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Author: Grafiati

Published: 11 March 2023

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1

Volyar, Alexander, Eugeny Abramochkin, Yana Akimova, and Mikhail Bretsko. "Astigmatic-Invariant Structured Singular Beams." Photonics 9, no. 11 (November 8, 2022): 842. http://dx.doi.org/10.3390/photonics9110842.

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We investigate the transformation of structured Laguerre–Gaussian (sLG) beams after passing through a cylindrical lens. The resulting beam, ab astigmatic structured Laguerre–Gaussian (asLG) beam, depends on quantum numbers (n,ℓ) and three parameters. Two of them are control parameters of the initial sLG beam, the amplitude ϵ and phase θ. The third one is the ratio of the Rayleigh length z0 and the focal length f of the cylindrical lens. It was theoretically revealed and experimentally confirmed that the asLG beam keeps the intensity shape of the initial sLG beam when the parameters satisfy simple conditions: ϵ is unity and the tangent of the phase parameter θ/2 is equal to the above ratio. We also found sharp bursts and dips of the orbital angular momentum (OAM) in the asLG beams in the vicinity of the point where the OAM turns to zero. The heights and depths of these bursts and dips significantly exceed the OAM maximum and minimum values of the initial sLG beam and are controlled by the radial number n.

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2

Plachenov, A. B., V. N. Kudashov, and A. M. Radin. "Simple formula for a Gaussian beam with general astigmatism in a homogeneous medium." Optics and Spectroscopy 106, no. 6 (June 2009): 910–12. http://dx.doi.org/10.1134/s0030400x09060204.

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3

Repasky, K. S., J. K. Brasseur, J. G. Wessel, and J. L. Carlsten. "Correcting an astigmatic, non-Gaussian beam." Applied Optics 36, no. 7 (March 1, 1997): 1536. http://dx.doi.org/10.1364/ao.36.001536.

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4

Vinogradov, D. V. "Mirror conversion of gaussian beams with simple astigmatism." International Journal of Infrared and Millimeter Waves 16, no. 11 (November 1995): 1945–63. http://dx.doi.org/10.1007/bf02072550.

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5

Tuvi, Ram, and Timor Melamed. "Astigmatic Gaussian Beam Scattering by a PEC Wedge." IEEE Transactions on Antennas and Propagation 67, no. 11 (November 2019): 7014–21. http://dx.doi.org/10.1109/tap.2019.2925928.

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6

Bilger, Hans R., and Taufiq Habib. "Knife-edge scanning of an astigmatic Gaussian beam." Applied Optics 24, no. 5 (March 1, 1985): 686. http://dx.doi.org/10.1364/ao.24.000686.

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7

Huang, Yong-Liang, and Chi-Kuang Sun. "Z-scan measurement with an astigmatic Gaussian beam." Journal of the Optical Society of America B 17, no. 1 (January 1, 2000): 43. http://dx.doi.org/10.1364/josab.17.000043.

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8

Kotlyar, V. V., A. A. Kovalev, and A. P. Porfirev. "ORBITAL ANGULAR MOMENTUM OF AN ASTIGMATIC HERMITE-GAUSSIAN BEAM." Computer Optics 42, no. 1 (March 30, 2018): 13–21. http://dx.doi.org/10.18287/2412-6179-2018-42-1-13-21.

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An explicit formula for the normalized orbital angular momentum (OAM) of an elliptical Hermite-Gaussian (HG) beam of orders (0, n) focused by a cylindrical lens is obtained. In modulus, this OAM can be both greater and smaller than n. If the cylindrical lens focuses not an elliptical, but a conventional HG beam, the latter will also have an OAM that can be both larger and smaller in modulus than that of an elliptical HG beam. For n = 0, this beam converts to an astigmatic Gaussian beam, but, as before, it will still have OAM. With the help of two interferograms, a phase of the astigmatic Gaussian beam is reconstructed, which is then used to calculate the normalized OAM. The values of the OAM calculated by the theoretical formula and using a hybrid method combining modeling with experiment differ only by 6 %.

