Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams

Chen, Yung-Fu; Chang, Chia‐Fu; Lee, C. Y.; Tung, J. C.; Liang, H. C.; Huang, Kai–Feng

doi:10.1088/1555-6611/aa9625

Cited by 33 publications

(14 citation statements)

References 28 publications

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“…Kotlyar 1,2 , E.G. Abramochkin 3 , A.A. Kovalev 1,2 , A.G. Nalimov 1,2 1 IPSI RAS -Branch of the FSRC "Crystallography and Photonics" RAS, 443001, Samara, Russia, Molodogvardeyskaya 151, 2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34, 3 Lebedev Physical Institute, 443034, Samara, Russia Novo-Sadovaya 221…”

Section: Astigmatic Transformation Of a Fractional-order Edge Disloca...mentioning

confidence: 99%

“…Позже во многих работах изучалось преобразование различных лазерных пучков с помощью астигматических преобразований. Так, в [2,3] изучалось прохождение пучка Эрмита-Гаусса через 4×4 оптическую систему, в том числе с астигматизмом. В [4] рассмотрено прохождение пучков Эрмита-Лагерра-Гаусса через астигматический модовый конвертор.…”

Section: Introductionunclassified

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Astigmatic transformation of a fractional-order edge dislocation

et al. 2022

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It is shown theoretically that an astigmatic transformation of an edge dislocation (straight line of zero intensity) of the ν-th order (ν=n+α is a real positive number, n is integer, 0<α<1 is the fractional part of the number) forms at twice the focal length from a cylindrical lens n optical elliptical vortices (screw dislocations) with a topological charge of –1, located on a straight line perpendicular to the edge dislocation. Coordinates of these points are zeros of the Tricomi function. At some distance from these vortices and on the same straight line, another additional vortex with a topological charge of –1 is also generated, which moves to the periphery if α decreases to zero, or approaches n vortices if α tends to 1. In addition, at the periphery in the beam cross-section, a countable number of optical vortices (intensity zeros) are formed, all with a topological charge of –1, which are located on diverging curved lines (such as hyperbolas) equidistant from a straight line on which the main n intensity zeros are located. These "accompanying" vortices approach the center of the beam, following the additional "passenger" vortex, if 0<α<0.5, or move to the periphery, leaving the "passenger" next to the main vortices, if 0.5<α<1. At α=0 and α=1, the "accompanying" vortices are situated at infinity. The topological charge of the entire beam at fractional ν is infinite. The numerical simulation confirms theoretical predictions.

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Section: Astigmatic Transformation Of a Fractional-order Edge Disloca...mentioning

confidence: 99%

Section: Introductionunclassified

Astigmatic transformation of a fractional-order edge dislocation

et al. 2022

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“…2 are astigmatic Gaussian beam waist parameters [102,103]. Then we can get the spatial wave-packet of astigmatic geometric beam by substituting equation ( 100) into equation (53) as…”

Section: Astigmatic Hybrid Su(2) Geometric Beamsmentioning

confidence: 99%

Rays, waves, SU(2) symmetry and geometry: toolkits for structured light

Shen

2021

J. Opt.

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Structured light refers to the ability to tailor optical patterns in all its degrees of freedom, from conventional 2D transverse patterns to exotic forms of 3D, 4D, and even higher-dimensional modes of light, which break fundamental paradigms and open new and exciting applications for both classical and quantum scenarios. The description of diverse degrees of freedom of light can be based on different interpretations, e.g. rays, waves, and quantum states, that are based on different assumptions and approximations. In particular, recent advances highlighted the exploiting of geometric transformation under general symmetry to reveal the ‘hidden’ degrees of freedom of light, allowing access to higher dimensional control of light. In this tutorial, I outline the basics of symmetry and geometry to describe light, starting from the basic mathematics and physics of SU(2) symmetry group, and then to the generation of complex states of light, leading to a deeper understanding of structured light with connections between rays and waves, quantum and classical. The recent explosion of related applications are reviewed, including advances in multi-particle optical tweezing, novel forms of topological photonics, high-capacity classical and quantum communications, and many others, that, finally, outline what the future might hold for this rapidly evolving field.

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“…The eigenmodes of the spherical cavities are analytically found to be Hermite-Gaussian (HG) modes in rectangular coordinates and Laguerre-Gaussian (LG) modes in polar coordinates [3]. The development of diode-pumped solid-state lasers enables us to experimentally generate both high-order HG and LG modes with the selectively focused excitation [4][5][6][7][8][9][10][11]. Besides the HG and LG eigenmodes, the so-called geometric modes with ray-wave duality can be systematically generated in the degenerate cavities [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Laser Transverse Modes with Ray-Wave Duality: A Review

et al. 2021

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We present a systematic overview on laser transverse modes with ray-wave duality. We start from the spectrum of eigenfrequencies in ideal spherical cavities to display the critical role of degeneracy for unifying the Hermite–Gaussian eigenmodes and planar geometric modes. We subsequently review the wave representation for the elliptical modes that generally carry the orbital angular momentum. Next, we manifest the fine structures of eigenfrequencies in a spherical cavity with astigmatism to derive the wave-packet representation for Lissajous geometric modes. Finally, the damping effect on the formation of transverse modes is generally reviewed. The present overview is believed to provide important insights into the ray-wave correspondence in mesoscopic optics and laser physics.

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Characterizing the propagation evolution of wave patterns and vortex structures in astigmatic transformations of Hermite–Gaussian beams

Cited by 33 publications

References 28 publications

Astigmatic transformation of a fractional-order edge dislocation

Astigmatic transformation of a fractional-order edge dislocation

Rays, waves, SU(2) symmetry and geometry: toolkits for structured light

Laser Transverse Modes with Ray-Wave Duality: A Review

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