonizável e do deslocador de fase realizouse baseada nos conceitos de DMTL - Distributed MEMS Trasmission Lines - onde tanto a seleção da frequência central de passagem do filtro, quanto o comprimento elétrico total do deslocador são controladas pela capacitância variável da chave MEMS, de acordo com uma tensão de controle DC aplicada.
Abstract: The purpose of this work is, based on transmission line concepts, filter theory and the pioneer knowledge of this group about RF MEMS Switches, propose two physical applications employing this singular structure: a phase shifter and a tunable filter at 0.1 - 35GHz range and Ku band respectively. A purely electromechanical approach is done at the initial step, observing the switch pull-in voltages for several structural geometries, demystifying the mechanical hysteresis, intrinsic phenomena of this kind of device. On the second phase of the work, the MEMS switch electromagnetic behavior is detailed, strongly exploring the electrical parameters extraction and its application on other types of circuits. Finally, the tunable filter and phase shifter are implemented through DMTL - Distributed MEMS Transmission Lines - concepts, where frequency selection and the amount of phase shifting are controlled by the variable switch capacitance according to the applied DC control voltage.
Mestrado
Telecomunicações e Telemática
Mestre em Engenharia Elétrica

Nowadays, silicon photonics is a widely studied research topic. Its high-index-contrast and compatibility with the complementary metal-oxide-semiconductor technology make it a promising platform for low cost high density integration. Several general problems have been brought up, including the lack of silicon active devices, the difficulty of light coupling, the polarization dependence, etc. This thesis aims to give new attempts to novel solutions for some of these problems. Both theoretical modeling and experimental work have been done. Several numerical methods are reviewed first. The semi-vectorial finite-difference mode solver in cylindrical coordinate system is developed and it is mainly used for calculating the eigenmodes of the waveguide structures employed in this thesis. The finite-difference time-domain method and beam propagation method are also used to analyze the light propagation in complex structures. The fabrication and characterization technologies are studied. The fabrication is mainly based on clean room facilities, including plasma assisted film deposition, electron beam lithography and dry etching. The vertical coupling system is mainly used for characterization in this thesis. Compared with conventional butt-coupling system, it can provide much higher coupling efficiency and larger alignment tolerance. Two novel couplers related to silicon photonic wires are studied. In order to improve the coupling efficiency of a grating coupler, a nonuniform grating is theoretically designed to maximize the overlap between the radiated light profile and the optical fiber mode. Over 60% coupling efficiency is obtained experimentally. Another coupler facilitating the light coupling between silicon photonic wires and slot waveguides is demonstrated, both theoretically and experimentally. Almost lossless coupling is achieved in experiments. Two approaches are studied to realize polarization insensitive devices based on silicon photonic wires. The first one is the use of a sandwich waveguide structure to eliminate the polarization dependent wavelength of a microring resonator. By optimizing the multilayer structure, we successfully eliminate the large birefringence in an ultrasmall ring resonator. Another approach is to use polarization diversity scheme. Two key components of the scheme are studied. An efficient polarization beam splitter based on a one-dimensional grating coupler is theoretically designed and experimentally demonstrated. This polarization beam splitter can also serve as an efficient light coupler between silicon-on-insulator waveguides and optical fibers. Over 50% coupling efficiency for both polarizations and -20dB extinction ratio between them are experimentally obtained. A compact polarization rotator based on silicon photonic wire is theoretically analyzed. 100% polarization conversion is achievable and the fabrication tolerance is relatively large by using a compensation method. A novel integration platform based on nano-epitaxial lateral overgrowth technology is investigated to realize monolithic integration of III-V materials on silicon. A silica mask is used to block the threading dislocations from the InP seed layer on silicon. Technologies such as hydride vapor phase epitaxy and chemical-mechanical polishing are developed. A thin dislocation free InP layer on silicon is obtained experimentally.
QC20100705

Ces travaux ont porté dans un premier temps sur la mise en forme et l’étude de la densification de céramiques transparentes de YAG:Nd de grandes dimensions. Le choix des paramètres de coulage sous pression et de compaction isostatique à froid ont permis de contrôler les dimensions et la microstructure des pièces crues élaborées. Le frittage sous vide de ces céramiques a cependant conduit à une hétérogénéité microstructurale entre le coeur et le bord des échantillons. Plus particulièrement, des pores résiduels ont été détectés au coeur des céramiques, altérant les propriétés optiques. Des post-traitements HIP (Hot Isostatic Pressing) ont alors été mis en oeuvre pour mieux contrôler la microstructure des céramiques. Cette voie a démontré son efficacité pour réduire en nombre et en taille les pores résiduels, avec cependant certaines limites concernant notamment la réoxydation des céramiques de grandes dimensions. Finalement, les céramiques élaborées ont montré des performances laser proches de celles des monocristaux de même composition.Dans un second temps, un procédé de coulage en bande pour l’élaboration de céramiques transparentes de YAG multicouches a été développé. Plus particulièrement, un travail original a été mené sur l’étude de l’influence de la formulation des suspensions sur les propriétés mécaniques des bandes céramiques crues. Cette étude a ainsi permis d’élaborer des bandes pouvant être ultérieurement manipulées et transformées. Une céramique multicouche avec une bande centrale dopée en ion Nd3+ d’épaisseur contrôlée a alors pu être mise en forme par thermocompression de bandes de différentes compositions (YAG et YAG:Nd). Après déliantage et frittage, une céramique transparente de type « guide d’onde planaire » a finalement été obtenue
The first step of this work was focused on the shaping and sintering of large sized Nd:YAG transparent ceramics. The choice of the pressure casting and cold isostatic pressing parameters allowed to control the thickness and the microstructure of the green bodies. However, vacuum sintering of these parts led to a microstructural heterogeneity between the core and the edge of the samples. More particularly, residual pores have been detected in the core of the ceramics, decreasing the optical properties. Then, HIP (Hot Isostatic Pressing) post-treatments were implemented to control the ceramics microstructure. This route helped to reduce the number and size of residual pores. But limitations appeared, especially concerning the large ceramics. Finally, the obtained ceramics showed laser performances close to those of the single crystals of same composition.The second part was devoted to the development of a tape casting process for the elaboration of YAG multilayered transparent ceramics. More particularly, the influence of the slurry formulation on the mechanical properties of the green tapes was studied. This original work allowed the shaping of green tapes with good mechanical properties and a controlled organic content. Then, a multilayered ceramic with a central Nd-doped layer could be elaborated by thermolamination of layers with different compositions (YAG and YAG: Nd). After debinding and sintering, a transparent ceramic planar waveguide was finally obtained