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9

Zhu, Kaicheng, Chang Gao, Jiahui Li, Dengjuan Ren, and Jie Zhu. "Propagations of Sin-Gaussian Beam with Astigmatism through Oceanic Turbulence." E3S Web of Conferences 299 (2021): 03013. http://dx.doi.org/10.1051/e3sconf/202129903013.

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The propagation behaviours of a sin-Gaussian beam (SiGB) with astigmatism in oceanic water is analysed. The analytical expressions for the average intensity of such a beam are derived by using the extended Huygens-Fresnel integral. Its average intensity and on-axial intensity distributions in oceanic water are numerically examined. Then, we mainly focus on the effect of the beam parameters and the medium structure constant on the propagation behaviours for the astigmatic SiGBs in oceanic water, revealing that the evolutions of the intensity distributions can be effectively modulated by adjusting the astigmatic parameter, coherence length and the atmosphere turbulence strength.

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10

Kotlyar, V. V., A. A. Kovalev, and A. P. Porfirev. "Measurement of the orbital angular momentum of an astigmatic Hermite–Gaussian beam." Computer Optics 43, no. 3 (June 2019): 356–67. http://dx.doi.org/10.18287/2412-6179-2019-43-3-356-367.

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Here we study three different types of astigmatic Gaussian beams, whose complex amplitude in the Fresnel diffraction zone is described by the complex argument Hermite polynomial of the order (n, 0). The first type is a circularly symmetric Gaussian optical vortex with and a topological charge n after passing through a cylindrical lens. On propagation, the optical vortex "splits" into n first-order optical vortices. Its orbital angular momentum per photon is equal to n. The second type is an elliptical Gaussian optical vortex with a topological charge n after passing through a cylindrical lens. With a special choice of the ellipticity degree (1: 3), such a beam retains its structure upon propagation and the degenerate intensity null on the optical axis does not “split” into n optical vortices. Such a beam has fractional orbital angular momentum not equal to n. The third type is the astigmatic Hermite-Gaussian beam (HG) of order (n, 0), which is generated when a HG beam passes through a cylindrical lens. The cylindrical lens brings the orbital angular momentum into the original HG beam. The orbital angular momentum of such a beam is the sum of the vortex and astigmatic components, and can reach large values (tens and hundreds of thousands per photon). Under certain conditions, the zero intensity lines of the HG beam "merge" into an n-fold degenerate intensity null on the optical axis, and the orbital angular momentum of such a beam is equal to n. Using intensity distributions of the astigmatic HG beam in foci of two cylindrical lenses, we calculate the normalized orbital angular momentum which differs only by 7 % from its theoretical orbital angular momentum value (experimental orbital angular momentum is –13,62, theoretical OAM is –14.76).

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11

Zhu, Kaicheng, Xiaolei Ma, Chang Gao, Dengjuan Ren, and Jie Zhu. "Propagation Properties of an Astigmatic Cos-Gaussian Beam through Turbulent Atmosphere." E3S Web of Conferences 299 (2021): 02003. http://dx.doi.org/10.1051/e3sconf/202129902003.

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We use the extended Huygens-Fresnel integral to investigate the propagation properties of a cos-Gaussian beam (cosGB) with astigmatism in atmospheric turbulence. The intensity distribution behaviour along the propagation distance for an astigmatic cosGB in atmospheric turbulence are analytically and numerically demonstrated. Some novel phenomena are presented graphically, indicating that the intensity distribution and the on-axial intensity closely depend on the astigmatic parameter and the turbulent structure constant of the cosGBs in the atmospheric turbulence.

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12

Kotlyar, V. V., and A. A. Kovalev. "ORBITAL ANGULAR MOMENTUM OF AN ASTIGMATIC GAUSSIAN LASER BEAM." Computer Optics 41, no. 5 (January 1, 2017): 609–16. http://dx.doi.org/10.18287/2412-6179-2017-41-5-609-616.

