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Journal articles on the topic 'Circular caustic; Gaussian beams'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

Alexandrov, A., V. Zhdanov, and A. Kuybarov. "Gravitational microlensing of an elliptical source near a fold caustic." Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 57 (2018): 10–15. http://dx.doi.org/10.17721/btsnua.2018.57.10-15.

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We consider the amplification factor for the luminosity of an extended source near the fold caustic of the gravitational lens. It is assumed that the source has elliptical shape, and the brightness distribution along the radial directions is Gaussian. During the microlensing event the total brightness of all microimages is observed, which changes when the source moves relative to the caustic. The main contribution to the variable component is given by the so-called critical images that arise/disappear at the intersection of the caustic by the source. In the present paper we obtained an analogous formula for elliptical Gaussian source. The formula involves a dependence on the coordinates of the source centre, its geometric dimensions, and its orientation relative to the caustic. We show that in the linear caustic approximation the amplification of the circular and elliptical sources is described by the same (rescaled) formula. However, in the next approximations the differences are significant. We compare analytical calculations of the amplification curves for different orientations of an elliptical source and for a circular source with the same luminosity for the model example.

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2

Lamsoudi, Redouane. "Parametric Characterization of Truncated Circular Flattened Gaussian Beams." American Journal of Optics and Photonics 3, no. 1 (2015): 1. http://dx.doi.org/10.11648/j.ajop.20150301.11.

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3

Zhou, G., and X. Chu. "Analytic vectorial structure of circular flattened Gaussian beams." Applied Physics B 102, no. 1 (2010): 215–24. http://dx.doi.org/10.1007/s00340-010-4156-x.

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4

Liu Pu-Sheng and Lü Bai-Da. "Nonparaxial vector Gaussian beams diffracted at a circular screen." Acta Physica Sinica 53, no. 11 (2004): 3724. http://dx.doi.org/10.7498/aps.53.3724.

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5

Zheng, Chongwei, Yaoju Zhang, and Ling Wang. "Propagation of vectorial Gaussian beams behind a circular aperture." Optics & Laser Technology 39, no. 3 (2007): 598–604. http://dx.doi.org/10.1016/j.optlastec.2005.10.003.

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6

Chen, Xingyu, Dongmei Deng, Jingli Zhuang, Xiangbo Yang, Hongzhan Liu, and Guanghui Wang. "Nonparaxial propagation of abruptly autofocusing circular Pearcey Gaussian beams." Applied Optics 57, no. 28 (2018): 8418. http://dx.doi.org/10.1364/ao.57.008418.

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7

Campbell, Charles. "Fresnel Diffraction Of Gaussian Laser Beams By Circular Apertures." Optical Engineering 26, no. 3 (1987): 263270. http://dx.doi.org/10.1117/12.7974061.

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8

Barnes, Norman P., and Peter J. Walsh. "Loss of Gaussian beams through off-axis circular apertures." Applied Optics 27, no. 7 (1988): 1230. http://dx.doi.org/10.1364/ao.27.001230.

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9

Cherif, Sabah, Aicha Medjahed, and Ahmed Manallah. "Conversion of Laguerre–Gaussian beams into Gaussian beams of reduced focal spot by use of a circular echelon." Optik 127, no. 5 (2016): 3134–37. http://dx.doi.org/10.1016/j.ijleo.2015.12.035.

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10

Chen, Xingyu, Dongmei Deng, Guanghui Wang, Xiangbo Yang, and Hongzhan Liu. "Abruptly autofocused and rotated circular chirp Pearcey Gaussian vortex beams." Optics Letters 44, no. 4 (2019): 955. http://dx.doi.org/10.1364/ol.44.000955.

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11

Matikas, T. E. "Asymptotic analysis of Gaussian focused ultrasonic beams of circular symmetry." Journal of Physics D: Applied Physics 27, no. 4 (1994): 714–18. http://dx.doi.org/10.1088/0022-3727/27/4/006.

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12

Ni, Yongzhou, Yimin Zhou, Guoquan Zhou, and Ruipin Chen. "Characteristics of Partially Coherent Circular Flattened Gaussian Vortex Beams in Turbulent Biological Tissues." Applied Sciences 9, no. 5 (2019): 969. http://dx.doi.org/10.3390/app9050969.