Dans cette thèse, nous avons étudié les propriétés optiques de boîtes quantiques InAs/GaAs contenues dans un fil photonique. Des résultats antérieurs à cette thèse ont montré que ces fils photoniques permettent d’extraire les photons avec une efficacité très élevée.Le premier résultat original de ce travail est l’observation de la dérive temporelle de la raie d’émission de la photoluminescence d’une boîte quantique. Cet effet a été attribué à la lente modification de la charge de surface du fil due à l’absorption des molécules d’oxygène présentes dans le vide résiduel du cryostat. Nous avons montré qu’une fine couche de Si3N4 permettait de supprimer cette dérive. La dérive temporelle pouvant être différente pour différentes boites quantiques, nous avons pu tirer partie de cet effet pour mettre en résonance deux boites quantiques contenues dans le même fil.Le deuxième résultat original est la mise en évidence de la modification de l’énergie d’émission d’une boîte quantique soumise à une contrainte mécanique induite par la vibration du fil. Nous avons observé que le spectre de la raie d’émission d’une boîte quantique s’élargit considérablement lorsque le fil est mécaniquement excité à sa fréquence de résonance. A l’aide d’une illumination stroboscopique synchronisée avec l’excitation mécanique, nous avons pu reconstruire l’évolution du spectre d’une boîte quantique au cours d’une période de la vibration mécanique. L’amplitude de l’oscillation spectrale de la raie de luminescence dépend de la position de la boîte dans le fil à cause d’un très fort gradient de contrainte. En utilisant deux modes d’oscillation mécanique de polarisations linéaires et orthogonales, nous pouvons extraire une cartographie complète de la position des boîtes quantiques à l’intérieur du fil. Enfin, grâce à ce gradient, on peut, dans certains cas, trouver une position du fil pour laquelle deux boites quantiques peuvent être amenées en résonance
In the framework of this thesis, single InAs/GaAs quantum dot devices were studied by optical means. Starting with a general description of self-assembled InAs QDs, two types of single QD devices were presented. The first approach was a tapered GaAs photonic wire embedding single InAs QDs whose efficiency as a single photon source was previously shown to be 90%. We investigated several optical properties of the single QDs. The charged and neutral states of the QD were identified and selectively excited using quasi-resonant excitation.The first original result of this thesis is the observation of a continuous temporal blue-drift of the QD emission energy. We attributed this blue drift to oxygen adsorption onto the sidewall of the wire, which modified the surface charge and hence the electric field seen by the QD. Moreover, we demonstrated that a proper coating of the GaAs photonic nanowire surface suppressed the drift. The temperature effect on this phenomenon revealed an adsorption peak around 20K, which corresponds to the adsorption of oxygen on GaAs. This observation is in good agreement with previous temperature studies with a tapered photonic wire. This was the first study of the spectral stability of photonic wires embedding QDs, crucial for resonant quantum optics experiments. As an alternative, we took advantage of this temporal drift to tune QD emission energies. In a controlled way, we tuned into resonance two different QDs which were embedded in the same photonic nanowire. In the last part of this work, we studied the influence of the stress on single QDs contained in a trumpet-like GaAs photonic wire. The main effect of stress is to shift the luminescence lines of a QD. We applied the stress by exciting mechanical vibration modes of the wire. When the wire is driven at its the mechanical resonance the time-integrated photoluminescence spectrum is broaden up to 1 meV owing to the oscillating stress, The measured spectral modulation is a first signature of strain-mediated coupling between a mechanical resonator and embedded QD single light emitter. With a stroboscopic technique, we isolated a certain phase of the oscillating wire and thereby selected a value of QD emission energies. As a highlight of our study, we managed to bring two different QDs contained in the same wire into resonance by controlling their relative phase. In addition, we could extract the 2D spatial positioning of embedded QDs from the spectral shifts observed for two orthogonal mechanical polarizations.. The investigation of the strain-mediated tuning of QDs can, therefore, be an effective tool to explore the QD positions without destroying the sample

In recent years, chalcogenide glasses have established their usefulness as attractive candidates for the fabrication of all-optical devices and mid infra-red lasers. These glasses possess low phonon energy and hence high luminescence quantum efficiency, which make them suitable for fabricating active photonic devices. Further, chalcogenide glasses exhibit a variety of photo-induced phenomena upon irradiation with energies above band gap under suitable conditions; the energy deposited at the focal point creates a localized refractive index change which can be used to fabricate a dielectric channel waveguide by translating the material through the laser focus. In this thesis work, different chalcogenide glasses have been prepared by melt quenching technique and their response to irradiation with ultrafast laser pulses has been studied. Photosensitivity studies undertaken have shown that the shape and magnitude of the index profile strongly vary with irradiation conditions. An optimal waveguide by ULI is the result of the successful interplay of a variety of inscription parameters that depend on the inscription laser, steering & focusing optics, translational stage parameters and the material under study. Thus, the waveguide properties can be tailored by optimizing these inscription parameters. The optical characterization of ultrafast laser inscribed, single-scan, as well as multi-scan waveguides, has been carried out at 1550 nm. The multi-scan technique reduces the number of scattering and absorbing defects induced in the modified material by the inscription process, hence reducing the optical losses. Mechanical and structural characterization has been carried out on ultrafast laser inscribed waveguides by nanoindentation and micro-Raman spectroscopy. Nanoindentation studies on single-scan waveguides show a position dependent mechanical behavior in the photo-modified region. At the laser focus, the photo-modified region exhibits same mechanical properties as those of bulk glass. This observation indicates that the material is getting quenched during re-solidification after waveguide inscription. At top of the waveguide, which is away from the focus, the elastic modulus and hardness are reported to be lower than bulk indicating the material is getting annealed at this region. This position dependent mechanical behaviour is correlated with the structural changes using micro-Raman studies. Nanoindentation studies undertaken on multi-scan waveguides reveal lower elastic modulus and hardness values compared to the bulk glass. The lower pulse energy and longer thermal accumulation during multiple passes cause annealing in the photo-modified region. Micro-Raman studies show a decrease in network connectivity in the photo-modified region resulting in lower mechanical properties. The change in mechanical properties in the photo-modified region is found to be greatly influenced by the net-fluence used for waveguide fabrication. The waveguides fabricated at different net-fluence show different local structures as a result of different rates of localized heating/cooling, which determine bond order and the local structure in a glassy network.

