Gotowe bibliografie tematyczne / Double Gaussian Distribution

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  1. Artykuły w czasopismach
  2. Rozprawy doktorskie
  3. Części książek
  4. Streszczenia konferencji

Gotowa bibliografia na temat „Double Gaussian Distribution”

Autor: Grafiati
Data publikacji: 6 września 2023

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Artykuły w czasopismach na temat "Double Gaussian Distribution"

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Khatoon, Rukaiya, Zahir Shah, Ranjeev Misra i Rupjyoti Gogoi. "Study of long-term flux and photon index distributions of blazars using RXTE observations". Monthly Notices of the Royal Astronomical Society 491, nr 2 (11.11.2019): 1934–40. http://dx.doi.org/10.1093/mnras/stz3108.

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ABSTRACT We present a detailed study of flux and index distributions of three blazars [one flat-spectrum radio quasar (FSRQ) and two BL Lacertae objects (BL Lacs)] by using 16 yr of Rossi X-ray Timing Explorer (RXTE) archival data. The three blazars were chosen such that their flux and index distributions have sufficient number of data points (≥90) with relatively less uncertainty $\left(\overline{\sigma _{\rm err}^{2}}/\sigma ^{2} < 0.2\right)$ in light curves. Anderson–Darling (AD) test and histogram fitting show that flux distribution of FSRQ 3C 273 is lognormal, while its photon index distribution is Gaussian. This result is consistent with linear Gaussian perturbation in the particle acceleration time-scale, which produces lognormal distribution in flux. However, for two BL Lacs, viz. Mrk 501 and Mrk 421, AD test shows that their flux distributions are neither Gaussian nor lognormal, and their index distributions are non-normal. The histogram fitting of Mrk 501 and Mrk 421 suggests that their flux distributions are more likely to be a bimodal, and their index distributions are double Gaussian. Since, Sinha et al. had shown that Gaussian distribution of index produces a lognormal distribution in flux, double Gaussian distribution of index in Mrk 501 and Mrk 421 indicates that their flux distributions are probably double lognormal. Observation of double lognormal flux distribution with double Gaussian distribution in index reaffirms two flux states hypothesis. Further, the difference observed in the flux distribution of FSRQ (3C 273) and BL Lacs (Mrk 501 and Mrk 421) at X-rays suggests that the low-energy emitting electrons have a single lognormal flux distribution, while the high-energy ones have a double lognormal flux distribution.
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Schreiber, Johannes, Amr Balbaa i Carlo L. Bottasso. "Brief communication: A double-Gaussian wake model". Wind Energy Science 5, nr 1 (14.02.2020): 237–44. http://dx.doi.org/10.5194/wes-5-237-2020.

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Abstract. In this paper, an analytical wake model with a double-Gaussian velocity distribution is presented, improving on a similar formulation by Keane et al. (2016). The choice of a double-Gaussian shape function is motivated by the behavior of the near-wake region that is observed in numerical simulations and experimental measurements. The method is based on the conservation of momentum principle, while stream-tube theory is used to determine the wake expansion at the tube outlet. The model is calibrated and validated using large eddy simulations replicating scaled wind turbine experiments. Results show that the tuned double-Gaussian model is superior to a single-Gaussian formulation in the near-wake region.
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Crandall, Sara, Stephen Houston i Bharat Ratra. "Non-Gaussian error distribution of 7Li abundance measurements". Modern Physics Letters A 30, nr 25 (30.07.2015): 1550123. http://dx.doi.org/10.1142/s0217732315501230.

