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Academic literature on the topic 'Quadratic nonlinearity'

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Published: 4 June 2021
Last updated: 6 September 2023

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Journal articles on the topic "Quadratic nonlinearity"

1

Mosolov, A. B., and O. Yu Dinartsev. "Filtration law with quadratic nonlinearity." Journal of Engineering Physics 51, no. 5 (November 1986): 1292–95. http://dx.doi.org/10.1007/bf00870683.

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2

Defever, F., W. Troost, and Z. Hasiewicz. "Superconformal algebras with quadratic nonlinearity." Physics Letters B 273, no. 1-2 (December 1991): 51–55. http://dx.doi.org/10.1016/0370-2693(91)90552-2.

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3

TRAN, H. T. "QUADRATIC NONLINEAR SURFACE WAVES." Journal of Nonlinear Optical Physics & Materials 05, no. 01 (January 1996): 133–38. http://dx.doi.org/10.1142/s021886359600012x.

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Nonlinear surface waves at an interface between a linear medium and another medium with quadratic nonlinearity are possible due to the phenomenon of nonlinearity-induced phase matching. The waves are numerically calculated, along with their dispersion, stability, and comparison with their cubic counterparts. An extension to guided waves is also discussed.
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4

CHANDRAN, VINOD, STEVE ELGAR, and CHARLES PEZESHKI. "BISPECTRAL AND TRISPECTRAL CHARACTERIZATION OF TRANSITION TO CHAOS IN THE DUFFING OSCILLATOR." International Journal of Bifurcation and Chaos 03, no. 03 (June 1993): 551–57. http://dx.doi.org/10.1142/s021812749300043x.

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Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.
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5

Darmanyan, S. A., and M. Nevière. "Eigenmodes of waveguides with quadratic nonlinearity." Optics Communications 176, no. 1-3 (March 2000): 231–37. http://dx.doi.org/10.1016/s0030-4018(00)00479-x.

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6

Babin, A., and A. Figotin. "Nonlinear photonic crystals: I. Quadratic nonlinearity." Waves in Random Media 11, no. 2 (April 2001): R31—R102. http://dx.doi.org/10.1088/0959-7174/11/2/201.

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7

Gu, Wen-ju, Zhen Yi, Li-hui Sun, and Yan Yan. "Enhanced quadratic nonlinearity with parametric amplifications." Journal of the Optical Society of America B 35, no. 4 (March 2, 2018): 652. http://dx.doi.org/10.1364/josab.35.000652.

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8

Wang, Ke, Jing Li, Fan Dai, Mengshuai Wang, Chuanhang Wang, Qiang Wang, Chenghou Tu, Yongnan Li, and Huitian Wang. "Robust Pulse-Pumped Quadratic Soliton Assisted by Third-Order Nonlinearity." Photonics 10, no. 2 (February 2, 2023): 155. http://dx.doi.org/10.3390/photonics10020155.

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The generation of a quadratic soliton in a pulse-pumped microresonator has attracted significant interest in recent years. The strong second-order nonlinearity and high peak power of pumps offer a straightforward way to increase efficiency. In this case, the influence of the third-order nonlinearity effect becomes significant and cannot be ignored. In this paper, we study the quadratic soliton in a degenerate optical parametric oscillator driven synchronously by the pulse pump with third-order nonlinearity. Our simulations verify that the robustness of quadratic soliton generation is enhanced when the system experiences a perturbation from pump power, cavity detuning, and pump pulse width. These results represent a new way of manipulating frequency comb in resonant microphotonic structures.
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9

Zhang, Wen, Jian Zhang, and Heilong Mi. "Ground states and multiple solutions for Hamiltonian elliptic system with gradient term." Advances in Nonlinear Analysis 10, no. 1 (July 30, 2020): 331–52. http://dx.doi.org/10.1515/anona-2020-0113.

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Abstract This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient term $$\begin{array}{} \displaystyle \left\{\,\, \begin{array}{ll} -{\it\Delta} u +\vec{b}(x)\cdot \nabla u+V(x)u = H_{v}(x,u,v)\,\,\hbox{in}\,\mathbb{R}^{N},\\[-0.3em] -{\it\Delta} v -\vec{b}(x)\cdot \nabla v +V(x)v = H_{u}(x,u,v)\,\,\hbox{in}\,\mathbb{R}^{N}.\\ \end{array} \right. \end{array}$$ Compared with some existing issues, the most interesting feature of this paper is that we assume that the nonlinearity satisfies a local super-quadratic condition, which is weaker than the usual global super-quadratic condition. This case allows the nonlinearity to be super-quadratic on some domains and asymptotically quadratic on other domains. Furthermore, by using variational method, we obtain new existence results of ground state solutions and infinitely many geometrically distinct solutions under local super-quadratic condition. Since we are without more global information on the nonlinearity, in the proofs we apply a perturbation approach and some special techniques.
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10

Wu, Junyao, Chunbiao Li, Xu Ma, Tengfei Lei, and Guanrong Chen. "Simplification of Chaotic Circuits With Quadratic Nonlinearity." IEEE Transactions on Circuits and Systems II: Express Briefs 69, no. 3 (March 2022): 1837–41. http://dx.doi.org/10.1109/tcsii.2021.3125680.