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13

L�, Baida, Guoying Feng, and Bangwei Cai. "Complex ray representation of the astigmatic Gaussian beam propagation." Optical and Quantum Electronics 25, no. 4 (April 1993): 275–84. http://dx.doi.org/10.1007/bf00419005.

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14

Zhu, Kaicheng, Jie Zhu, Qin Su, and Huiqin Tang. "Propagation Property of an Astigmatic sin–Gaussian Beam in a Strongly Nonlocal Nonlinear Media." Applied Sciences 9, no. 1 (December 25, 2018): 71. http://dx.doi.org/10.3390/app9010071.

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Based on the Snyder and Mitchell model, a closed-form propagation expression of astigmatic sin-Gaussian beams through strongly nonlocal nonlinear media (SNNM) is derived. The evolutions of the intensity distributions and the corresponding wave front dislocations are discussed analytically and numerically. It is generally proved that the light field distribution varies periodically with the propagation distance. Furthermore, it is demonstrated that the astigmatism and edge dislocation nested in the initial sin-Gaussian beams greatly influence the pattern configurations and phase singularities during propagation. In particular, it is found that, when the beam parameters are properly selected, a vortex beam with perfect doughnut-shaped profile can be obtained for astigmatic sin-Gaussian beams with two-lobe pattern propagating in SNNM.

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15

Li, Chang Wei, Xiao Ping Kang, and Zhong He. "Changes in the Beam Parameters of Partially Coherent Sinh-Gaussian Beams after Passage through an Astigmatic Lens." Applied Mechanics and Materials 738-739 (March 2015): 434–39. http://dx.doi.org/10.4028/www.scientific.net/amm.738-739.434.

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Based on the propagation law of partially coherent beams, the analytical expression of the beam width, waist positions and the far-field divergence angle of partially coherent sinh-Gaussian (ShG) beams through an astigmatic lens were derived. The effect of astigmatism and spatial coherence parameter on the beam parameters was mainly analyzed. It is found that the beam width depends on the astigmatic coefficient, spatial coherence parameter, decentered parameter, fresnel number and propagation distance in general. The astigmatism results in a difference between the beam widths, waist positions and far-field divergence angles in thexandydirections.

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16

Zeng-Hui, Gao, and Lü Bai-Da. "Off-Axis Astigmatic Gaussian Beam Combination Beyond the Paraxial Approximation." Chinese Physics Letters 24, no. 9 (August 23, 2007): 2575–78. http://dx.doi.org/10.1088/0256-307x/24/9/031.

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17

Tao, Shishi, Jiayun Xue, Jiewei Guo, Xing Zhao, Zhi Zhang, Lie Lin, and Weiwei Liu. "Investigation of Focusing Properties on Astigmatic Gaussian Beams in Nonlinear Medium." Sensors 22, no. 18 (September 15, 2022): 6981. http://dx.doi.org/10.3390/s22186981.

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Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar.

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18

Greffet, Jean-Jacques, and Christophe Baylard. "Nonspecular astigmatic reflection of a 3D gaussian beam on an interface." Optics Communications 93, no. 5-6 (October 1992): 271–76. http://dx.doi.org/10.1016/0030-4018(92)90184-s.

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19

Kotlyar, V. V., A. A. Kovalev, and A. G. Nalimov. "Astigmatic transformation of a set of edge dislocations embedded in a Gaussian beam." Computer Optics 45, no. 2 (April 2021): 190–99. http://dx.doi.org/10.18287/2412-6179-co-849.

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It is theoretically shown how a Gaussian beam with a finite number of parallel lines of intensity nulls (edge dislocations) is transformed using a cylindrical lens into a vortex beam that carries orbital angular momentum (OAM) and has a topological charge (TC). In the initial plane, this beam already carries OAM, but does not have TC, which appears as the beam propagates further in free space. Using an example of two parallel lines of intensity nulls symmetrically located relative to the origin, we show the dynamics of the formation of two intensity nulls at the double focal length: as the distance between the vertical lines of intensity nulls is being increased, two optical vortices are first formed on the horizontal axis, before converging to the origin and then diverging on the vertical axis. At any distance between the zero-intensity lines, the optical vortex has the topological charge TC=–2, which conserves at any on-axis distance, except the initial plane. When the distance between the zero-intensity lines changes, the OAM that the beam carries also changes. It can be negative, positive, and at a certain distance between the lines of intensity nulls OAM can be equal to zero. It is also shown that for an unlimited number of zero-intensity lines, a beam with finite OAM and an infinite TC is formed.