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We construct the error distribution of [Formula: see text] abundance measurements for 66 observations (with error bars) used by Spite et al. (2012) that give [Formula: see text] (median and [Formula: see text] symmetrized error). This error distribution is somewhat non-Gaussian, with larger probability in the tails than is predicted by a Gaussian distribution. The 95.4% confidence limits are [Formula: see text] in terms of the quoted errors. We fit the data to four commonly used distributions: Gaussian, Cauchy, Student’s t and double exponential with the center of the distribution found with both weighted mean and median statistics. It is reasonably well described by a widened [Formula: see text] Student’s t distribution. Assuming Gaussianity, the observed A(Li) is [Formula: see text] away from that expected from standard Big Bang Nucleosynthesis (BBN) given the Planck observations. Accounting for the non-Gaussianity of the observed A(Li) error distribution reduces the discrepancy to [Formula: see text], which is still significant.
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Jung, Hak-Kee. "Subthreshold Characteristics of Double Gate MOSFET for Gaussian Function Distribution". Journal of the Korean Institute of Information and Communication Engineering 16, nr 6 (30.06.2012): 1260–65. http://dx.doi.org/10.6109/jkiice.2012.16.6.1260.

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Tang, Heng-Song, Wei-Lie Meng i Neng-Hui Zhang. "Mechanical properties of double-stranded DNA biofilm with Gaussian distribution". Acta Mechanica Sinica 30, nr 1 (luty 2014): 15–19. http://dx.doi.org/10.1007/s10409-014-0023-z.

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Fitch, A. C. "An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function". Journal of the Atmospheric Sciences 76, nr 1 (1.01.2019): 285–304. http://dx.doi.org/10.1175/jas-d-18-0149.1.

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Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.
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Jung, Hak Kee. "Projected Range Dependent Tunneling Current of Asymmetric Double Gate MOSFET". International Journal of Electrical and Computer Engineering (IJECE) 6, nr 1 (1.02.2016): 113. http://dx.doi.org/10.11591/ijece.v6i1.9342.

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This study is to analyze the changes of tunneling current according to projected range, a variable of Gaussian function of channel doping function of Asymmetric Double Gate; ADG MOSFET. In MOSFET with channel length below 10 nm, tunneling current occupies a large percentage among off-currents. The increase of tunneling current has a large effect on the characteristics of subthreshold such as threshold voltage movement and the decline of subthreshold swing value, so the accurate analysis of this is being required. To analyze this, potential distribution of series form was obtained using Gaussian distribution function, and using this hermeneutic potential distribution, thermionic emission current and tunneling current making up off-current were obtained. At this point, the effect that the changes of projected range, a variable of Gaussian distribution function, have on the ratio of tunneling current among off-currents was analyzed. As a result, the smaller projected range was, the lower the ratio of tunneling current was. When projected range increased, tunneling current increased largely. Also, it was observed that the value of projected range which the ratio of tunneling current increased changed according to maximum channel doping value, channel length, and channel width.
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Jung, Hak Kee. "Projected Range Dependent Tunneling Current of Asymmetric Double Gate MOSFET". International Journal of Electrical and Computer Engineering (IJECE) 6, nr 1 (1.02.2016): 113. http://dx.doi.org/10.11591/ijece.v6i1.pp113-119.

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This study is to analyze the changes of tunneling current according to projected range, a variable of Gaussian function of channel doping function of Asymmetric Double Gate; ADG MOSFET. In MOSFET with channel length below 10 nm, tunneling current occupies a large percentage among off-currents. The increase of tunneling current has a large effect on the characteristics of subthreshold such as threshold voltage movement and the decline of subthreshold swing value, so the accurate analysis of this is being required. To analyze this, potential distribution of series form was obtained using Gaussian distribution function, and using this hermeneutic potential distribution, thermionic emission current and tunneling current making up off-current were obtained. At this point, the effect that the changes of projected range, a variable of Gaussian distribution function, have on the ratio of tunneling current among off-currents was analyzed. As a result, the smaller projected range was, the lower the ratio of tunneling current was. When projected range increased, tunneling current increased largely. Also, it was observed that the value of projected range which the ratio of tunneling current increased changed according to maximum channel doping value, channel length, and channel width.
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Ohmasa, Yoshinori, i Ayano Chiba. "Intensity distribution profile of double Bragg scattering in the small-angle region from highly oriented pyrolytic graphite". Acta Crystallographica Section A Foundations and Advances 74, nr 6 (12.10.2018): 681–98. http://dx.doi.org/10.1107/s2053273318012469.