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Dissertations / Theses on the topic "Quadratic nonlinearity"

1

Braun, Michael Rainer. "Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26566.

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Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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2

Kuechler, Sebastian. "Wave Propagation in an Elastic Half-Space with Quadratic Nonlinearity." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19823.

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This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.
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Howard, Timothy G. "Predicting the asymptotic behavior for differential equations with a quadratic nonlinearity." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/28823.

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4

Xue, Linfeng. "Theoretical Characterization of Internal Resonance in Micro-Electro-Mechanical Systems (MEMS)." The Ohio State University, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1593296130150349.

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5

Patra, Harisadhan. "Mechanisms of remote masking." Columbus, Ohio : Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1199309775.

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6

Mak, William Chi Keung Electrical Engineering &amp Telecommunications Faculty of Engineering UNSW. "Coupled Solitary Waves in Optical Waveguides." Awarded by:University of New South Wales. Electrical Engineering and Telecommunications, 1998. http://handle.unsw.edu.au/1959.4/17494.

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Soliton states in three coupled optical waveguide systems were studied: two linearly coupled waveguides with quadratic nonlinearity, two linearly coupled waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear waveguide with resonant gratings, which enable three-wave interaction. The methods adopted to tackle the problems were both analytical and numerical. The analytical method mainly made use of the variational approximation. Since no exact analytical method is available to find solutions for the waveguide systems under study, the variational approach was proved to be very useful to find accurate approximations. Numerically, the shooting method and the relaxation method were used. The numerical results verified the results obtained analytically. New asymmetric soliton states were discovered for the coupled quadratically nonlinear waveguides, and for the coupled waveguides with both cubic nonlinearity and Bragg gratings. Stability of the soliton states was studied numerically, using the Beam Propagation Method. Asymmetric couplers with quadratic nonlinearity were also studied. The bifurcation diagrams for the asymmetric couplers were those unfolded from the corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound states due to three-wave interaction were discovered for a quadratically nonlinear waveguide equipped with resonant gratings. Since the coupled optical waveguide systems are controlled by a larger number of parameters than in the corresponding single waveguide, the coupled systems can find a much broader field of applications. This study provides useful background information to support these applications.
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7

Bhattacharya, Mily. "Quadratic Nonlinearity In Covalently And Non-Covalently Linked Molecules In Solution." Thesis, 2006. https://etd.iisc.ac.in/handle/2005/366.

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This thesis deals with the investigation of the first hyperpolarizabilities (β) of a large number of molecules linked to other molecules either covalently or noncovalently. Chapter 1 gives a brief introduction to supramolecular chemistry and Nonlinear Optics (NLO). A survey of literature pertinent to noncovalently interacting supramolecular assembly and their NLO properties as well as NLO properties of oligomeric systems has been presented. The scope of the present investigation has been described at the end of the chapter. Chapter 2 discusses all the methods used in carrying out this thesis work. The first hyperpolarizabilities (β) of all the compounds have been measured by the hyper Rayleigh scattering (HRS) technique; the experimental details of which are written in this chapter. Various spectroscopic techniques such as NMR, IR, UV-Vis, etc. that were used in the investigation have been presented. The subsequent chapters 3-5 deal with the actual results obtained in this work. In chapter 3 first hyperpolarizabilities of o-, m-, and p-aminobenzoic acids and their oligomers viz., dimer, trimer and tetramer (covalently linked) have been studied. The compounds are synthesized and characterized by various spectroscopic methods and their β values have been measured by HRS. The hyperpolarizability increases in going from the monomer to the dimer but decreases subsequently from the dimer to the trimer to the tetramer. This unexpected trend in β has been attributed to the formation of molecular aggregates in the trimers and tetramers. Further evidences of aggregation come from the results of1H NMR spectroscopy and conductivity measurements. In chapter 4, synthesis, characterization and HRS investigation to probe the formation, dissociation and binding constants of hydrogen bonded supramolecular complexes (noncovalent interaction) formed in solution between 6-amino-2-(pivaloylamino)pyridine and ferrocene functionalized barbituric acid and 5-methoxy-N,N′-bis(6-amino-2-pyridinyl)-1,3-benzenedicarboxamide and ferrocenyl barbituric acid have been described. From the HRS data the stoichiometry of the supramolecular complexes has been determined and compared to that from the NMR data. Some of the complex stoichiometries that are measured by HRS have not been seen in the NMR data and vice versa. The results have been rationalized in terms of the strengths and weaknesses of various spectroscopic methods as applied to this problem. Many fold increase in the β value has been realized in the supramolecular complex formation process. Depolarized HRS experiments have been carried out to obtain structural information on the complexes. In the last chapter the synthesis, characterization and measurements on the first hyperpolarizabilities of unsubstituted tetraphenylporphyrin and its metallated complexes have been presented. Synthesis of supramolecular complexes of ferrocenyl barbituric acid with functionalized porphyrin compounds has been carried out although the amount of the final complex was insufficient for HRS measurements. This chapter ends with a perspective for the future work in the direction.
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8