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20

Bilger, H. R. "Power transfer of an astigmatic Gaussian beam to a stigmatic optical system." Applied Optics 28, no. 11 (June 1, 1989): 1971. http://dx.doi.org/10.1364/ao.28.001971.

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21

Bayraktar, Mert. "Average intensity of astigmatic hyperbolic sinusoidal Gaussian beam propagating in oceanic turbulence." Physica Scripta 96, no. 2 (December 8, 2020): 025501. http://dx.doi.org/10.1088/1402-4896/abce36.

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22

Zhong, Yuan-Hong, Jin Li, Yao Zhou, and Qi-Lun Lei. "Electromagnetic Resonance of Astigmatic Gaussian Beam to the High Frequency Gravitational Waves." Chinese Physics Letters 33, no. 10 (October 2016): 100402. http://dx.doi.org/10.1088/0256-307x/33/10/100402.

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23

Liu Xiao-Li, Feng Guo-Ying, Li Wei, Tang Chun, and Zhou Shou-Huan. "Theoretical and experimental study on M2 factor matrix for astigmatic elliptical Gaussian beam." Acta Physica Sinica 62, no. 19 (2013): 194202. http://dx.doi.org/10.7498/aps.62.194202.

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24

Zhu Jie, 朱洁, and 唐慧琴 Tang Huiqin. "Focusing Sinh-Gaussian Beams Using Astigmatic Lens and Generation of Dark Hollow Beam." Acta Optica Sinica 36, no. 10 (2016): 1005001. http://dx.doi.org/10.3788/aos201636.1005001.

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25

Verrier, Nicolas, Sébastien Coëtmellec, Marc Brunel, Denis Lebrun, and Augustus J. E. M. Janssen. "Digital in-line holography with an elliptical, astigmatic Gaussian beam: wide-angle reconstruction." Journal of the Optical Society of America A 25, no. 6 (May 30, 2008): 1459. http://dx.doi.org/10.1364/josaa.25.001459.

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26

Yuan, Y. J., K. F. Ren, S. Coëtmellec, and D. Lebrun. "Rigorous description of holograms of particles illuminated by an astigmatic elliptical Gaussian beam." Journal of Physics: Conference Series 147 (February 1, 2009): 012052. http://dx.doi.org/10.1088/1742-6596/147/1/012052.

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27

Yang, Zhen-Feng, Xue-Song Jiang, Zhen-Jun Yang, Jian-Xing Li, and Shu-Min Zhang. "Beam width evolution of astigmatic hollow Gaussian beams in highly nonlocal nonlinear media." Results in Physics 6 (2016): 163–64. http://dx.doi.org/10.1016/j.rinp.2016.03.007.

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28

Bucker, Homer. "Simple 3‐D Gaussian beam propagation model." Journal of the Acoustical Society of America 90, no. 4 (October 1991): 2372. http://dx.doi.org/10.1121/1.402093.

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29

Melnikov, L. A., V. L. Derbov, and A. I. Bychenkov. "Dynamics of a misaligned astigmatic twisted Gaussian beam in a Kerr-nonlinear parabolic waveguide." Physical Review E 60, no. 6 (December 1, 1999): 7490–96. http://dx.doi.org/10.1103/physreve.60.7490.

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30

Tari, T., and P. Richter. "Correction of astigmatism and ellipticity of an astigmatic Gaussian laser beam by symmetrical lenses." Optical and Quantum Electronics 24, no. 9 (September 1992): S865—S872. http://dx.doi.org/10.1007/bf01588591.