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It is observed that radial streak patterns of double Bragg scattering appear in the small-angle X-ray scattering from highly oriented pyrolytic graphite (HOPG). The intensity profile of double Bragg scattering from an HOPG sample is calculated theoretically. Assuming that the c axes of the graphite crystallites in the HOPG sample are distributed around an orientation vector and their distribution function has a Gaussian form, it is found that the intensity profile of double Bragg scattering is expressed by a double Gaussian function of the scattering angle and the azimuthal angle of the streak. The calculated intensity profile is compared with the experimental one. The method developed in this article can be used to estimate the orientational distribution of crystallites in uniaxial polycrystalline materials.
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Bobby, A., S. Verma, K. Asokan, P. M. Sarun i B. K. Antony. "Phase transition induced double-Gaussian barrier height distribution in Schottky diode". Physica B: Condensed Matter 431 (grudzień 2013): 6–10. http://dx.doi.org/10.1016/j.physb.2013.08.037.

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Rozprawy doktorskie na temat "Double Gaussian Distribution"

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Chowdhury, Arun Malla. "Self-powered Broadband and Ultrafast Photoresponse using InN and InGaN grown on AlN/Si (111) by Plasma-assisted Molecular Beam Epitaxy". Thesis, 2020. https://etd.iisc.ac.in/handle/2005/5411.

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Group III-nitride semiconductors have enabled revolution in solid-state lighting and high-power/high-frequency electronics. Now-a-days, III-nitride based photodetectors are of great importance because of their various applications from everyday consumer electronics such as compact disc players, smoke detectors, remote control etc. to more elegant applications such as environmental monitoring, space research and in optical communications. Materials such as AlN and AlGaN have been used as solar blind photodetectors, whereas AlGaN and GaN based devices have been extensively used as UV photodetectors that depend on the concentration of Ga. On the other hand, InGaN and InN based devices are well-established for broad band and infrared photodetection applications, respectively. The key point of a broad band photodetector is that it occupies multiple wavelength region and therefore, allows much higher throughput over a single medium. Furthermore, along with broad band detection, the infrared detection in the optical telecommunication range (1550 nm) is also a demanding research area in the scientific community. Most of the photodetectors require an applied bias for appreciable detectivity, which needs a constant electrical power source. However, a self-powered photodetector can operate at zero bias without any external power source. The self-powered photodetectors such as p-n junction, heterojunction, Schottky junctions and organic/inorganic hybrid junctions can immediately separate the electron-hole pairs due to the built-in electric field, exhibiting faster photo response and higher responsivity at zero bias. Therefore, InN and InGaN based self-powered photodetectors in the present work will enthuse the scientific community considering the recent energy crisis. In our work, we have optimised InN epilayer on AlN/Si (111) template and achieved the self-powered infrared photoresponse with appreciable responsivity. Furthermore, InGaN epilayers were grown on AlN template to realize the UV and visible photodetection. We had grown three InGaN epilayers on AlN template with different Indium concentration. The point defects dominate on lower indium content sample due to hydrostatic strain and trench and sub-interfacial extended defects dominate on higher indium content sample due to in-plane biaxial strain. Moreover, the localised states dominate on higher indium content sample over electron-phonon interaction and therefore, we have chosen the InGaN sample with low In content for UV-Visible photodetection. The InGaN/AlN/n-Si (111) devices exhibit excellent self-powered photoresponse under UV-Visible (300-800 nm) light illumination. Furthermore, to cover the broad band range and as well as the infrared optical fibre communication range (1550 nm) with the help of binary (InN) and ternary (InGaN) compounds we have combined the InN binary layer with InGaN ternary layer in the form of nanorods and epilayer junction. The InN nanorods and InGaN epilayers were grown on AlN/n-Si (111) template by using plasma-assisted molecular beam epitaxy. The device structure displays outstanding self-powered photodetection from UV, visible to infrared (300 – 800 nm and 1550 nm) wavelength range. This work is thus believed to make a great impact in nanoelectronics, optoelectronics and in optical fibre communication due to its superior device structure.
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El-Khatib, Mayar. "Highway Development Decision-Making Under Uncertainty: Analysis, Critique and Advancement". Thesis, 2010. http://hdl.handle.net/10012/5741.