Controlling light at the nanoscale is a current research frontier, as advanced nanofabrication techniques allow fabrication of complex nanophotonic structures. Such structures offer a path to integrable on-chip applications including signal processing, switching and routing. In specially designed flexible nanocircuits, the force exerted by light can significantly deform the structure, and in turn, change the optical response of the structure accordingly, resulting in opto-mechanical interactions. These interactions present new possibilities to achieve novel optical functionalities in tunable nanophotonic devices. This thesis formulates and discusses several approaches for tailoring the opto-mechanical interactions in nanowire waveguides, which can be suspended in air, enabling flexible structure tuning by optical forces. Chapter 1 introduces and reviews the field of opto-mechanics and the current state-of-the-art with a particular focus on opto-mechanical interactions in nanophotonic structures. I also introduce the key physical concepts and theoretical framework underpinning the following chapters. In Chapter 2 I develop approaches for controlling optically induced forces between side-coupled waveguide nanocavities by introducing a longitudinal shift. The analysis predicts that optical cavity enhanced transverse forces can be tuned from repulsive to attractive, or even suppressed for particular longitudinal shifts. Additionally, the shift induces longitudinal forces on the waveguides, in contrast to unshifted structures. In chapter 3 I show that a similar approach can control forces between photonic-crystal nanowires in the slow-light regime. In this case, the increased optical energy density of waveguide modes close to the photonic band edge can significantly enhance the optical forces. I also compare the relative benefits of slow-light and cavity structures for opto-mechanical applications. Chapter 4 presents a theoretical analysis of nonlinear dynamics associated with opto-mechanical self-action. Novel nonlinear opto-mechanical interactions are revealed in coupled suspended nanocavities that are driven by two detuned laser frequencies. Such driving enables simultaneous excitation of odd and even optical supermodes, which induce gradient forces of opposite signs. Competition between these forces produces opto-mechanical potentials with large barriers and narrow wells. These types of potentials were suggested for precise displacement control in the static regime. However I find that self-induced oscillations appear even at the deep global potential minima for mechanical damping rates below a certain threshold, and I identify a new regime of chaotic switching between mechanical deformations of opposite signs. Chapter 5 presents experimental results for suspended chalcogenide (Ge11.5As24Se64.5) waveguide nanocavities designed to experience an attractive optical force due to substrate coupling. This chalcogenide material features strong Kerr nonliearity and low two-photon absorption, which is attractive for fast nonlinear signal processing combined with opto-mechanical tunability. Optical cavities of quality factor {u0303}104 were fabricated and comprehensively characterized, revealing a strong thermo-optic response. Experimental measurements and theoretical simulations reveal that a Fabry-Perot cavity formed by the waveguide end facets strongly modifies the optical bistability, suggesting new possibilities for engineering the thermo-optic response of nanostructures. Theoretical modelling predicts that such structures could be suitable for opto-mechanical experiments when placed in a vacuum chamber to avoid air damping of mechanical oscillations. I present conclusions and discuss future directions in the final chapter 6.

碩士
國立清華大學
光電工程研究所
99
An optical phase shifter for integrated optics is proposed and demonstrated in a single SOI chip. By monolithic integration of deformable silicon wire waveguides and micro-electro-mechanical- system (MEMS) actuators, the optical phase shifter for a guided wave can be realized by mechanically stretching the waveguide length using the electrostatic force. Besides, in order to realize highly compact photonic integrated circuits based on silicon photonic wires, multimode interference (MMI) couplers were introduced for performing light splitting and combing due to the advantages of wide optical bandwidth(about 20nm), polarization independence and large fabrication tolerance. In experimental measurement, the maximum phase shift of 0.35? is attained at 200V around the wavelength 1550nm for the TM-polarized light. The dynamic actuation speed is also verified to be near 103?酨 for the proposed device.

This thesis has two parts: In the first part, we study the dispersion characteristics of structural-acoustic waveguides by obtaining closed-form solutions for the coupled wave numbers. Two representative systems are considered for the above study: an infinite two-dimensional rectangular waveguide and an infinite fluid- filled orthotropic circular cylindrical shell. In the second part, these asymptotic expressions are used to study the nonlinear wave propagation in the same two systems. The first part involves obtaining asymptotic expansions for the fluid-structure coupled wave numbers in both the systems. Certain expansions are already available in the literature. Hence, the gaps in the literature are filled. Thus, for cylindrical shells even in vacuo wavenumbers are obtained as part of the objective. Here, singular and regular perturbation methods are used by taking the thickness parameter as the asymptotic parameter. Valid wavenumber expressions are obtained at all the frequencies. A transition in the behavior of the flexural wavenumbers occurs in the neighborhood of the ring frequency. This frequency of transition is identified for the orthotropic shells also. The closed-form expressions for the orthotropic shells are obtained in the limit of slight orthotropy for the circumferential orders n > 0 at all the frequency ranges. Following this, we derive the coupled wavenumber expressions for the two systems for an arbitrary fluid loading. Here, the two-dimensional rectangular waveguide is considered first. This rectangular waveguide has a one-dimensional plate and a rigid surface as its lateral boundaries. The effects due to the structural boundary are studied by analyzing the phase change due to the structure on an incident plane wave. The complications due to the cross-sectional modes are eliminated by ignoring the presence of the other rigid boundary. Dispersion characteristics are predicted at various regions of the dispersion diagram based on the phase change. Moreover, the also identified. Next, the rigid boundary is considered and the coupled dispersion relation for the waveguide is solved for the wavenumber expressions. The coupled wavenumbers are obtained as the coupled rigid-duct, the coupled structural and the coupled pressure-release wavenumbers. Next, based on the above asymptotic analysis on a two-dimensional rectangular waveguide, the asymptotic expansions are obtained for the coupled wavenumbers in isotropic and orthotropic fluid- filled cylindrical shells. The asymptotic expansions of the wavenumbers are obtained without any restriction on the fluid loading. They are compared with the numerical solutions and a good match is obtained. In the second part or the nonlinear section of the thesis, the coupled wavenumber expressions are used to study the propagation of small but a finite amplitude acoustic potential in the above structural-acoustic waveguides. It must be mentioned here that for the rst time in the literature, for a structural-acoustic system having a contained fluid, both the structure and the acoustic fluid are nonlinear. Standard nonlinear equations are used. The focus is restricted to non-planar modes. The study of the cylindrical shell parallels that of the 2-D rectangular waveguide, except in that the former is more practical and complicated due to the curvature. Thus, with regard to both systems, a narrow-band wavepacket of the acoustic potential centered around a frequency is considered. The approximate solution of the acoustic velocity potential is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that the amplitude modulation is governed by the Nonlinear Schr•odinger equation (NLSE). The nonlinear term in the NLSE is analyzed, since the sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. This sign change is predicted using the coupled wavenumber expressions. Secondly, at specific frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonic. This happens when the phase speeds of the waves match. The frequencies of such interactions are identified, again using the coupled wavenumber expressions. The novelty of this work lies firstly in considering nonlinear acoustic wave prop-agation in nonlinear structural waveguides. Secondly, in deriving the asymptotic expansions for the coupled wavenumbers for both the two-dimensional rectangular waveguide and the fluid- filled circular cylindrical shell. Then in using the same to study the behavior of the nonlinear term in NLSE. And lastly in identifying the frequencies of nonlinear interactions in the respective waveguides.