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31

Kochkina, Evgenia, Gudrun Wanner, Dennis Schmelzer, Michael Tröbs, and Gerhard Heinzel. "Modeling of the general astigmatic Gaussian beam and its propagation through 3D optical systems." Applied Optics 52, no. 24 (August 19, 2013): 6030. http://dx.doi.org/10.1364/ao.52.006030.

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32

Zhu, Jie, Kaicheng Zhu, Huiqin Tang, and Hui Xia. "Average intensity and spreading of an astigmatic sinh-Gaussian beam with small beam width propagating in atmospheric turbulence." Journal of Modern Optics 64, no. 18 (May 15, 2017): 1915–21. http://dx.doi.org/10.1080/09500340.2017.1326638.

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33

Lu, Shi-Zhuan, Kai-Ming You, Deng-Yu Zhang, and Feng Gao. "Investigation of astigmatic Gaussian beam Z scan with simultaneous third- and fifth-order nonlinear refraction." Optik 123, no. 8 (April 2012): 744–47. http://dx.doi.org/10.1016/j.ijleo.2011.06.035.

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34

Savchenko, E. V., O. A. Yevtikhieva, and B. S. Rinkevicius. "Determination of the parameters of an astigmatic Gaussian beam in problems of laser gradient refractometry." Measurement Techniques 50, no. 4 (April 2007): 390–96. http://dx.doi.org/10.1007/s11018-007-0080-9.

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35

Laptev, Alexei V., Gleb V. Kuptsov, Vladimir A. Petrov, and Victor V. Petrov. "ASTIGMATISM COMPENSATION IN BLOCK OF TEMPORAL BROADENING OF PULSE FOR PUMP CHANNEL OF HIGH POWER LASER SYSTEM." Vestnik SSUGT (Siberian State University of Geosystems and Technologies) 25, no. 4 (2020): 205–12. http://dx.doi.org/10.33764/2411-1759-2020-25-4-205-212.

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A high peak and high average power femtosecond laser system based on media doped with Yb3+ ions is being developed at the Institute of Laser Physics of the SB RAS. For efficient laser amplification and to avoid optical damage is actually to compensate wave front distortion caused by grating astigmatism in pump channel. Based on theory of propagation of gaussian beam in space and through optical elements the calculation of optimal parameters of two lenses telescope and comparison with experimental data has been performed. The obtained results can be used for decrease of astigmatic effect on beam profile quality in design of laser systems with elements involving astigmatism.

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36

Rohani, A., A. A. Shishegar, and S. Safavi-Naeini. "A fast Gaussian beam tracing method for reflection and refraction of general vectorial astigmatic Gaussian beams from general curved surfaces." Optics Communications 232, no. 1-6 (March 2004): 1–10. http://dx.doi.org/10.1016/j.optcom.2003.11.044.

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37

Nemes, G., and A. E. Siegman. "Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics." Journal of the Optical Society of America A 11, no. 8 (August 1, 1994): 2257. http://dx.doi.org/10.1364/josaa.11.002257.

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38

Kovalev, A. A. "Optical vortices with an infinite number of screw dislocations." Computer Optics 45, no. 4 (July 2021): 497–505. http://dx.doi.org/10.18287/2412-6179-co-866.

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In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

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39

Kovalev, A. A. "Optical vortices with an infinite number of screw dislocations." Computer Optics 45, no. 4 (July 2021): 497–505. http://dx.doi.org/10.18287/10.18287/2412-6179-co-866.

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In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

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40

Nicolas, F., A. J. E. M. Janssen, S. Coëtmellec, M. Brunel, D. Allano, and D. Lebrun. "Application of the fractional Fourier transformation to digital holography recorded by an elliptical, astigmatic Gaussian beam." Journal of the Optical Society of America A 22, no. 11 (November 1, 2005): 2569. http://dx.doi.org/10.1364/josaa.22.002569.