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While decision-making under uncertainty is a major universal problem, its implications in the field of transportation systems are especially enormous; where the benefits of right decisions are tremendous, the consequences of wrong ones are potentially disastrous. In the realm of highway systems, decisions related to the highway configuration (number of lanes, right of way, etc.) need to incorporate both the traffic demand and land price uncertainties. In the literature, these uncertainties have generally been modeled using the Geometric Brownian Motion (GBM) process, which has been used extensively in modeling many other real life phenomena. But few scholars, including those who used the GBM in highway configuration decisions, have offered any rigorous justification for the use of this model. This thesis attempts to offer a detailed analysis of various aspects of transportation systems in relation to decision-making. It reveals some general insights as well as a new concept that extends the notion of opportunity cost to situations where wrong decisions could be made. Claiming deficiency of the GBM model, it also introduces a new formulation that utilizes a large and flexible parametric family of jump models (i.e., Lévy processes). To validate this claim, data related to traffic demand and land prices were collected and analyzed to reveal that their distributions, heavy-tailed and asymmetric, do not match well with the GBM model. As a remedy, this research used the Merton, Kou, and negative inverse Gaussian Lévy processes as possible alternatives. Though the results show indifference in relation to final decisions among the models, mathematically, they improve the precision of uncertainty models and the decision-making process. This furthers the quest for optimality in highway projects and beyond.
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Części książek na temat "Double Gaussian Distribution"

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Ganesh, Talari, i Anithakumari Kattamanchi. "Inferential Aspects of Doubly Truncated Generalized Gaussian Distribution". W Advances in Intelligent Systems and Computing, 537–47. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-0751-9_50.

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Mathews, Joseph, Sumen Sen i Ishapathik Das. "Multivariate Doubly-Inflated Negative Binomial Distribution Using Gaussian Copula". W STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 147–61. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11431-2_8.

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Streszczenia konferencji na temat "Double Gaussian Distribution"

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O'Donoughue, Nicholas, i Jose M. F. Moura. "The complex Double Gaussian distribution". W ICASSP 2012 - 2012 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2012. http://dx.doi.org/10.1109/icassp.2012.6288693.

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Yang, C. C. "Probability distribution of laser beam intensity after propagating through turbulent media". W OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1985. http://dx.doi.org/10.1364/oam.1985.fk2.

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Laser beams experience random scattering when they are propagated in turbulent media. If the turbulences are strong and the propagation distance is long enough, the statistics of the laser beam intensity is expected to reach the saturation regime in which the intensity possesses a Gaussian probability distribution as a consequence of the central limit theorem. However, in many cases the condition for saturation is not reached, and K distributions, instead of Gaussian distributions, have been reported by experimentalists. To give interpretations for these distributions, although simple theoretical models were introduced, a more rigorous method is presented with more physical insight. The theory behind these K distributions includes the conceptions of double-scattering by large and small irregularities and narrow laser beamwidth. Statistical fourth moments of laser intensities are evaluated and discussed thoroughly to show different properties of K distribution from those of Gaussian distribution. In mathematical computations, the path integral technique is applied under the assumption of forward scattering.
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Kumar Reddy, N. Nanda, I. Jyothi, V. Rajagopal Reddy, Alka B. Garg, R. Mittal i R. Mukhopadhyay. "Double Gaussian Distribution of Inhomogeneous Barrier Height in Ru∕Pt∕n-GaN Schottky Barrier Diodes". W SOLID STATE PHYSICS, PROCEEDINGS OF THE 55TH DAE SOLID STATE PHYSICS SYMPOSIUM 2010. AIP, 2011. http://dx.doi.org/10.1063/1.3606230.

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Zhang, Feng, i John W. Y. Lit. "Properties of polarization in double-clad elliptical fibers". W OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/oam.1989.mll1.

