Laser transverse modes of spherical resonators: a review [Invited]

Chen, Yung-Fu; Lee, C. C.; Hsieh, M. X.

doi:10.3788/col202018.091404

Cited by 18 publications

(7 citation statements)

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“…182 Such beams with more universality are called generalized Gaussian beams or Hermite-Laguerre-Gaussian (HLG) beams. 41,175,182,183 The expression of HLG beam is as follows:…”

Section: Bðn:m; Kþmentioning

confidence: 99%

“…Such beams with more universality are called generalized Gaussian beams or Hermite–Laguerre–Gaussian (HLG) beams. 41 , 175 , 182 , 183 The expression of HLG beam is as follows: HLGn,m(r,z|α)=12N−1n!m! exp(−π|r|2w)HLn,m(rπw|α)×exp[ikz+ikr22R−i(m+n+1)Ψ(z)],where HLn,m(•) are Hermite–Laguerre (HL) polynomials, r=(x,y)T=(r cos ϕ,r sin ϕ)T, …”

Section: Eigenmode Superposition-based Pattern Formationmentioning

confidence: 99%

“…Such beams have brought various breakthroughs to many fields, including imaging, 24 , 25 microscopy, 26 , 27 metrology, 28 – 30 communication, 31 – 33 optical trapping, 34 – 36 and quantum information processing 37 – 39 In the most recent five years, the number of reviews on structured light has boomed, with the majority of reviews focusing on technical-level research into the phenomenon, 40 – 54 such as the generation and detection technology of structured light, 44 , 45 application in the field of optical trapping 46 , 47 and anti-turbulence, 48 progress in optical vortices 49 – 51 and higher-dimensional structured light, 52 as well as research on structured light in flat optics 53 and nonlinear optics 54 . In contrast, there have been few studies on the evolution of the investigations and corresponding understandings of the pattern formation of structured laser beams.…”

Section: Introductionmentioning

confidence: 99%

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Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Wang

Zhang

et al. 2023

Adv. Photon. Nexus

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Spatial patterns are a significant characteristic of lasers. The knowledge of spatial patterns of structured laser beams is rapidly expanding, along with the progress of studies on laser physics and technology. Particularly in the last decades, owing to the in-depth attention on structured light with multiple degrees of freedom, the research on spatial and spatiotemporal structures of laser beams has been promptly developed. Such beams have hatched various breakthroughs in many fields, including imaging, microscopy, metrology, communication, optical trapping, and quantum information processing. Here, we would like to provide an overview of the extensive research on several areas relevant to spatial patterns of structured laser beams, from spontaneous organization to multiple transformations. These include the early theory of beam pattern formation based on the Maxwell-Bloch equations, the recent eigenmodes superposition theory based on the time-averaged Helmholtz equations, the beam patterns extension of ultrafast lasers to the spatiotemporal beam structures, and the structural transformations in the nonlinear frequency conversion process of structured beams.

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“…182 Such beams with more universality are called generalized Gaussian beams or Hermite-Laguerre-Gaussian (HLG) beams. 41,175,182,183 The expression of HLG beam is as follows:…”

Section: Bðn:m; Kþmentioning

confidence: 99%

Section: Eigenmode Superposition-based Pattern Formationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Wang

Zhang

et al. 2023

Adv. Photon. Nexus

View full text Add to dashboard Cite

show abstract

“…In paraxial approximation, the wave equation for spherical resonators was verified to be analogous to the Schrödinger equation for two-dimensional (2D) harmonic oscillators [1]. This analogy has been fruitfully employed to visualize the quantum wave functions from generating various laser transverse modes in spherical cavities [2]. 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].…”

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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“…Despite various works devoted to the investigation of isolated optical vortex beams, the generation of optical vortex arrays or vortex lattices has attracted considerable attention for decades for photonic crystal fabrication, optical metrology, and optical manipulation [9][10][11]. Optical vortex arrays can, not only be directly generated in diode-pumped solid-state lasers with spherical cavity [12][13][14], but also be obtained by exploiting external optical devices, such as holographic grating [15,16], astigmatic mode converters [17][18][19], and spatial light modulators [20][21][22][23]. Since J. Masajada et al demonstrated a regular optical vortex array with crystal structures by a three wave interference [24], the multi-beam interference method has often been exploited to generate optical vortex arrays with crystal and quasicrystal structures [23,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Systematically Investigating the Structural Variety of Crystalline and Kaleidoscopic Vortex Lattices by Using Laser Beam Arrays

et al. 2021

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We theoretically demonstrate that a family of vortex-lattice structures can be flexibly generated using a multi-beam interference approach. Numerical calculation presents a variety of crystalline and kaleidoscopic patterns. Based on the numerical analysis, we experimentally realized these structure beams by combining an amplitude mask with multiple apertures and a spiral phase plate. The excellent agreement between the experimental and theoretical results not only validates the presented method, but also manifests the structure of vortex lattices.

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Laser transverse modes of spherical resonators: a review [Invited]

Cited by 18 publications

References 0 publications

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Evolution on spatial patterns of structured laser beams: from spontaneous organization to multiple transformations

Laser Transverse Modes with Ray-Wave Duality: A Review

Systematically Investigating the Structural Variety of Crystalline and Kaleidoscopic Vortex Lattices by Using Laser Beam Arrays

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