Bhattacharya, Mily. "Quadratic Nonlinearity In Covalently And Non-Covalently Linked Molecules In Solution." Thesis, 2006. http://hdl.handle.net/2005/366.

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This thesis deals with the investigation of the first hyperpolarizabilities (β) of a large number of molecules linked to other molecules either covalently or noncovalently. Chapter 1 gives a brief introduction to supramolecular chemistry and Nonlinear Optics (NLO). A survey of literature pertinent to noncovalently interacting supramolecular assembly and their NLO properties as well as NLO properties of oligomeric systems has been presented. The scope of the present investigation has been described at the end of the chapter. Chapter 2 discusses all the methods used in carrying out this thesis work. The first hyperpolarizabilities (β) of all the compounds have been measured by the hyper Rayleigh scattering (HRS) technique; the experimental details of which are written in this chapter. Various spectroscopic techniques such as NMR, IR, UV-Vis, etc. that were used in the investigation have been presented. The subsequent chapters 3-5 deal with the actual results obtained in this work. In chapter 3 first hyperpolarizabilities of o-, m-, and p-aminobenzoic acids and their oligomers viz., dimer, trimer and tetramer (covalently linked) have been studied. The compounds are synthesized and characterized by various spectroscopic methods and their β values have been measured by HRS. The hyperpolarizability increases in going from the monomer to the dimer but decreases subsequently from the dimer to the trimer to the tetramer. This unexpected trend in β has been attributed to the formation of molecular aggregates in the trimers and tetramers. Further evidences of aggregation come from the results of1H NMR spectroscopy and conductivity measurements. In chapter 4, synthesis, characterization and HRS investigation to probe the formation, dissociation and binding constants of hydrogen bonded supramolecular complexes (noncovalent interaction) formed in solution between 6-amino-2-(pivaloylamino)pyridine and ferrocene functionalized barbituric acid and 5-methoxy-N,N′-bis(6-amino-2-pyridinyl)-1,3-benzenedicarboxamide and ferrocenyl barbituric acid have been described. From the HRS data the stoichiometry of the supramolecular complexes has been determined and compared to that from the NMR data. Some of the complex stoichiometries that are measured by HRS have not been seen in the NMR data and vice versa. The results have been rationalized in terms of the strengths and weaknesses of various spectroscopic methods as applied to this problem. Many fold increase in the β value has been realized in the supramolecular complex formation process. Depolarized HRS experiments have been carried out to obtain structural information on the complexes. In the last chapter the synthesis, characterization and measurements on the first hyperpolarizabilities of unsubstituted tetraphenylporphyrin and its metallated complexes have been presented. Synthesis of supramolecular complexes of ferrocenyl barbituric acid with functionalized porphyrin compounds has been carried out although the amount of the final complex was insufficient for HRS measurements. This chapter ends with a perspective for the future work in the direction.
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9

Ghosh, Sampa. "Quadratic Optical Nonlinearity And Geometry Of 1:1 Electron Donor Acceptor Complexes In Solution." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/711.