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The characteristics of partially coherent circular flattened Gaussian vortex beams in turbulent biological tissues are investigated, and the analytical formula for the cross-spectral density of this beam is derived. According to the cross-spectral density matrix, the average intensity and degree of polarization can be obtained. By numerical simulation, the distributions of the normalized average intensity and degree of polarization of partially coherent circular flattened Gaussian vortex beams are demonstrated on the research plane of turbulent biological tissues. The effects of the two beam parameters, the topological charge, the two transverse coherent lengths, and the structural constant of biological turbulence on the normalized average intensity and degree of polarization are analyzed. This study is of great significance for the potential application of partially coherent circular flattened Gaussian vortex beams in medical imaging and medical diagnosis.

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13

Chu, Xiuxiang, Yongzhou Ni, and Guoquan Zhou. "Propagation analysis of flattened circular Gaussian beams with a circular aperture in turbulent atmosphere." Optics Communications 274, no. 2 (2007): 274–80. http://dx.doi.org/10.1016/j.optcom.2007.02.035.

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14

Guo, Kuangling, Jintao Xie, Gengxin Chen, et al. "Abruptly autofocusing properties of the chirped circular Airy Gaussian vortex beams." Optics Communications 477 (December 2020): 126369. http://dx.doi.org/10.1016/j.optcom.2020.126369.

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15

Guo, Jiang, and Zao Li. "Propagation of nonparaxial vector hollow Gaussian beams through a circular aperture." Optics Communications 285, no. 24 (2012): 4856–60. http://dx.doi.org/10.1016/j.optcom.2012.08.032.

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16

Lü, Baida, and Kailiang Duan. "Nonparaxial propagation of vectorial Gaussian beams diffracted at a circular aperture." Optics Letters 28, no. 24 (2003): 2440. http://dx.doi.org/10.1364/ol.28.002440.

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17

Xueju, Shen, Wang Long, Shen Hongbin, and Han Yudong. "Propagation analysis of flattened circular Gaussian beams with a misaligned circular aperture in turbulent atmosphere." Optics Communications 282, no. 24 (2009): 4765–70. http://dx.doi.org/10.1016/j.optcom.2009.08.064.

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18

Deng, Dongmei. "Generalized -factor of hollow Gaussian beams through a hard-edge circular aperture." Physics Letters A 341, no. 1-4 (2005): 352–56. http://dx.doi.org/10.1016/j.physleta.2005.04.081.

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19

Zhang, Yaoju. "Nonparaxial propagation analysis of elliptical Gaussian beams diffracted by a circular aperture." Optics Communications 248, no. 4-6 (2005): 317–26. http://dx.doi.org/10.1016/j.optcom.2004.12.020.

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20

Gu, Juguan, Ping Yang, and Qinghua Zhu. "Propagation characteristics of Gaussian beams through 2 × 2 square matrix circular apertures." Optik 123, no. 20 (2012): 1817–19. http://dx.doi.org/10.1016/j.ijleo.2011.12.061.

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21

Pang, Zeyue, Zhe Wang, Fengbei Shen, and Weiyi Hong. "Phase-matching control of high-order harmonics with circular Airy-Gaussian beams." Optics Express 29, no. 18 (2021): 29308. http://dx.doi.org/10.1364/oe.436029.

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22

Tu, Siyu, Jinsong Liu, Tianyi Wang, Zhengang Yang, and Kejia Wang. "Design of a 94 GHz Millimeter-Wave Four-Way Power Combiner Based on Circular Waveguide Structure." Electronics 10, no. 15 (2021): 1795. http://dx.doi.org/10.3390/electronics10151795.

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This paper introduces a four-way power combiner operating in the 94 GHz millimeter-wave based on spatial power combining technology. The four millimeter-waves with Gaussian beams are combined in the waveguide, increasing the output power. The combiner is composed of five circular waveguides connected by four long and narrow coupling slots. Four sub-waveguides are separately connected to four input ports and one main waveguide is connected to a common output port. The TE11-mode is used as the input mode, which has two vertical and horizontal polarization directions. Four sub-waveguides are respectively input corresponding to polarization directions TE11-wave with Gaussian beams. The power of TE11-wave is transmitted to the main waveguide by the coupling slots, combined in the main waveguide, and output with the common port. We analyze the combiner and verify the availability of the design structure by numerical stimulation with CST MWS (Microwave Studio) software. The power-combining efficiency can be over 97%, and the output beams remain Gaussian beams with nearly fourfold increased power. The proposed model provides technological approaches for power combiner application in millimeter-wave.