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41

Volyar, A. V., E. G. Abramochkin, Yu Egorov, M. Bretsko, and Ya Akimova. "Digital sorting of Hermite-Gauss beams: mode spectra and topological charge of a perturbed Laguerre-Gauss beam." Computer Optics 44, no. 4 (August 2020): 501–9. http://dx.doi.org/10.18287/2412-6179-co-747.

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We developed and implemented an intensity moments technique for measuring amplitude and initial phase spectra, the topological charge (TC) and orbital angular momentum (OAM) of the Laguerre-Gauss (LG) beams decomposed into the basis of Hermite-Gaussian (HG) modes. A rigorous theoretical justification is given for measuring the TC of unperturbed LG beams with different values of radial and azimuthal numbers by means of an astigmatic transformation on a cylindrical lens. We have shown that the measured amplitude and phase spectra of the HG modes make it possible to find the orbital OAM and TC, as well as digitally sorting the HG modes and then restoring the initial singular beam.

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42

Khonina, Svetlana Nikolaevna, Nikolay Lvovich Kazanskiy, Sergey Vladimirovich Karpeev, and Muhammad Ali Butt. "Bessel Beam: Significance and Applications—A Progressive Review." Micromachines 11, no. 11 (November 11, 2020): 997. http://dx.doi.org/10.3390/mi11110997.

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Diffraction is a phenomenon related to the wave nature of light and arises when a propagating wave comes across an obstacle. Consequently, the wave can be transformed in amplitude or phase and diffraction occurs. Those parts of the wavefront avoiding an obstacle form a diffraction pattern after interfering with each other. In this review paper, we have discussed the topic of non-diffractive beams, explicitly Bessel beams. Such beams provide some resistance to diffraction and hence are hypothetically a phenomenal alternate to Gaussian beams in several circumstances. Several outstanding applications are coined to Bessel beams and have been employed in commercial applications. We have discussed several hot applications based on these magnificent beams such as optical trapping, material processing, free-space long-distance self-healing beams, optical coherence tomography, superresolution, sharp focusing, polarization transformation, increased depth of focus, birefringence detection based on astigmatic transformed BB and encryption in optical communication. According to our knowledge, each topic presented in this review is justifiably explained.

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43

Thirunavukkarasu, G., M. Mousley, M. Babiker, and J. Yuan. "Normal modes and mode transformation of pure electron vortex beams." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2087 (February 28, 2017): 20150438. http://dx.doi.org/10.1098/rsta.2015.0438.

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Electron vortex beams constitute the first class of matter vortex beams which are currently routinely produced in the laboratory. Here, we briefly review the progress of this nascent field and put forward a natural quantum basis set which we show is suitable for the description of electron vortex beams. The normal modes are truncated Bessel beams (TBBs) defined in the aperture plane or the Fourier transform of the transverse structure of the TBBs (FT-TBBs) in the focal plane of a lens with the said aperture. As these modes are eigenfunctions of the axial orbital angular momentum operator, they can provide a complete description of the two-dimensional transverse distribution of the wave function of any electron vortex beam in such a system, in analogy with the prominent role Laguerre–Gaussian (LG) beams played in the description of optical vortex beams. The characteristics of the normal modes of TBBs and FT-TBBs are described, including the quantized orbital angular momentum (in terms of the winding number l ) and the radial index p >0. We present the experimental realization of such beams using computer-generated holograms. The mode analysis can be carried out using astigmatic transformation optics, demonstrating close analogy with the astigmatic mode transformation between LG and Hermite–Gaussian beams. This article is part of the themed issue ‘Optical orbital angular momentum’.

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Raman, Swati, Nandan S. Bisht, B. K. Yadav, R. Mehrotra, M. Husain, and H. C. Kandpal. "Experimental observation of the effect of astigmatic aperture lens on the spectral switches of polychromatic Gaussian beam." Journal of Modern Optics 55, no. 10 (June 10, 2008): 1629–38. http://dx.doi.org/10.1080/09500340701750941.