This thesis has two parts: In the first part, we study the dispersion characteristics of structural-acoustic waveguides by obtaining closed-form solutions for the coupled wave numbers. Two representative systems are considered for the above study: an infinite two-dimensional rectangular waveguide and an infinite fluid- filled orthotropic circular cylindrical shell. In the second part, these asymptotic expressions are used to study the nonlinear wave propagation in the same two systems. The first part involves obtaining asymptotic expansions for the fluid-structure coupled wave numbers in both the systems. Certain expansions are already available in the literature. Hence, the gaps in the literature are filled. Thus, for cylindrical shells even in vacuo wavenumbers are obtained as part of the objective. Here, singular and regular perturbation methods are used by taking the thickness parameter as the asymptotic parameter. Valid wavenumber expressions are obtained at all the frequencies. A transition in the behavior of the flexural wavenumbers occurs in the neighborhood of the ring frequency. This frequency of transition is identified for the orthotropic shells also. The closed-form expressions for the orthotropic shells are obtained in the limit of slight orthotropy for the circumferential orders n > 0 at all the frequency ranges. Following this, we derive the coupled wavenumber expressions for the two systems for an arbitrary fluid loading. Here, the two-dimensional rectangular waveguide is considered first. This rectangular waveguide has a one-dimensional plate and a rigid surface as its lateral boundaries. The effects due to the structural boundary are studied by analyzing the phase change due to the structure on an incident plane wave. The complications due to the cross-sectional modes are eliminated by ignoring the presence of the other rigid boundary. Dispersion characteristics are predicted at various regions of the dispersion diagram based on the phase change. Moreover, the also identified. Next, the rigid boundary is considered and the coupled dispersion relation for the waveguide is solved for the wavenumber expressions. The coupled wavenumbers are obtained as the coupled rigid-duct, the coupled structural and the coupled pressure-release wavenumbers. Next, based on the above asymptotic analysis on a two-dimensional rectangular waveguide, the asymptotic expansions are obtained for the coupled wavenumbers in isotropic and orthotropic fluid- filled cylindrical shells. The asymptotic expansions of the wavenumbers are obtained without any restriction on the fluid loading. They are compared with the numerical solutions and a good match is obtained. In the second part or the nonlinear section of the thesis, the coupled wavenumber expressions are used to study the propagation of small but a finite amplitude acoustic potential in the above structural-acoustic waveguides. It must be mentioned here that for the rst time in the literature, for a structural-acoustic system having a contained fluid, both the structure and the acoustic fluid are nonlinear. Standard nonlinear equations are used. The focus is restricted to non-planar modes. The study of the cylindrical shell parallels that of the 2-D rectangular waveguide, except in that the former is more practical and complicated due to the curvature. Thus, with regard to both systems, a narrow-band wavepacket of the acoustic potential centered around a frequency is considered. The approximate solution of the acoustic velocity potential is found using the method of multiple scales (MMS) involving both space and time. The calculations are presented up to the third order of the small parameter. It is found that the amplitude modulation is governed by the Nonlinear Schr•odinger equation (NLSE). The nonlinear term in the NLSE is analyzed, since the sign of the nonlinear term in the NLSE plays a role in determining the stability of the amplitude modulation. This sign change is predicted using the coupled wavenumber expressions. Secondly, at specific frequencies, the primary pulse interacts with its higher harmonics, as do two or more primary pulses with their resultant higher harmonic. This happens when the phase speeds of the waves match. The frequencies of such interactions are identified, again using the coupled wavenumber expressions. The novelty of this work lies firstly in considering nonlinear acoustic wave prop-agation in nonlinear structural waveguides. Secondly, in deriving the asymptotic expansions for the coupled wavenumbers for both the two-dimensional rectangular waveguide and the fluid- filled circular cylindrical shell. Then in using the same to study the behavior of the nonlinear term in NLSE. And lastly in identifying the frequencies of nonlinear interactions in the respective waveguides.

Silicon photonics is a promising platform for photonic devices and circuits, largely driven by advanced complementary metal-oxide-semiconductor (CMOS) processing technology. An extremely crucial component for a photonic device is the optical waveguide, which guides optical signals. A key development in this research area was the availability of high-quality silicon-on-insulator (SOI) wafers. SOI offers the possibility of highly integrated and scaled photonic devices, due to strong optical confinement as a result of high-index contrast between silicon and silicon-oxide layer. SOI waveguides have wide applications ranging from telecommunication, optical interconnection, to chemical and biosensing. In this work, we have presented a conceptual design for sensing applications. A 220 nm thin silicon microcantilever acts as an optical waveguide, end-coupled to another microcantilever waveguide. The sensitivity of this device is dependent on vertical misalignment and the transversal gap between the coupled microcantilever waveguides. We have fabricated SOI-based end-coupled waveguides with 50 nm vertical misalignment and varying transversal gap. The insertion loss is measured across the end-coupled microcantilever waveguides having gaps ranging from 200 nm to 600 nm. The gaps were created by milling SOI microbeams using focused ion beam (FIB). The effect of ion beam milling on these structures has also been investigated. This device is designed to operate as a single sensor for two different parameters, namely, refractive index change arising from molecular binding and strain induced by temperature changes, which usually requires individual sensor elements dedicated to each parameter. Our design overcomes this multiplexing challenge by utilizing a suspended Bragg grating with a single defect which respond differently to refractive index changes and geometric changes due to strain. Hence, the signal from this device effectively contains two channels each carrying unique information about the molecular binding event. We have fabricated such suspended Bragg grated waveguide devices with defect mode and characterized their performance.
CSIR