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23

Konar, S., and Manoj Mishra. "Effect of higher order nonlinearities on induced focusing and on the conversion of circular Gaussian laser beams into elliptic Gaussian laser beams." Journal of Optics A: Pure and Applied Optics 7, no. 10 (2005): 576–84. http://dx.doi.org/10.1088/1464-4258/7/10/009.

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24

Bencheikh, Abdelhalim. "Comment on the paper “Conversion of Laguerre-Gaussian beams into Gaussian beams of reduced focal spot by use of a circular echelon”." Optik 127, no. 24 (2016): 11884–85. http://dx.doi.org/10.1016/j.ijleo.2016.09.125.

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25

Koushki, E., and M. H. Majles Ara. "Comparison of the Gaussian-decomposition and the Fresnel–Kirchhoff diffraction methods in circular and elliptic Gaussian beams." Optics Communications 284, no. 23 (2011): 5488–94. http://dx.doi.org/10.1016/j.optcom.2011.08.028.

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26

Mei, Zhangrong, and Daomu Zhao. "Generalized beam propagation factor of hard-edged circular apertured diffracted Bessel–Gaussian beams." Optics & Laser Technology 39, no. 7 (2007): 1389–94. http://dx.doi.org/10.1016/j.optlastec.2006.10.011.

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27

Acosta, E., and C. Gomez-Reino. "Fresnel Diffraction of Gaussian Beams by a Circular Aperture in Gradient-index Media." Journal of Modern Optics 38, no. 9 (1991): 1659–72. http://dx.doi.org/10.1080/09500349114551801.

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28

胡, 前欢. "Anomalous Spectral Behavior of Ultrashort Pulsed Laguerre-Gaussian Beams Diffracted by Circular Ring." Applied Physics 05, no. 12 (2015): 195–201. http://dx.doi.org/10.12677/app.2015.512027.

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29

Jiang, Huilian, and Daomu Zhao. "Studies of propagation characteristics of elliptical Gaussian beams through circular apertured optical systems." Optik 118, no. 4 (2007): 181–86. http://dx.doi.org/10.1016/j.ijleo.2006.02.005.

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30

Crenn, J. P. "Optical propagation of the HE11 mode and Gaussian beams in hollow circular waveguides." International Journal of Infrared and Millimeter Waves 14, no. 10 (1993): 1947–73. http://dx.doi.org/10.1007/bf02096365.

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31

Chu, X., Y. Ni, and G. Zhou. "Propagation of cosh-Gaussian beams diffracted by a circular aperture in turbulent atmosphere." Applied Physics B 87, no. 3 (2007): 547–52. http://dx.doi.org/10.1007/s00340-007-2615-9.

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32

Huang, T. W., C. T. Zhou, and X. T. He. "Self-shaping of a relativistic elliptically Gaussian laser beam in underdense plasmas." Laser and Particle Beams 33, no. 2 (2015): 347–53. http://dx.doi.org/10.1017/s026303461500018x.

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AbstractSelf-shaping and propagation of intense laser beams of different radial profiles in plasmas is investigated. It is shown that when a relativistic elliptically Gaussian beam propagates through an underdense plasma, its radial profile will self-organize into a circularly symmetric self-similar smooth configuration. Such self-similar propagation can be attributed to a soliton-like structure of the laser pulse. The anisotropic electron distribution results in a circular electric field that redistributes the electrons and modulates the laser pulse to a circular radial shape.

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33

Zhang Liangjun, 张亮君, 张军勇 Zhang Junyong, 张艳丽 Zhang Yanli, et al. "Vectorial Non-Paraxial Propagation of Four-Petal Gaussian Beams through an Eccentric Circular Aperture." Chinese Journal of Lasers 38, no. 9 (2011): 0902005. http://dx.doi.org/10.3788/cjl201138.0902005.

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34

Duan, Kailiang, and Baida Lü. "Nonparaxial analysis of far-field properties of Gaussian beams diffracted at a circular aperture." Optics Express 11, no. 13 (2003): 1474. http://dx.doi.org/10.1364/oe.11.001474.

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35

Zhang, Liping, Shangling He, Xi Peng, et al. "Tightly focusing evolution of the auto-focusing linear polarized circular Pearcey Gaussian vortex beams." Chaos, Solitons & Fractals 143 (February 2021): 110608. http://dx.doi.org/10.1016/j.chaos.2020.110608.

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36

Jiang, Huilian, and Daomu Zhao. "Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture." Optik 117, no. 5 (2006): 215–19. http://dx.doi.org/10.1016/j.ijleo.2005.08.015.