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Wu, You, Zejia Lin, Chuangjie Xu, Xinming Fu, Kaihui Chen, Huixin Qiu, and Dongmei Deng. "Off‐Axis and Multi Optical Bottles from the Ring Airy Gaussian Vortex Beam with the Astigmatic Phase." Annalen der Physik 532, no. 7 (June 11, 2020): 2000188. http://dx.doi.org/10.1002/andp.202000188.

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Kallmann, Ulrich, Michael Lootze, and Ulrich Mescheder. "Simulative and Experimental Characterization of an Adaptive Astigmatic Membrane Mirror." Micromachines 12, no. 2 (February 5, 2021): 156. http://dx.doi.org/10.3390/mi12020156.

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Abstract:

Adaptive optical (AO) components play an important role in numerous optical applications, from astronomical telescopes to microscope imaging systems. For most of these AO components, the induced wavefront correction, respectively added optical power, is based on a rotationally symmetric or segmented design of the AO component. In this work, we report on the design, fabrication, and characterization of a micro-electronic-mechanical system (MEMS) adaptive membrane mirror in the shape of a parabolic cylinder. In order to interpret the experimental characterization results correctly and provide a tool for future application development, this is accompanied by the setup of an optical simulation model. The characterization results showed a parabolically deformable membrane mirror with an aperture of 8 × 2 mm2 and an adaptive range for the optical power from 0.3 to 6.1 m−1 (dpt). The optical simulation model, using the Gaussian beamlet propagation method, was successfully validated by laser beam profile measurements taken in the optical characterization setup. This MEMS-based adaptive astigmatic membrane mirror, together with the accompanying simulation model, could be a key component for the rapid development of new optical systems, e.g., adaptive laser line generators.

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Zhao Gui-Yan, Zhang Yi-Xin, Wang Jian-Yu, and Jia Jian-Jun. "Defocus and astigmatic aberration of the turbulent atmosphere and the intensity distribution of a vortex carrying Gaussian beam." Acta Physica Sinica 59, no. 2 (2010): 1378. http://dx.doi.org/10.7498/aps.59.1378.

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Cai, Yangjian, Q. Lin, H. T. Eyyuboğlu, and Y. Baykal. "Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere." Applied Physics B 94, no. 2 (December 12, 2008): 319–25. http://dx.doi.org/10.1007/s00340-008-3339-1.

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Al-Saidi, I. A. "Using a simple method: conversion of a Gaussian laser beam into a uniform beam." Optics & Laser Technology 33, no. 2 (March 2001): 75–79. http://dx.doi.org/10.1016/s0030-3992(00)00113-4.

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Zhu, Tianfei, Samuel H. Gray, and Daoliu Wang. "Prestack Gaussian-beam depth migration in anisotropic media." GEOPHYSICS 72, no. 3 (May 2007): S133—S138. http://dx.doi.org/10.1190/1.2711423.

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Gaussian-beam depth migration is a useful alternative to Kirchhoff and wave-equation migrations. It overcomes the limitations of Kirchhoff migration in imaging multipathing arrivals, while retaining its efficiency and its capability of imaging steep dips with turning waves. Extension of this migration method to anisotropic media has, however, been hampered by the difficulties in traditional kinematic and dynamic ray-tracing systems in inhomogeneous, anisotropic media. Formulated in terms of elastic parameters, the traditional anisotropic ray-tracing systems aredifficult to implement and inefficient for computation, especially for the dynamic ray-tracing system. They may also result inambiguity in specifying elastic parameters for a given medium.To overcome these difficulties, we have reformulated the ray-tracing systems in terms of phase velocity.These reformulated systems are simple and especially useful for general transversely isotropic and weak orthorhombic media, because the phase velocities for these two types of media can be computed with simple analytic expressions. These two types of media also represent the majority of anisotropy observed in sedimentary rocks. Based on these newly developed ray-tracing systems, we have extended prestack Gaussian-beam depth migration to general transversely isotropic media. Test results with synthetic data show that our anisotropic, prestack Gaussian-beam migration is accurate and efficient. It produces images superior to those generated by anisotropic, prestack Kirchhoff migration.

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