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The knowledge of geometry of molecular complexes formed via molecular association in solution through weak interactions is always important to understand the origin of stability and function of an array of molecules, supramolecular assemblies, and macromolecular networks. Simple 1:1 molecular complexes are very useful in this regard as they provide a model to understand both the nature of these interactions and their structural implications. Several weak noncovalent forces from long range (van der Waal’s, electrostatic, induction, dispersion) to short range (charge transfer) govern the geometry, that is, relative orientation of the two molecules in such a complex. On one hand, we find 1:1 electron donor acceptor (EDA) complexes such as naphthalene-tetracyanobenzene, hexamethylbenzene-chloranil etc. which stack parallel or in slipped parallel geometry in their crystals. On the other, benzene dimer has been found to stabilize in T shaped geometry in all its three physical states. In this thesis, I focus on 1:1 EDA complexes in solution. A good volume of literature is available which deals with the optical studies on the formation of such complexes. It has been suggested that the nature of the intermolecular interactions stabilizing these complexes in the gas phase or in their crystals is modified by the presence of solvent-solute interactions in solution thus bringing in difference in the solution geometry. However, the existing experimental techniques, both optical and magnetic, are unable to determine the exact geometries of 1:1 EDA complexes in solution. This opens an opportunity to probe their geometry in solution. The quadratic nonlinearity or first hyperpolarizability (β) of a molecule is a measure of the change in dipole moment (or polarization) in the second order of the applied electrical field and thus has a purely electronic origin. It is a tensorial property and can be resolved in components along the three dimensions. The number of β components and the nonlinear optical anisotropies in a typical donor-acceptor type dipolar molecule, defined as (equation) (where1, 2, 3 axes define the molecular frame, 1 being the direction along the principal axis of symmetry and pointing from the acceptor toward the donor), are determined by the symmetry /structure of the molecule. It has been shown theoretically that the 1:1 EDA complexes possess large hyperpolarizabilities. In the case of pNA dimers calculation revealed that the geometry of the dimer and its symmetry is important for obtaining the correct estimate of β from its tensorial components. Therefore, it should be possible to use the values of tensorial β components to construct the unknown geometry of such complexes. Experimentally macroscopic depolarization ratios (D and D′) in the laboratory fixed frame (XYZ, X being the direction of polarization and Z the direction of propagation of the incident light), are measured from the polarization resolved intensities of second harmonic scattering from molecules in solution using the hyper-Rayleigh scattering technique. The depolarization ratios are correlated to the anisotropy parameters, u and v through a co-ordinate transformation. In this thesis I, have first, characterized the quadratic nonlinear optical property of a variety of 1:1 electron donor acceptor complexes and used the values of u and v obtained from depolarized hyper-Rayleigh scattering to deduce their geometry in solution. Chapter 1 provides an introduction to the 1:1 electron donor acceptor complexes, their relevance to chemistry and biology. It also contains an introduction to nonlinear optical processes in molecules. The objective of the present work and scope of the investigation carried out in this thesis is presented in this chapter. Chapter 2 describes the details of the experimental polarization resolved HRS technique. The geometrical model adopted for the analysis of the HRS data has also been introduced and the method of analysis has been described in detail in this chapter. Chapter 3 presents the measurement of β values of two series of 1:1 EDA complexes of variously substituted methylbenzenes donors with tetrachloro-p-benzoquinone (CHL) and dicyanodichloro-p-benzoquinone (DDQ) acceptors at 1064 nm. In agreement with recent theoretical results we find large first hyperpolarizabilities for these complexes. The β values are greater than that of the typical push-pull molecule p-nitroaniline (pNA). We also find that in general β decreases with decrease in the donor strength. Chapter 4 presents the β values for the two series of EDA complexes of CHL and DDQ acceptors at 1907 nm. The values of β are less in magnitude at 1907 nm than that at 1064 nm which is due to the dispersion effect in β. In Chapter 5 and 6, it is described how depolarized hyper-Rayleigh scattering can be utilized to probe geometries of 1:1 complexes in solution. Chapter 5 concentrates mainly on 1:1 EDA complexes of CHL and DDQ and TCNB (tetracyanobenzene), while chapter 6 contains examples of other 1:1 molecular complexes where the noncovalent interactions are much weaker, such as in benzene-naphthalene, benzene-methoxybenzene, benzene-hexafluorobenzene and benzene-chlorobenzene pairs. We find the geometry of 1:1 EDA complexes in solution in terms of tilt angle (θ) and twist angle (ϕ) between the donor and acceptor pairs. The angle θ varies from 29°-47° for different pairs of EDA complexes, while ϕ varies within 34° and 38°. We find that the geometry of 1:1 EDA complexes in solution is different (twisted and tilted cofacial and twisted ‘V’) from those in the crystalline or gaseous states (cofacial), if known. We find that both benzene-naphthalene and benzene-chlorobenzene pairs assume twisted ‘T’ shape geometry with θ = 82° and 85°, respectively, and φ = 38°, while benzene-hexafluorobenzene assumes a twisted ‘V’ shape. A strong solvent effect is seen in the geometry of the benzene- methoxybenzene complex. The tilt angle is 55° when chloroform is used as a solvent and it is 82° without chloroform. Chapter 7 is the concluding chapter where the main work done in this thesis is summarized and future directions are presented.
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10

Ghosh, Sampa. "Quadratic Optical Nonlinearity And Geometry Of 1:1 Electron Donor Acceptor Complexes In Solution." Thesis, 2008. http://hdl.handle.net/2005/711.