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37

Savelyev, D. A. "The investigation of the features of focusing vortex super-Gaussian beams with a variable-height diffractive axicon." Computer Optics 45, no. 2 (2021): 214–21. http://dx.doi.org/10.18287/2412-6179-co-862.

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Spatial intensity distributions of the Laguerre-superGauss modes (1,0) as well as a super-Gaussian beam with radial and circular polarization were investigated versus changes in the height of a diffractive axicon. The height of the relief of the optical element varied from 0.25λ to 3λ. The modeling by a finite-difference time-domain method showed that variations in the height of the diffractive axicon significantly affect the diffraction pattern in the near field of the axicon. The smallest focal spot size for a super-Gaussian beam was obtained for radial polarization at a height equal to two wavelengths. The minimum size of the focal spot for the Laguerre-superGauss mode (1,0) was obtained for circular "–" polarization with an element height equal to a quarter of the wavelength.

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38

Volyar, A. V., M. Bretsko, Ya Akimova, and Yu Egorov. "Sorting Laguerre-Gaussian beams by radial numbers via intensity moments." Computer Optics 44, no. 2 (2020): 155–66. http://dx.doi.org/10.18287/2412-6179-co-677.

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We propose and experimentally implement a new technique for digitally sorting Laguerre-Gaussian (LG) modes by radial number at a constant topological charge, resulting from the pertur-bation of the original LG beam, or superposition thereof, by passing them through a thin dielectric diaphragm with various aperture radii. The technique is based on a digital analysis of higher-order intensity moments. Two types of perturbed beams are considered: non-degenerate and degenerate beams with respect to the initial radial number of the LG beam superposition. A diaphragm with a circular pinhole causes the appearance of a set of secondary LG modes with different radial num-bers, which are characterized by an amplitude spectrum. The digital amplitude spectrum makes it possible to recover the real LG modes and find the measure of uncertainty due to perturbation by means of information entropy. It is found that the perturbation of a complex beam leads to the appearance of a degenerate am-plitude spectrum since a single spectral line corresponds to a set of modes generated by M original Laguerre-Gaussian beams with different radial numbers. For the spectrum to be deciphered, we use M keys represented by the amplitude spectra of the nondegenerate perturbed beams in our ex-periment. However, the correlation degree decreases to 0.92.

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39

Khonina, Svetlana N., and Andrey V. Ustinov. "Thin Light Tube Formation by Tightly Focused Azimuthally Polarized Light Beams." ISRN Optics 2013 (August 19, 2013): 1–6. http://dx.doi.org/10.1155/2013/185495.

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Theoretical and numerical analysis of the transmission function of the focusing system with high numerical aperture was conducted. The purpose of the study was to form a thin light tube in a focal area using the azimuthally polarized radiation. It was analytically shown that, due to destructive interference of two beams formed by two narrow rings, it is possible to overcome not only the full aperture diffraction limit but also the circular aperture limit. In this case, however, the intensity at the center of the focal plane is significantly reduced, which practically leads to the tube rupture. It was numerically shown that long thin one-piece tubes may be formed through the aperture apodization with diffractive axicon phase function or with complex transmission function of Laguerre-Gaussian or Airy-Gaussian beams.

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40

Ren, Liangke, Zheqiang Zhong, and Bin Zhang. "Transversely polarized ultra-long optical needles generated by cylindrical polarized circular airy gaussian vortex beams." Optics Communications 483 (March 2021): 126618. http://dx.doi.org/10.1016/j.optcom.2020.126618.

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41

Jiang, Huilian, Daomu Zhao, and Zhangrong Mei. "Propagation characteristics of the rectangular flattened Gaussian beams through circular apertured and misaligned optical systems." Optics Communications 260, no. 1 (2006): 1–7. http://dx.doi.org/10.1016/j.optcom.2005.09.075.

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42

Xiao, Zhitao, Yongmin Guo, Lei Geng, et al. "Acoustic Field of a Linear Phased Array: A Simulation Study of Ultrasonic Circular Tube Material." Sensors 19, no. 10 (2019): 2352. http://dx.doi.org/10.3390/s19102352.