The thesis touches numerical solutions and wave propagation analysis using spectral methods for different classes of partial differential equations (PDEs) having applications in various fields. We address the solution of both linear and nonlinear PDEs. The different problems studied in the thesis are the one dimensional (1-D) wave equation for uniform and varying cross-sectional area, the coupled one dimensional Timoshenko beam with uniform and varying cross-section, the three dimensional linear Heat equation having real solution, the two dimensional linear Schroedinger equation having oscillatory solution, one dimensional nonlinear Korteg-de-Vries equation (KdV), two dimensional nonlinear Schroedinger (NLS) equation, and finally the coupled one-dimensional (1-D), two-dimensional (2-D) and three dimensional (3-D) quasicrystals with four, five and six variables. The major objective of the work is to bring out the versatility of the spectral methods to solution for the above listed equations. The solutions to these partial differential equations discussed in the thesis has been obtained by approximating the unknown function using spectral functions such as Legendre or Chebyshev polynomials as basis function in the frequency domain and also in the time domain. For the nonlinear partial differential equations, we have obtained solutions using Fourier spectral functions along the spatial direction in time domain. Another important area that was studied in the thesis is the wave propagation in the frequency domain. Wave propagation is a transient behaviour resulting from short duration loading, which have high frequency content. The key factor in the wave propagation is the propagating velocity of the waves, the level of attenuation of their response and their wavelengths. It is a multi-modal phenomenon and hence the analysis becomes difficult if the problem is solved in the time domain. W e have discussed the wave propagation analysis in rods, Timoshenko beam and 1-D, 2-D and 3-D quasicrystals. We have also shown that the numerical spectral methods effectively evolve the physical behaviour of the above equations. We also consider wave propagation in different quasicrystals on a beam type structure using 2-D spectral element formulation. An Aluminium Cantilever beam is reinforced with a layer of quasicrystal under different orientation and the wave propagation characteristics of the hybrid structure is studied. The analysis is performed using frequency domain spectral finite element formulation. For all the combinations of quasicrystal Aluminium beam combination, there is substantial suppression of responses both for the axial and the bending responses.

碩士
國立交通大學
電信工程研究所
102
In this thesis, W-band mechanical switches are proposed using the substrate integrated waveguide (SIW). The substrate integrated waveguiude is manufactured on a Rogers RT-Duroid 5880® low loss substrate with a dielectric constant of 2.2, and a thickness of 10mil. The first step to design the proposed single-pole-double-throw (SPDT) switch is to design a SIW single-pole-single-throw (SPST) switch with a center frequency of 90GHz. Then decide the size of the SIW by the formula of rectangular waveguide. Four different kind of SPST SIW switch structures are designed based on these rules. The on and off of the SPST switch is mechanically controlled by a piece of conducting material to lift or contact the specified area of the switch. Based on the design of SPST SIW switch, the same concept is applied to design the SPDT SIW switch. All the circuits are H-plane SIW circuits that they could be easily measured by a network analyzer with the W-band (WR-10) waveguide extenders through the newly developed SIW to rectangular waveguide transitions.

碩士
國立交通大學
電信工程研究所
104
In this thesis, a V-band phase shifters and a V-band mechanical switches are proposed using the substrate integrated waveguide (SIW). The substrate integrated waveguide is manufactured on a Rogers RT-Duroid 5880® low loss substrate with a dielectric constant of 2.2 and a thickness of 10 mil. The single-pole-single-throw (SPST) and single-pole-double-throw (SPDT) switches are proposed with a center frequency of 60 GHz where the so-called cross centered copper ring structure are adopted. The on and off of the switches are mechanically controlled by a piece of conducting material to lift or contact the specified area of the switch. On the other hand, the proposed phase shifter cascades three different phase shifters which include a 90 degree digital phase shifter, a 180 degree digital phase shifter and a 90 degree tunable phase shifter. Finally, the proposed switches and the proposed phase shifter are measured by a network analyzer with the V-band (WR-15) waveguide extenders through the newly developed SIW to rectangular waveguide transition. The advantage of this newly developed transition is no electrical contact with the metal of the rectangular waveguide.

The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena. The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoff plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic. The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations. In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.

The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena. The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoff plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic. The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations. In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.

We numerically investigate electron transport properties in an electron waveguide which can be constructed in 2DEG of the heterostructure of GaAs and AlGaAs. We apply R-matrix theory to solve a Schrödinger equation and construct a S-matrix, and we then calculate conductance of an electron waveguide. We study single impurity scattering in a waveguide. A [delta]-function model as a single impurity is very attractive, but it has been known that [delta]-function potential does not give a convergent result in two or higher space dimensions. However, we find that it can be used as a single impurity in a waveguide with the truncation of the number of modes. We also compute conductance for a finite size impurity by using R-matrix theory. We propose an appropriate criteria for determining the cut-off mode for a [delta]-function impurity that reproduces the conductance of a waveguide when a finite impurity presents. We find quantum scattering echoes in a ripple waveguide. A ripple waveguide (or cavity) is widely used for quantum chaos studies because it is easy to control a particle's dynamics. Moreover we can obtain an exact expression of Hamiltonian matrix with for the waveguide using a simple coordinate transformation. Having an exact Hamiltonian matrix reduces computation time significantly. It saves a lot of computational needs. We identify three families of resonance which correspond to three different classical phase space structures. Quasi bound states of one of those resonances reside on a hetero-clinic tangle formed by unstable manifolds and stable manifolds in the phase space of a corresponding classical system. Resonances due to these states appear in the conductance in a nearly periodic manner as a function of energy. Period from energy frequency gives a good agreement with a prediction of the classical theory. We also demonstrate wavepacket dynamics in a ripple waveguide. We find quantum echoes in the transmitted probability of a wavepacket. The period of echoes also agrees with the classical predictions. We also compute the electron transmission probability through a multi-ripple electron waveguide. We find an effect analogous to the Dicke effect in the multi-ripple electron waveguide. We show that one of the S-matrix poles, that of the super-radiant resonance state, withdraws further from the real axis as each ripple is added. The lifetime of the super-radiant state, for N quantum dots, decreases as [1/N] . This behavior of the lifetime of the super-radiant state is a signature of the Dicke effect.
text