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The knowledge of geometry of molecular complexes formed via molecular association in solution through weak interactions is always important to understand the origin of stability and function of an array of molecules, supramolecular assemblies, and macromolecular networks. Simple 1:1 molecular complexes are very useful in this regard as they provide a model to understand both the nature of these interactions and their structural implications. Several weak noncovalent forces from long range (van der Waal’s, electrostatic, induction, dispersion) to short range (charge transfer) govern the geometry, that is, relative orientation of the two molecules in such a complex. On one hand, we find 1:1 electron donor acceptor (EDA) complexes such as naphthalene-tetracyanobenzene, hexamethylbenzene-chloranil etc. which stack parallel or in slipped parallel geometry in their crystals. On the other, benzene dimer has been found to stabilize in T shaped geometry in all its three physical states. In this thesis, I focus on 1:1 EDA complexes in solution. A good volume of literature is available which deals with the optical studies on the formation of such complexes. It has been suggested that the nature of the intermolecular interactions stabilizing these complexes in the gas phase or in their crystals is modified by the presence of solvent-solute interactions in solution thus bringing in difference in the solution geometry. However, the existing experimental techniques, both optical and magnetic, are unable to determine the exact geometries of 1:1 EDA complexes in solution. This opens an opportunity to probe their geometry in solution. The quadratic nonlinearity or first hyperpolarizability (β) of a molecule is a measure of the change in dipole moment (or polarization) in the second order of the applied electrical field and thus has a purely electronic origin. It is a tensorial property and can be resolved in components along the three dimensions. The number of β components and the nonlinear optical anisotropies in a typical donor-acceptor type dipolar molecule, defined as (equation) (where1, 2, 3 axes define the molecular frame, 1 being the direction along the principal axis of symmetry and pointing from the acceptor toward the donor), are determined by the symmetry /structure of the molecule. It has been shown theoretically that the 1:1 EDA complexes possess large hyperpolarizabilities. In the case of pNA dimers calculation revealed that the geometry of the dimer and its symmetry is important for obtaining the correct estimate of β from its tensorial components. Therefore, it should be possible to use the values of tensorial β components to construct the unknown geometry of such complexes. Experimentally macroscopic depolarization ratios (D and D′) in the laboratory fixed frame (XYZ, X being the direction of polarization and Z the direction of propagation of the incident light), are measured from the polarization resolved intensities of second harmonic scattering from molecules in solution using the hyper-Rayleigh scattering technique. The depolarization ratios are correlated to the anisotropy parameters, u and v through a co-ordinate transformation. In this thesis I, have first, characterized the quadratic nonlinear optical property of a variety of 1:1 electron donor acceptor complexes and used the values of u and v obtained from depolarized hyper-Rayleigh scattering to deduce their geometry in solution. Chapter 1 provides an introduction to the 1:1 electron donor acceptor complexes, their relevance to chemistry and biology. It also contains an introduction to nonlinear optical processes in molecules. The objective of the present work and scope of the investigation carried out in this thesis is presented in this chapter. Chapter 2 describes the details of the experimental polarization resolved HRS technique. The geometrical model adopted for the analysis of the HRS data has also been introduced and the method of analysis has been described in detail in this chapter. Chapter 3 presents the measurement of β values of two series of 1:1 EDA complexes of variously substituted methylbenzenes donors with tetrachloro-p-benzoquinone (CHL) and dicyanodichloro-p-benzoquinone (DDQ) acceptors at 1064 nm. In agreement with recent theoretical results we find large first hyperpolarizabilities for these complexes. The β values are greater than that of the typical push-pull molecule p-nitroaniline (pNA). We also find that in general β decreases with decrease in the donor strength. Chapter 4 presents the β values for the two series of EDA complexes of CHL and DDQ acceptors at 1907 nm. The values of β are less in magnitude at 1907 nm than that at 1064 nm which is due to the dispersion effect in β. In Chapter 5 and 6, it is described how depolarized hyper-Rayleigh scattering can be utilized to probe geometries of 1:1 complexes in solution. Chapter 5 concentrates mainly on 1:1 EDA complexes of CHL and DDQ and TCNB (tetracyanobenzene), while chapter 6 contains examples of other 1:1 molecular complexes where the noncovalent interactions are much weaker, such as in benzene-naphthalene, benzene-methoxybenzene, benzene-hexafluorobenzene and benzene-chlorobenzene pairs. We find the geometry of 1:1 EDA complexes in solution in terms of tilt angle (θ) and twist angle (ϕ) between the donor and acceptor pairs. The angle θ varies from 29°-47° for different pairs of EDA complexes, while ϕ varies within 34° and 38°. We find that the geometry of 1:1 EDA complexes in solution is different (twisted and tilted cofacial and twisted ‘V’) from those in the crystalline or gaseous states (cofacial), if known. We find that both benzene-naphthalene and benzene-chlorobenzene pairs assume twisted ‘T’ shape geometry with θ = 82° and 85°, respectively, and φ = 38°, while benzene-hexafluorobenzene assumes a twisted ‘V’ shape. A strong solvent effect is seen in the geometry of the benzene- methoxybenzene complex. The tilt angle is 55° when chloroform is used as a solvent and it is 82° without chloroform. Chapter 7 is the concluding chapter where the main work done in this thesis is summarized and future directions are presented.
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Books on the topic "Quadratic nonlinearity"