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As ultrasonic wave field radiated by an ultrasonic transducer influences the results of ultrasonic nondestructive testing, simulation and emulation are widely used in nondestructive testing. In this paper, a simulation study is proposed to detect defects in a circular tube material. Firstly, the ultrasonic propagation behavior was analyzed, and a formulation of the Multi-Gaussian beam model (MGB) based on a superposition of Gaussian beams is described. The expression of the acoustic field from a linear phased-array ultrasonic transducer in the condition of a convex interface on the circular tube material is proposed. Secondly, in order to make the tapered probe wedge better fit the curved circular tube material and carry out the ultrasonic inspection of the curved surface, it was necessary to pare the angle probe wedge. Finally, acoustic field simulations in a circular tube were carried out and analyzed. The simulation results indicated that the method of ultrasonic phased-array inspection is feasible in circular tube testing. Tube materials with different curvatures need different array element lengths and widths to get the desired focused beam.

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43

Liu, Chang, Chai Hu, Dong Wei, et al. "Generating Convergent Laguerre-Gaussian Beams Based on an Arrayed Convex Spiral Phaser Fabricated by 3D Printing." Micromachines 11, no. 8 (2020): 771. http://dx.doi.org/10.3390/mi11080771.

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A convex spiral phaser array (CSPA) is designed and fabricated to generate typical convergent Laguerre-Gaussian (LG) beams. A type of 3D printing technology based on the two-photon absorption effect is used to make the CSPAs with different featured sizes, which present a structural integrity and fabricating accuracy of ~200 nm according to the surface topography measurements. The light field vortex characteristics of the CSPAs are evaluated through illuminating them by lasers with different central wavelength such as 450 nm, 530 nm and 650 nm. It should be noted that the arrayed light fields out from the CSPA are all changed from a clockwise vortex orientation to a circular distribution at the focal plane and then a counterclockwise vortex orientation. The circular light field is distributed 380–400 μm away from the CSPA, which is close to the 370 μm of the focal plane design. The convergent LG beams can be effectively shaped by the CASPs produced.

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44

Han, Jianguang, Qingtian Lü, Bingluo Gu, Jiayong Yan, and Hao Zhang. "2D anisotropic multicomponent Gaussian-beam migration under complex surface conditions." GEOPHYSICS 85, no. 2 (2020): S89—S102. http://dx.doi.org/10.1190/geo2018-0841.1.

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Elastic-wave migration in anisotropic media is a vital challenge, particularly for areas with irregular topography. Gaussian-beam migration (GBM) is an accurate and flexible depth migration technique, which is adaptable for imaging complex surface areas. It retains the dynamic features of the wavefield and overcomes the multivalued traveltimes and caustic problems of Kirchhoff migration. We have extended the GBM method to work for 2D anisotropic multicomponent migration under complex surface conditions. We use Gaussian beams to calculate the wavefield from irregular topography, and we use two schemes to derive the down-continued recorded wavefields. One is based on the local slant stack as in classic GBM, in which the PP- and PS-wave seismic records within the local region are directly decomposed into local plane-wave components from irregular topography. The other scheme does not perform the local slant stack. The Green’s function is calculated with a Gaussian beam summation emitted from the receiver point at the irregular surface. Using the crosscorrelation imaging condition and combining with the 2D anisotropic ray-tracing algorithm, we develop two 2D anisotropic multicomponent Gaussian-beam prestack depth migration (GB-PSDM) methods, i.e., using the slant stack and nonslant stack, for irregular topography. Numerical tests demonstrate that our anisotropic multicomponent GB-PSDM can accurately image subsurface structures under complex topography conditions.

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45

SHEN Xue-ju, 沈学举, 许芹祖 XU Qin-zu, 王龙 WANG Long, 韩玉东 HAN Yu-dong, and 王艳奎 WANG Yan-kui. "Propagation Properties of Flattened Gaussian Beams Passing Through an Misaligned Optical System with Misaligned Circular Aperture." ACTA PHOTONICA SINICA 39, no. 10 (2010): 1844–50. http://dx.doi.org/10.3788/gzxb20103910.1844.

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46

Nairat, Mazen. "Axial Angular Momentum of Bessel Light." Photonics Letters of Poland 10, no. 1 (2018): 23. http://dx.doi.org/10.4302/plp.v10i1.787.