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By using Gaussian approximation, the modal spot size equation of a weakly guiding double-clad elliptical (DCE) fiber has been numerically solved. The variations of both the spot size and the field intensity with core ellipticity are examined. The results show that, compared with single-clad elliptical fibers, a smaller spot size and a more confined field distribution can be obtained. The polarization properties are also examined and presented as curves in terms of the three parameters: major/minor core axis ratio, inner cladding and core index difference, and inner cladding/core radius ratio. The curves of birefringence as a function of normalized frequency for the different parameters show that high bire-fringence can be obtained within the single-mode region by using DCE fibers.
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Shokouhmand, Hossein, Maziar Aghvami, Mostafa Moghadami i Hamed Babazadeh. "Roughness Effect on Pressure Drop for Electroosmotic (EO) Flow in Microtubes". W ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2008. http://dx.doi.org/10.1115/icnmm2008-62114.

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This paper presents a theoretical model of the roughness effect on friction factor and pressure drop of fully developed, laminar flow in microtubes by considering the effect of the electrical double layer. The EDL potential distribution is calculated using the Poisson–Boltzmann equation and then the velocity profile is obtained by solving the fluid momentum equation with a body force term. The wall roughness in microtubes is modeled by utilizing a Gaussian, isotropic distribution. It is found that the effect of roughness is to increase the friction factor and pressure drop of the electroosmotic flow in microtubes.
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Ryan, Kevin M., Jesper Kristensen, You Ling, Sayan Ghosh, Isaac Asher i Liping Wang. "A Gaussian Process Modeling Approach for Fast Robust Design With Uncertain Inputs". W ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-77007.

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Many engineering design and industrial manufacturing applications are tasked with finding optimum designs while dealing with uncertainty in the design parameters. The performance or quality of the design may be sensitive to the input variation, making it difficult to optimize. Probabilistic and robust design optimization methods are used in these scenarios to find the designs that will perform best under the presence of known input uncertainty. Robust design optimization algorithms often require a two-level optimization problem (double-loop) to find a solution. The design optimization outer-loop repeatedly calls a series of inner loops that calculate uncertainty measures of the outputs. This nested optimization problem is computationally expensive and can sometimes render the task infeasible for practical engineering robust design problems. This paper details a single-level metamodel-assisted approach for probabilistic and robust design. An enhanced Gaussian Process (GP) metamodel formulation is used to provide exact values of output uncertainty in the presence of uncertain inputs. The GP model utilizes a squared-exponential kernel function and assumes normally distributed input uncertainty. These two factors together allow for an exact calculation of the first and second moments of the marginal predictive distribution. Predictions of output uncertainty are directly calculated, creating an efficient single-level robust optimization problem. We demonstrate the effectiveness of the single-level GP-assisted robust design approach on multiple engineering example problems, including a beam vibration problem, a cantilevered beam with multiple constraints, and a robust autonomous aircraft flight controller design problem. For the optimization problems investigated in this study, the single-level framework found the robust optimum with a 99.9% savings in function evaluations over the standard two-level approach.
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Cremanns, Kevin, Dirk Roos, Andreas Penkner, Simon Hecker i Christian Musch. "Steam Turbine Exhaust Optimization Based on Gaussian Covariance Networks Using Transient CFD Simulations". W ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75261.

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Renewable energies are increasingly contributing to the overall volume of the electricity grid and demand besides high efficiency, greater flexibility of the conventional fossil power plants. To optimize these objectives, extensive CFD calculations are required in most cases. For example, transient CFD calculations are only rarely combined with an optimizer because of their high demand on computational resources and time. Surrogate models, which are mathematical methods to learn and approximate the relationship between input and output parameters, are a common way to solve these problems. Once they are trained, they can perform the evaluations within seconds and replace the expensive simulation. Of course, real calculations are still needed to generate the training data. Therefore, it is useful to apply efficient and sequentially extensible design plans. This paper presents a new surrogate model method, based on a deep neural network learning the non-stationary hyperparameters of combined Gaussian process covariance matrices. It is used to approximate the complex and time consuming transient CFD simulation of a combined high-intermediate pressure steam turbine double shell outer casing. To minimize the exergy loss, the exhaust geometry is optimized in a single and multi-objective optimization on the surrogate models. The multi-objective optimization also includes the uniform velocity distribution of the steam in different areas of the casing, to predict the thermal loading of the steam turbine inner casing and to avoid an imbalanced thermal loading. A sequential sampling approach combined with a sensitivity analysis is used to find the minimum number of samples needed to train the surrogate models in order to gain sufficient prediction quality. Additionally, the paper describes the initial geometry, its numerical setup and the required control mechanisms to avoid noisy designs, which might complicate the surrogate model training. There is also a comparison of the initial and chosen optimal designs.
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Feit, David, i Daniel DiPerna. "Force Distribution Dependence of Sound Radiation From a Doubly Rib-Stiffened Plate". W ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0234.