1

America, Optical Society of, Institution of Electrical Engineers, and Institute of Physics, eds. Photosensitivity and quadratic nonlinearity in glass wave guides: Fundamentals and applications, September 9-11, 1995, Portland, Oregon : summaries of the papers presented at the topical meeting. Washington, DC: Optical Society of America, 1995.

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2

Isett, Philip. The Coarse Scale Flow and Commutator Estimates. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0016.

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This chapter derives estimates for the coarse scale flow and commutator. Instead of mollifying the velocity field in the time variable, it derives a Transport equation for vsubscript Element and some estimates that will be necessary for the proof. Here the quadratic term arises from the failure of the nonlinearity to commute with the averaging. Commutator estimates are then derived. To observe cancellation in the quadratic term, the control over the higher-frequency part of v is used, and cancellation is obtained from the lower-frequency parts. It becomes clear that the commutator terms can be estimated using the control of only the derivatives of v. The chapter concludes by presenting the theorem for coarse scale flow estimates.
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Physics, Institute Of. Photosensitivity and Quadratic Nonlinearity in Glass Waveguides: Fundamentals and Applications : Postconference Edition 1995 (Technical Digest Series (Optical Society of America), 1995, V. 22.). Optical Society of America, 1995.

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Book chapters on the topic "Quadratic nonlinearity"

1

Nevière, M., and S. A. Darmanyan. "Nonlinear Eigenmodes in Quadratic Film Waveguides." In Nonlinearity and Disorder: Theory and Applications, 423–33. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0542-5_36.

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Kobyakov, A., F. Kh Abdullaev, S. A. Darmanyan, E. Schmidt, and F. Lederer. "Spatial Solitons in Random Quadratic Media." In Nonlinearity and Disorder: Theory and Applications, 37–53. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0542-5_4.

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Conti, C., and S. Trillo. "Self-transparency and Localization in Gratings with Quadratic Nonlinearity." In Springer Series in Photonics, 73–105. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05144-3_5.

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Filippova, Tatiana F., and Elena V. Berezina. "On State Estimation Approaches for Uncertain Dynamical Systems with Quadratic Nonlinearity: Theory and Computer Simulations." In Large-Scale Scientific Computing, 326–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-78827-0_36.

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Vaidyanathan, Sundarapandian. "Analysis, Adaptive Control and Synchronization of a Novel 3-D Chaotic System with a Quartic Nonlinearity and Two Quadratic Nonlinearities." In Advances in Chaos Theory and Intelligent Control, 429–53. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30340-6_18.

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"Free oscillation systems with quadratic nonlinearity." In Modern Mechanics and Mathematics. Chapman and Hall/CRC, 2003. http://dx.doi.org/10.1201/9780203491164.ch12.

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Etrich, Christoph, Falk Lederer, Boris A. Malomed, Thomas Peschel, and Ulf Peschel. "Optical Solitons in Media with a Quadratic Nonlinearity." In Progress in Optics, 483–568. Elsevier, 2000. http://dx.doi.org/10.1016/s0079-6638(00)80022-0.

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Zaccarian, Luca, and Andrew R. Teel. "Analysis and Synthesis of Feedback Systems: Quadratic Functions and LMIs." In Modern Anti-windup Synthesis. Princeton University Press, 2011. http://dx.doi.org/10.23943/princeton/9780691147321.003.0003.

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This chapter describes the analysis and synthesis of feedback systems, with particular emphasis on quadratic functions and linear matrix inequalities (LMIs). It first considers the analysis of feedback loops with saturation, with the goal of developing tools for verifying internal stability and quantifying L₂ external stability for the feedback interconnection of a linear system with a saturation nonlinearity. It then discusses quadratic functions and semidefinite matrices, along with the use of quadratic functions to analyze unconstrained feedback systems. It also demonstrates how the LMI feasibility and eigenvalue problems can be solved efficiently using modern numerical software packages. Furthermore, it looks at the global vs. regional analysis of unconstrained feedback systems. A few examples of nonlinear gain computation are provided to illustrate the use of the LMIs. The chapter concludes by explaining regional synthesis in feedback loops with saturation based on the LMIs.
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Conference papers on the topic "Quadratic nonlinearity"

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Sugden, Kate, Lin Zhang, John Williams, and Ian Bennion. "Dissimilar wavefront technique for linear and quadratic chirps." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sub.12.