Wave propagation is a common phenomenon in aircraft structures resulting from high velocity transient loadings like bird hit, gust etc. Apart from understanding the behavior of structures under such loading, wave propagation analysis is also important to gain knowledge about their high frequency characteristics, which have several applications. The applications include structural health monitoring using diagnostic waves and control of wave transmission for reduction of noise and vibration. Transient loadings with high frequency content are associated with wave propagation. As a result, the higher modes of the structure participate in the response. Finite element (FE) modeling for such problem requires very fine mesh to capture these higher modes. This leads to large system size and hence large computational cost. Wave propagation problems are usually solved in frequency domain using fast Fourier transform (FFT) and spectral finite element method is one such technique which follows FE procedure in the transformed frequency domain. In this thesis, a novel wavelet based spectral finite element (WSFE) is developed for wave propagation analysis in finite dimension structures. In WSFE for 1-D waveguides, the partial differential wave equations are reduced to a set of ODEs using orthogonal compactly supported Daubechies scaling functions for temporal approximation. The localized nature of the Daubechies basis functions allows finite domain analysis and imposition of the boundary conditions. The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equation and hence, the exact elemental dynamic stiffness matrix is derived. Thus, In the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FE and after solution, the time domain responses are obtained using the inverse wavelet transform. The developed technique circumvents several serious limitations of the conventional FFT based Spectral Finite Element (FSFE). In FSFE, the wave equations are reduced to ODEs using FFT for time approximation. The remaining part of the formulation is quite similar to that of WSFE. The required assumption of periodicity in FSFE, however, does not allow modeling of finite length structures. It results in “wrap around” problem, which distorts the response simulated using FSFE and a semi-infinite (“throw-off”) element is required for imparting artificial damping. This artificial damping occurs as the “throw off” element allows leakage of energy. In some cases, a very high damping can also be considered instead of “throw off” element to remove wrap around effects. In either cases, the damping introduced is much larger than any inherent damping that may be present in the structure. It should also be mentioned that even in presence of the artificial damping, a larger time window is required for removing the distortions completely. The developed WSFE method is completely free from such problems and can efficiently handle undamped finite length structures irrespective of the time window considered. Apart from this, FSFE allows imposition of only zero initial condition and in contrary any initial conditions can be used in WSFE. Though FSFE has problem in modeling finite length undamped structures for time domain analysis, it is well suited for performing frequency domain study of wave characteristics, namely, the determination of spectrum and dispersion relations. WSFE is also capable of extracting these frequency dependent wave properties, however only up to a certain fraction of the Nyquist frequency. This constraint results from the loss in frequency resolution due to the increase in time resolution in wavelet analysis, where the basis functions are bounded both in time and frequency. A price has to be paid in frequency domain in order to obtain a bound in the time domain. The consequence of this analysis is to impose a constraint on the time sampling rate for the simulation with WSFE, to avoid spurious dispersion. WSFE for 2-D waveguides are formulated using Daubechies scaling functions for both temporal and spatial approximations. The initial and boundary conditions, however, are imposed using two different methods, which are wavelet extrapolation technique and periodic extension or restraint matrix respectively. The 2-D WSFE is bounded in both the spatial directions unlike 2-D FSFE, which is essentially unbounded in one spatial direction. Apart from this, 2-D WSFE is also free from “wrap around” problem similar to 1-D WSFE due to the localized nature of the basis functions used for temporal approximation. In this thesis, WSFE is developed for isotropic 1-D and 2-D waveguides for time and frequency domain analysis. These include elementary rod, Euler-Bernoulli and Timoshenko beams in 1-D modeling, and plates and axisymmetric cylinders in 2-D modeling. The wave propagation responses simulated using WSFE for these waveguides are validated using FE results. The advantages of the proposed technique over the corresponding FSFE method are also highlighted all through the numerical examples. Next part of the thesis involves the extension of the developed WSFE technique for modeling composite and nano-composite structures to study their wave propagation behavior. Due to their anisotropic nature, analysis of composite structures, particularly high frequency transient analysis is much more complicated compared to the corresponding metallic structures. This is due to the presence of stiffness coupling in these structures. Superior mechanical properties of composites, however, are making them integral parts of an aircraft and thus they often experience such short duration, high velocity impact Loadings. Very few literatures report the response of composite structures subjected to such high frequency excitations. Here, WSFE is formulated for a higher order composite beam with axial, flexural, shear and contractional degrees of freedom. WSFE is also formulated for composite plates using classical laminated plate theory with axial and flexural degrees of freedom. Simulations performed using these WSFE models are used to study the higher order and elastic coupling effects on the wave propagation responses. Carbon nanotubes (CNTs) and their composites are attracting a great deal of experimental and theoretical research world-wide. The recent trend in the literature shows a great interest in the dynamic and wave characteristics of CNTs and nano-composites because of their several applications. In most of these applications, CNTs are used in the embedded form as it does not requires precise alignment of the nano-tubes. In addition, the extraordinary mechanical properties of CNTs are being exploited to achieve high strength nano-composite. Apart from the experimental studies and atomistic simulation to study the mechanical properties of CNTs and nano-composites, continuum modeling is also receiving much attention, mainly due to its computational viability. In this thesis, a 1-D WSFE is formulated for multi-wall carbon nanotube (MWNT) embedded composite modeled as beam using higher order layer-wise theory. This theory allows to model partial interfacial shear stress transfer, which normally occurs due to improper dispersion of CNTs in nano-composites. The effects of different matrix materials and fraction of shear stress transfer on the wave characteristics are studied. The responses obtained using other beam theories are also compared. The beam modeling does not allow capturing the radial motions of the CNT, which are important for several applications. These can be effectively captured by modeling the CNT using a 2-D axisymmetric model. Hence, a 2-D WSFE model is constructed to capture the high frequency characteristics of single-walled carbon nanotubes (SWNTs). The response of SWNT simulated using the developed model is validated with experimental and atomistic simulation results reported in the literature. The comparison are done for dispersion relation and also radial breathing mode frequencies. The effects of geometrical parameters, namely the radius and the wall thickness of the SWNT on the higher radial, longitudinal and coupled radial-longitudinal vibrational modes are analyzed. These behaviors are studied in both time and frequency domains. Such time domain analyses of finite length SWNT are not possible with the Fourier transform based techniques reported in literature, although, such analyses are important particularly for sensor applications of SWNT. Spectral finite element method is very much suited for solution of inverse problems like force reconstruction from the measured wave response. This is because the technique is based on the concept of transfer function between the displacements (output) and applied forces (input). In the present work, WSFE is implemented for identification of impact force from the wave propagation responses simulated with FE and used as surrogate experimental results. The results show that WSFE can accurately reconstruct the impulse load applied to 1-D waveguides which include rod, Euler-Bernoulli beam and connected 2-D frame, even with highly truncated response. This is unlike FSFE, where the accuracy of the identified force depends largely on the time window of the measured responses. The detection of damage from the wave propagation analysis is another class of inverse problems considered in this thesis and is of utmost importance in the area of aircraft structural health monitoring. Here, the detection scheme is based on arrival time of the waves reflected from the damage. A novel detection technique based on wavelet filtering is proposed here and it is shown to work efficiently even in the presence of noise in the measured wave responses. Detection of damage requires an efficient damage model to simulate the mode of structural failure. In this regard, two spectrally formulated wavelet elements are proposed, one to model isotropic beam with through-width notch and the second to model composite beam with embedded de-lamination. In the first case, the response of the damaged beam is considered as the perturbation of the undamaged response and the linear perturbation analysis leads to a completely new set of dynamic stiffness matrix. In the second case, the delamination is modeled by subdividing the de-laminated region into separate waveguides and full damage model is established by imposing the kinematics. These models help to simulate wave propagation in such damaged beams to study the effect of damage on the wave response. Noise and vibration are often transmitted from the source to the other parts of the structure in the form of wave propagation. Thus, control of such wave transmission is essential for reduction of noise and vibration, which are the main cause of discomfort and in many cases cause failure of structure. Here, techniques for both passive and active controls of wave are proposed. For active control, a closed loop system is modeled using WSFE with magnetostrictive actuator for control of axial and flexural wave propagations in connected isotropic 1-D waveguides. The feedback is negative velocity and/or acceleration measured at different sensor points. A very new application of CNT reinforced composite for passive control of vibration and wave response is explored in this thesis. For this, a novel concept of nano-composite inserts is proposed. This insert can be made from CNTs dispersed in polymer. The high stiffness of the inserts helps to regulate the power flow in the form of wave propagation from the point of application of the loads to other parts of the structures. The length of the insert, volume fraction of CNTs and position are changed to achieve the required reduction in wave amplitudes. The entire thesis is split up into eight chapters. Chapter 1 presents a brief introduction, the motivation and objective of the thesis. Chapters 2 and 3 give a detail account of wavelet spectral finite element formulation for 1-D and 2-D isotropic waveguides, while Chapter 4 gives the same for composite waveguides. Chapter 5 brings out essential wave characteristics in carbon nanotubes and nano-composite structures, while Chapters 6 and 7 exclusively deal with application of WSFE to some real world problems. The thesis ends with summary and directions of future research. In summary, the thesis has brought out several new aspects of wave propagation in isotropic, composite and nano-composite structures. In addition to establishing wavelet spectral finite element as a useful tool for wave propagation analysis, several new techniques are presented, several new algorithm are proposed and several new concepts are explored.

