Model of commensurate harmonic oscillators with SU(2) coupling interactions: Analogous observation in laser transverse modes

Lin, Yu-Ting; Lü, Ting; Huang, Kai–Feng; Chen, Y. F.

doi:10.1103/physreve.85.046217

Cited by 9 publications

(5 citation statements)

References 31 publications

(51 reference statements)

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“…When a resonator cavity fulfils the reentrant condition of a coupled quantum harmonic oscillator in SU(2) Lie algebra 90 , the laser mode undergoes frequency degeneracy with a photon performing as an SU(2) quantum coherent state coupled with a classical periodic trajectory 91 , which is called an SU(2) geometric mode (GM) 92 . The frequency degeneracy means that should be a simple rational number, where P and Q are two coprime integers, and () is the longitudinal (transverse) mode spacing.…”

Section: Properties Of Ovsmentioning

confidence: 99%

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

et al. 2019

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Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin–orbital interactions, Bose–Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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Section: Properties Of Ovsmentioning

confidence: 99%

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

et al. 2019

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“…These kinds of exotic SU(2) structured light mentioned above are the cases of classical structured light corresponding to SU(2) coherent state. Here we will introduce another exotic structured light with SU(2) symmetry, an eigenstate of SU(2) coupled commensurate harmonic oscillator [128]. For a generalized anisotropic Hamiltonian in equation ( 26), the coupling term j Ω j J j can be regarded as SU(2) coupling interaction and the corresponding eigenstate can be expressed as [128]:…”

Section: Commensurate Harmonic Oscillator Coupled Geometric Beams And...mentioning

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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“…To fulfill the reentrant condition of coupled harmonic oscillators in SU(2) Lie algebra, the cavity configuration requires a frequency-degenerate state of Ω = ∆f T /∆f L = P/Q ∈ Q, where P and Q are coprime integers, and ∆f L (∆f T ) is the longitudinal (transverse) mode spacing [20,21]. In frequency-degenerate cavity under off-axis pumping along x-axis, it has been proved that the emission mode is performed as SU(2) coherent state [14]:…”

Section: B Diffraction Of Vortex Su(2) Wave-packetmentioning

confidence: 99%

“…As a new kind of special vortex beams, nonplanar SU(2) geometric mode [14] has recently arouse great interest due to its peculiar properties like periodic ray trajectory [15,16], drastic increase of power [16,17], multiple singularities [18], and fractional OAM [19]. When a resonator cavity fulfills the reentrant condition of SU(2)-Lie coupled harmonic oscillation, the laser modes undergo frequency degeneracy and the photon wave-packet performs as SU (2) quantum coherent states [20,21]. The exotic modes in the frequency degenerate cavity under * shenyj15@mails.tsinghua.edu.cn off-axis pumping are always called geometric modes [14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes

Shen¹,

Fu²,

Gong³

2018

Opt. Express

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We for the first time report the truncated diffraction with a triangular aperture of the SU(2) geometric modes and propose a method to detect the complicated orbital angular momentum (OAM) of an SU(2) wave-packet, to the best of our knowledge. As a special vortex beam, a nonplanar SU(2) mode carrying special intensity and OAM distributions brings exotic patterns in truncated diffraction lattice. A meshy structure is unveiled therein by adjusting the illuminated aperture in vicinity of the partial OAM regions, which can be elaborately used to evaluate the partial topological charge and OAM of an SU(2) wave-packet by counting the dark holes in the mesh. Moreover, through controlling the size and position of the aperture at the center region, the truncated triangular lattice can be close to the classical spot-array lattice for measuring the center OAM. These effects being fully validated by theoretical simulations greatly extend the versatility of topological structures detection of special beams.

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Model of commensurate harmonic oscillators with SU(2) coupling interactions: Analogous observation in laser transverse modes

Cited by 9 publications

References 31 publications

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

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

Truncated triangular diffraction lattices and orbital-angular-momentum detection of vortex SU(2) geometric modes

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