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In this paper, we discuss and characterise two variations on the dissimilar wavefront technique1 that give near-linearly and quadratically chirped gratings. This technique is advantageous over others that have been proposed for the fabrication of chirped gratings because of its simplicity and flexibility. A high level of bandwidth control is demonstrated for gratings of bandwidths in the range of 0.5-23nm.
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Booth, I. J., J. L. Archambault, and B. F. Ventrudo. "Photodarkening in Upconversion Pumped Thulium Doped Fluorozirconate Fibre Lasers." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.pmd.6.

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Upconversion pumped lasing in rare earth doped fluorozirconate optical fibre offers the potential for compact blue green laser sources pumped by commercially available infrared laser diodes. A promising candidate for such a source is the thulium system first demonstrated by Steve Grubb and co-workers [1], which lases in the blue at 482 nm with a single pump source at about 1130 nm. Figure 1 illustrates the relevant energy levels of the trivalent thulium ion, and the upconversion mechanism. Ions excited to the short lived H5 and F23 levels decay rapidly by phonon emission to the metastable H4 and F4 levels from which further upconversion transitions occur. The centre wavelengths of the three transitions are respectively 1220 nm (H6 to Hs), 1130 nm (H4 to F2), and 1150 nm (F4 to G4), but because of the broadening of the transitions in glass it is possible to excite all three with a single wavelength pump in the range 1110 nm to 1160 nm. The next energy level above G4 in thulium is D2 with a transition of 1480 nm separating the two, so that further upconversion above G4 should not occur, or only very weakly. A low phonon energy host material such as ZBLAN fluorozirconate glass is necessary so that the metastable levels do not decay rapidly by phonon emission.
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Watanabe, Yuichi, Naoyuki Takeshita, Toshio Tsuchiya, Hideo Hosono, and Hiroshi Kawazoe. "A large second-order nonlinearity in poled phosphate glass containing mobile protons." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sub.1.

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Recently, Myers et al. reported that a large second-order nonlinearity [χ(2)~1pm/V] was induced in the near surface region (~4μm) of commercial fused silica by electric-field (5× 104V/cm) poling process at 300°C1. Since the large nonlinearity that they observed were remarkable in the glass containing a small amount of alkali (Na+) impurity, they proposed a model, based on the formation of space-charge layer due to drift of Na+ during poling process, that could explain the nonlinearity. Here we report second-order nonlinearity in poled phosphate glass. The observed nonlinearity is explained tentatively by considering the drift of protons in the poled glasses.
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Poumellec, B., P. Niay, M. Douay, and J. F. Bayon. "U. V. induced densification during Bragg grating writing." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sub.6.

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It was expected that the bleaching of the 240-260 nm absorption band and creation of others were sufficient to explain all part of the index change through Kramers-Kronig conjugation. However, Williams et al. [1] taking into account the UV absorption change showed that at most 20% of the index change can be accounted for by this effect. This statement was confirmed also by Eric Fertein [2] in various type of fibers and in taking into account the VUV absorption change. In addition, some recent experiments by Albert et al. [3] using 193 nm light indicates that the bleaching of absorption bands near 242 nm is not essential to induce refractive index changes. A second phase of the process may be that transformed defects lead to a change in the microstructure of the silica. The first idea is a change of volume and so we can expect to see corrugations at the surface of irradiated flat substrate close as the ones of preform slices.
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Magruder, Robert H. "The Formation of Nonlinear Optical Materials by Ion Implantation." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.pma.1.

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There are several potential candidate systems for nonlinear optical materials including resonant and non-resonant semiconductor quantum dots, organic materials and glass systems. Two of the glass systems are based on glasses containing transition metal ions. The first system exploits the polarization of the transition metal ions (Ti, V, Nb) incorporated in the glass matrix, while the second is based on glasses with metallic nanoclusters of the transition ions (Cu, Ag, Au). While both systems have been shown to have desirable properties for nonlinear media each systems has different nonlinear properties.
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Dianov, E. M., V. I. Karpov, A. S. Kurkov, O. I. Medvedkov, A. M. Prokhorov, V. N. Protopopov, and S. A. Vasil'ev. "Gain Spectrum Flattening of Erbium-Doped Fiber Amplifier Using Long-Period Fiber Grating." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sab.3.

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The gain spectrum nonuniformity is one of the most important problems in using erbium-doped fiber amplifiers (EDFA) in wavelength-division-multiplexing transmission systems. Several techniques for the gain spectrum flattening with the use of passive filters have been proposed: mechanical deformation of the fiber to couple fundamental and leaky modes [1], etching of the grating at the surface of a D-fiber [2], utilization of a twin-core fiber filter [3], application of photoinduced fiber Bragg grating [4], application of a Fourier filter based on the incorporation of the glass plate [5] or a tapered fiber filter [6].
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Martin, Jean, Graham Atkins, François Ouellette, Michel Têtu, Jean Deslauriers, and Michel A. Duguay. "Direct Correlation Between UV-Excited Photo-Luminescence and Refrative Index Change in Photosensitive Ge-Doped and Hydrogenated Optical Fibre." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.pma.2.