Wave propagation is a common phenomenon in aircraft structures resulting from high velocity transient loadings like bird hit, gust etc. Apart from understanding the behavior of structures under such loading, wave propagation analysis is also important to gain knowledge about their high frequency characteristics, which have several applications. The applications include structural health monitoring using diagnostic waves and control of wave transmission for reduction of noise and vibration. Transient loadings with high frequency content are associated with wave propagation. As a result, the higher modes of the structure participate in the response. Finite element (FE) modeling for such problem requires very fine mesh to capture these higher modes. This leads to large system size and hence large computational cost. Wave propagation problems are usually solved in frequency domain using fast Fourier transform (FFT) and spectral finite element method is one such technique which follows FE procedure in the transformed frequency domain. In this thesis, a novel wavelet based spectral finite element (WSFE) is developed for wave propagation analysis in finite dimension structures. In WSFE for 1-D waveguides, the partial differential wave equations are reduced to a set of ODEs using orthogonal compactly supported Daubechies scaling functions for temporal approximation. The localized nature of the Daubechies basis functions allows finite domain analysis and imposition of the boundary conditions. The reduced ODEs are usually solved exactly, the solution of which gives the dynamic shape functions. The interpolating functions used here are exact solution of the governing differential equation and hence, the exact elemental dynamic stiffness matrix is derived. Thus, In the absence of any discontinuities, one element is sufficient to model 1-D waveguide of any length. This elemental stiffness matrix can be assembled to obtain the global matrix as in FE and after solution, the time domain responses are obtained using the inverse wavelet transform. The developed technique circumvents several serious limitations of the conventional FFT based Spectral Finite Element (FSFE). In FSFE, the wave equations are reduced to ODEs using FFT for time approximation. The remaining part of the formulation is quite similar to that of WSFE. The required assumption of periodicity in FSFE, however, does not allow modeling of finite length structures. It results in “wrap around” problem, which distorts the response simulated using FSFE and a semi-infinite (“throw-off”) element is required for imparting artificial damping. This artificial damping occurs as the “throw off” element allows leakage of energy. In some cases, a very high damping can also be considered instead of “throw off” element to remove wrap around effects. In either cases, the damping introduced is much larger than any inherent damping that may be present in the structure. It should also be mentioned that even in presence of the artificial damping, a larger time window is required for removing the distortions completely. The developed WSFE method is completely free from such problems and can efficiently handle undamped finite length structures irrespective of the time window considered. Apart from this, FSFE allows imposition of only zero initial condition and in contrary any initial conditions can be used in WSFE. Though FSFE has problem in modeling finite length undamped structures for time domain analysis, it is well suited for performing frequency domain study of wave characteristics, namely, the determination of spectrum and dispersion relations. WSFE is also capable of extracting these frequency dependent wave properties, however only up to a certain fraction of the Nyquist frequency. This constraint results from the loss in frequency resolution due to the increase in time resolution in wavelet analysis, where the basis functions are bounded both in time and frequency. A price has to be paid in frequency domain in order to obtain a bound in the time domain. The consequence of this analysis is to impose a constraint on the time sampling rate for the simulation with WSFE, to avoid spurious dispersion. WSFE for 2-D waveguides are formulated using Daubechies scaling functions for both temporal and spatial approximations. The initial and boundary conditions, however, are imposed using two different methods, which are wavelet extrapolation technique and periodic extension or restraint matrix respectively. The 2-D WSFE is bounded in both the spatial directions unlike 2-D FSFE, which is essentially unbounded in one spatial direction. Apart from this, 2-D WSFE is also free from “wrap around” problem similar to 1-D WSFE due to the localized nature of the basis functions used for temporal approximation. In this thesis, WSFE is developed for isotropic 1-D and 2-D waveguides for time and frequency domain analysis. These include elementary rod, Euler-Bernoulli and Timoshenko beams in 1-D modeling, and plates and axisymmetric cylinders in 2-D modeling. The wave propagation responses simulated using WSFE for these waveguides are validated using FE results. The advantages of the proposed technique over the corresponding FSFE method are also highlighted all through the numerical examples. Next part of the thesis involves the extension of the developed WSFE technique for modeling composite and nano-composite structures to study their wave propagation behavior. Due to their anisotropic nature, analysis of composite structures, particularly high frequency transient analysis is much more complicated compared to the corresponding metallic structures. This is due to the presence of stiffness coupling in these structures. Superior mechanical properties of composites, however, are making them integral parts of an aircraft and thus they often experience such short duration, high velocity impact Loadings. Very few literatures report the response of composite structures subjected to such high frequency excitations. Here, WSFE is formulated for a higher order composite beam with axial, flexural, shear and contractional degrees of freedom. WSFE is also formulated for composite plates using classical laminated plate theory with axial and flexural degrees of freedom. Simulations performed using these WSFE models are used to study the higher order and elastic coupling effects on the wave propagation responses. Carbon nanotubes (CNTs) and