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Both linear and angular momentum densities of Bessel, Gaussian-Bessel, and Hankel-Bessel lasers are determined. Angular momentum of the three Bessel beams is illustrated at linear and circular polarization. Axial Angular momentum is resolved in particular interpretation: the harmonic order of the physical light momentum. Full Text: PDF ReferencesG. Molina-Terriza, J. Torres, and L. Torner, "Twisted photons", Nature Physics 3, 305 - 310 (2007). CrossRef J Arlt, V Garces-Chavez, W Sibbett, and K Dholakia "Optical micromanipulation using a Bessel light beam", Opt. Commun., 197, 4-6, (2001). CrossRef L. Ambrosio and H. Hernández-Figueroa, "Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime", Opt Exp, 18, 23 (2010). CrossRef I. Litvin, A. Dudley and A. Forbes, "Poynting vector and orbital angular momentum density of superpositions of Bessel beams", Opt Exp, 19, 18 (2011). CrossRef K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt and K Dholakia "Orbital angular momentum of a high-order Bessel light beam" , JOP B 4 (2). 2002. CrossRef M. Verma, S. Pal, S. Joshi, P. Senthilkumaran, J. Joseph, and H Kandpal, "Singularities in cylindrical vector beams", Jou. of Mod. Opt., 62 (13), 2015. CrossRef R. Borghi, M. Santarsiero, and M. Porras, "Nonparaxial Bessel?Gauss beams", J. Opt. Soc. Am. A, 18 (7) (2011). CrossRef L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes", Phys Rev A, 45 (11): 8185-8189 (1992). CrossRef D. Mcglion and K. Dholakia, "Bessel beams: diffraction in a new light", Cont. Phys, 46(1) 15 ? 28. (2005). CrossRef F. Gori, G. Guattari and C. Padovani," Bessel-Gauss Beams", Opt. Commun., 64, 491, (1987). CrossRef V. Kotlyar, A. Kovalev, and A. Soifer, "Hankel?Bessel laser beams" J. Opt. Soc. Am. A, 29 (5) (2012). CrossRef L. Allen and M. Babiker "Spin-orbit coupling in free-space Laguerre-Gaussian light beams", Phys. Rev. A 53, R2937. CrossRef

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47

Wang, Li, Miao Li, Xiqing Wang, and Zhiming Zhang. "Focal switching of partially coherent modified Bessel–Gaussian beams passing through an astigmatic lens with circular aperture." Optics & Laser Technology 41, no. 5 (2009): 586–89. http://dx.doi.org/10.1016/j.optlastec.2008.10.008.

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48

Overfelt, P. L., and C. S. Kenney. "Comparison of the propagation characteristics of Bessel, Bessel–Gauss, and Gaussian beams diffracted by a circular aperture." Journal of the Optical Society of America A 8, no. 5 (1991): 732. http://dx.doi.org/10.1364/josaa.8.000732.

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49

Zhang, Junyong, Qinfeng Xu, and Xingqiang Lu. "Propagation properties of Gaussian beams through the anamorphic fractional Fourier transform system with an eccentric circular aperture." Optik 122, no. 4 (2011): 277–80. http://dx.doi.org/10.1016/j.ijleo.2009.11.032.

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50

George, Th, J. Virieux, and R. Madariaga. "Seismic wave synthesis by Gaussian beam summation: A comparison with finite differences." GEOPHYSICS 52, no. 8 (1987): 1065–73. http://dx.doi.org/10.1190/1.1442372.

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We apply Gaussian beam summation to the calculation of seismic reflections from complex interfaces, introducing several modifications of the original method. First, we use local geographical coordinates for the representation of paraxial rays in the vicinity of the recording surface. In this way we avoid the time‐consuming evaluation of the ray‐centered coordinates of the observation points. Second, we propose a method for selecting the beams that ensures numerical stability of the synthetic seismograms. Third, we introduce a simple source wave packet that simplifies and stabilizes the calculations of inverse Fourier transforms. We compare reflection seismograms computed using the Gaussian beam‐summation method with those calculated by finite differences. Two simple models are used. The first is a continuous curved interface separating an elastic layer from a free half‐space. A double caustic, or degenerate focal point, appears due to the crossing of reflected rays. In this instance the finite‐difference simulation and the Gaussian beam summation are in excellent agreement. Both phase and amplitude are modeled correctly for both the direct and reverse branches. When compared to geometrical ray theory, Gaussian beam summation provides a good approximation of the field near the caustics while geometrical ray theory does not. The second, more complex, model we consider is a trapezoidal dome with sharp corners in the interface. The corners of the dome in this model produce rather strong diffractions. Also, creeping head waves propagate along the interface. The results compare well with the finite‐difference simulation except for the diffracted branches, where the traveltime of diffracted waves is poorly approximated by the Gaussian beam‐summation method.

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