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Many studies have been devoted to the origin of photosensitivity since its discovery in the 70's [1]. The time dependence of the UV-excited blue photoluminescence (PL) has been related to photosensitivity, but up to now the only correlation reported [2] is the relation between the decrease of the blue PL and the refractive index change. In this paper we intend to show a direct correlation between the increase of the blue PL and the refractive index change.
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Zhang, L., K. Sugden, J. A. R. Williams, I. Bennion, D. C. J. Reid, and C. M. Ragdale. "In-Fiber Transmission Filters with Broad Stopbands using Chirped Bragg Gratings." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sub.11.

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Many optical fiber applications, such as wavelength division multiplexing/demultiplexing, frequency-guiding in soliton systems, and the filtering out of spontaneous emission noise from fiber amplifiers require transmission band-pass filters with a wide range of finesses and free spectral ranges. Bragg gratings written directly into the optical fiber by direct UV exposure [1] show particular promise in this area and there have been many reported techniques to date proposed for fabricating fiber grating transmission filters (e.g. [2–7]) Most of these techniques however do not allow independent arbitrary selection of the pass and stop band characteristics thus limiting their usefulness for many applications. While the recently reported wide stop band transmission filters based on resonant chirped grating Moiré and Fabry-Perot designs [2,3] do allow a large degree of control of the pass and stop band characteristics, in practice the parameters of the filter including transmissivity, transmission wavelength and linewidth are difficult to tailor during fabrication. Where multiple pass bands are required the number of passbands and the free spectral range are inherently fixed by the phase shift between the two interacting gratings.
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Kester, John J., Iyad Dajani, Peter Ranon, and Thomas Alley. "Modal and Polarization Properties of SHG in Doped-Silica Waveguides: Transverse Modulation Effects." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sac.5.

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The generation of second harmonic light in optically modified fibers1 and thin films2 has been shown to arise from a periodic modulation of the second-order susceptibility, χ(2), along the direction of propagation.3 This longitudinal modulation allows the phase matching of the generated second harmonic light with the fundamental wave. The efficiency of the second harmonic for different waveguiding modes and different polarizations is governed by an additional modulation in the transverse direction. The overlap of χ(2) with the transverse profiles of the optical electric fields across the waveguide, as described by the overlap integral, governs the modal response of the waveguide generated light.4 Unlike the traditional second harmonic generation (SHG) processes, the overlap integrals describing higher order modal combinations may be on the same order as the overlap integral describing the combination of the lowest order modes. In planar waveguides the difference in the transverse charge density governs the polarization dependence.
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Moss, D., F. Ouellette, M. Faith, P. Leech, P. Kemeny, M. Ibsen, O. Leistiko, C. V. Poulsen, J. D. Love, and F. J. Ladouceur. "All Optically Written Planar Germanosilicate Waveguide Gratings." In Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/pqn.1995.sub.8.

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Photo-induced index changes in germanosilicate glass is a well known effect and has provided the basis for much recent activity on photoinduced refractive index gratings in fibres1. Since then, very large (>10-3) index changes in hydrogen loaded waveguide structures have been observed and used as the basis for patterning channel waveguides2 and directional couplers3. Recently, we have demonstrated waveguide structures patterned in PECVD grown material without the aid of hydrogen loading4,5, and in this paper we report the fabrication of all optically patterned buried waveguide grating structures, again without the aid of hydrogen loading. This demonstrates that the achievable index changes (without hydrogen loading) in this material is large enough to simultaneously support both waveguide and grating structures. The elimination of hydrogen loading is an important practical issue because, unlike fibres, planar waveguides need anomalously large overcladding layers to prevent rapid out diffusion of hydrogen during writing.
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Reports on the topic "Quadratic nonlinearity"

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Dimova, Milena, Natalia Kolkovska, and Nikolay Kutev. Orbital Stability or Instability of Solitary Waves to Generalized Boussinesq Equation with Quadratic-cubic Nonlinearity. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, August 2018. http://dx.doi.org/10.7546/crabs.2018.08.01.

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OPTICAL SOCIETY OF AMERICA WASHINGTON DC. Postdeadline Papers on Photosensitivity and Quadratic Nonlinearity in Glass Waveguides. Fundamentals and Applications Held in Portland, Oregon on 9-11 September 1995. Technical Digest Series. Volume 22. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada306074.

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