their composites are attracting a great deal of experimental and theoretical research world-wide. The recent trend in the literature shows a great interest in the dynamic and wave characteristics of CNTs and nano-composites because of their several applications. In most of these applications, CNTs are used in the embedded form as it does not requires precise alignment of the nano-tubes. In addition, the extraordinary mechanical properties of CNTs are being exploited to achieve high strength nano-composite. Apart from the experimental studies and atomistic simulation to study the mechanical properties of CNTs and nano-composites, continuum modeling is also receiving much attention, mainly due to its computational viability. In this thesis, a 1-D WSFE is formulated for multi-wall carbon nanotube (MWNT) embedded composite modeled as beam using higher order layer-wise theory. This theory allows to model partial interfacial shear stress transfer, which normally occurs due to improper dispersion of CNTs in nano-composites. The effects of different matrix materials and fraction of shear stress transfer on the wave characteristics are studied. The responses obtained using other beam theories are also compared. The beam modeling does not allow capturing the radial motions of the CNT, which are important for several applications. These can be effectively captured by modeling the CNT using a 2-D axisymmetric model. Hence, a 2-D WSFE model is constructed to capture the high frequency characteristics of single-walled carbon nanotubes (SWNTs). The response of SWNT simulated using the developed model is validated with experimental and atomistic simulation results reported in the literature. The comparison are done for dispersion relation and also radial breathing mode frequencies. The effects of geometrical parameters, namely the radius and the wall thickness of the SWNT on the higher radial, longitudinal and coupled radial-longitudinal vibrational modes are analyzed. These behaviors are studied in both time and frequency domains. Such time domain analyses of finite length SWNT are not possible with the Fourier transform based techniques reported in literature, although, such analyses are important particularly for sensor applications of SWNT. Spectral finite element method is very much suited for solution of inverse problems like force reconstruction from the measured wave response. This is because the technique is based on the concept of transfer function between the displacements (output) and applied forces (input). In the present work, WSFE is implemented for identification of impact force from the wave propagation responses simulated with FE and used as surrogate experimental results. The results show that WSFE can accurately reconstruct the impulse load applied to 1-D waveguides which include rod, Euler-Bernoulli beam and connected 2-D frame, even with highly truncated response. This is unlike FSFE, where the accuracy of the identified force depends largely on the time window of the measured responses. The detection of damage from the wave propagation analysis is another class of inverse problems considered in this thesis and is of utmost importance in the area of aircraft structural health monitoring. Here, the detection scheme is based on arrival time of the waves reflected from the damage. A novel detection technique based on wavelet filtering is proposed here and it is shown to work efficiently even in the presence of noise in the measured wave responses. Detection of damage requires an efficient damage model to simulate the mode of structural failure. In this regard, two spectrally formulated wavelet elements are proposed, one to model isotropic beam with through-width notch and the second to model composite beam with embedded de-lamination. In the first case, the response of the damaged beam is considered as the perturbation of the undamaged response and the linear perturbation analysis leads to a completely new set of dynamic stiffness matrix. In the second case, the delamination is modeled by subdividing the de-laminated region into separate waveguides and full damage model is established by imposing the kinematics. These models help to simulate wave propagation in such damaged beams to study the effect of damage on the wave response. Noise and vibration are often transmitted from the source to the other parts of the structure in the form of wave propagation. Thus, control of such wave transmission is essential for reduction of noise and vibration, which are the main cause of discomfort and in many cases cause failure of structure. Here, techniques for both passive and active controls of wave are proposed. For active control, a closed loop system is modeled using WSFE with magnetostrictive actuator for control of axial and flexural wave propagations in connected isotropic 1-D waveguides. The feedback is negative velocity and/or acceleration measured at different sensor points. A very new application of CNT reinforced composite for passive control of vibration and wave response is explored in this thesis. For this, a novel concept of nano-composite inserts is proposed. This insert can be made from CNTs dispersed in polymer. The high stiffness of the inserts helps to regulate the power flow in the form of wave propagation from the point of application of the loads to other parts of the structures. The length of the insert, volume fraction of CNTs and position are changed to achieve the required reduction in wave amplitudes. The entire thesis is split up into eight chapters. Chapter 1 presents a brief introduction, the motivation and objective of the thesis. Chapters 2 and 3 give a detail account of wavelet spectral finite element formulation for 1-D and 2-D isotropic waveguides, while Chapter 4 gives the same for composite waveguides. Chapter 5 brings out essential wave characteristics in carbon nanotubes and nano-composite structures, while Chapters 6 and 7 exclusively deal with application of WSFE to some real world problems. The thesis ends with summary and directions of future research. In summary, the thesis has brought out several new aspects of wave propagation in isotropic, composite and nano-composite structures. In addition to establishing wavelet spectral finite element as a useful tool for wave propagation analysis, several new techniques are presented, several new algorithm are proposed and several new concepts are explored.