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Abstract Analytical formulae for both the velocity spectrum and the acoustic far-field radiated sound pressure for a doubly rib-stiffened (small frames and bulkheads) fluid-loaded elastic plate, excited by several different force distributions, are derived. The force distributions are (1) a line-force applied at a single point and (2) two Gaussian distributed force intensities whose effective width either spans the small rib spacing or the large rib spacing. The far-field sound pressure as a function of frequency is calculated. The concentrated line force case shows evidence of frame interference effects (sometimes referred to as Bloch waves) in the radiated pressure fields. These arise from coherent interaction of the pressure fields emanating from the frame reaction forces and the applied force pressure field. The frequencies at which these coherence effects are manifest depend on the stiffeners’ spacing as compared to the fluid-loaded flexural wavelength. The Gaussian force distribution eliminates these interaction effects depending on whether or not the effective force width is greater or less than the respective rib spacing.
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Qi Li, Zhaoji Li i Bo Zhang. "Analytical Model for the Surface Electrical field Distributions of Double RESURF Devices with Gaussian-doped P-top Region". W 2007 5th International Conference on Communications, Circuits and Systems. IEEE, 2007. http://dx.doi.org/10.1109/icccas.2007.4348281.

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Altmann, Konrad, i Nikolaus Schmitt. "ABCD matrix modeling of thermal lensing and gain guiding in diode pumped solid state lasers". W The European Conference on Lasers and Electro-Optics. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/cleo_europe.1996.cthi69.

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In the paraxial wave equation for a complex gaussian duct the term describing the combined effect of thermal lensing and gain guiding is given by the complex expression in the round brackets with the real and the imaginary part corresponding to thermal lensing and gain guiding, respectively. If both parts are of comparable magnitude or if the imaginary part is smaller than the real one, as found in many practical resonator configurations, the expression obtained from this equation for the spot size is dominated by the real part, the expression obtained for the phase front curvature on the other hand is dominated by the imaginary part. Therefore, in monolithic configurations with short resonators gain guiding must only be taken into account for laser materials with negligible thermal lensing i. e. with very small or negative derivative of the index of refraction with respect to temperature. This case has been analyzed in previous papers. However, in heterogeneous resonator configurations e.g. with external mirrors or other mode shaping elements the additional phase front curvature due to gain guiding may become very important even in the presence of thermal lensing. An example for this situation is shown in Fig. 1 where a short crystal is combined with an external mirror and where the distance between crystal and mirror is chosen several times larger than the crystal’s length. As one can see, in this case the splitting of the mode shape for both directions of propagation due to gain guiding can be considerable. As can be shown by parameter variation, this splitting depends very sensitive on the relative values of the resonator’s length, the mirror’s curvature, and the parabolic coefficients n2 and α2 of refractive index and gain, respectively. In the present example, for fixed values of n2 and α2 the splitting can be nearly suppressed by an appropriate choice of the mirror’s curvature. The configuration, however, remains sensitive with respect to fluctuations of pumping power and temperature distribution. An even more complicated situation arises, if a frequency doubler is present in the resonator, which induces an antiguiding effect due to a transversely varying conversion efficiency. This examples show that a parametric study of the combined effect of thermal lensing and gain guiding can be very important to find out an appropriate resonator design. For this purpose a program was developed by the use of the complex ABCD matrix formalism which offers a very fast and valuable tool to get better insight into the behavior of resonator configurations even though it allows only a parabolic approximation.
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