Control of spatially rotating structures in diffractive Kerr cavities

Research output: Contribution to journalArticle

Abstract

Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) m are shown to rotate with an angular velocity ω=2m/R2 on rings of radii R. We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range −2m/R2≤ω≤2m/R2 is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM. Using Poincaré beams that consist of orthogonally polarized eigenmodes with different magnitudes of OAM, the resultant angular velocity is ω=(mL+mR)/R2, where mL,mR are the OAMs of the eigenmodes, assuming good overlap between the eigenmodes. If there is no, or very little, overlap between the modes then concentric Turing pattern rings, each with angular velocity ω=2mL,R/R2 will result. This can lead to, for example, concentric, counter-rotating Turing patterns creating an optical peppermill-type structure. Full control over the speeds of multiple rings has potential applications in particle manipulation and stretching, atom trapping, and circular transport of cold atoms and BEC wavepackets.
LanguageEnglish
Pages31273-31289
Number of pages17
JournalOptics Express
Volume27
Issue number22
DOIs
Publication statusPublished - 28 Oct 2019

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angular velocity
angular momentum
orbitals
cavities
rings
pumps
atoms
manipulators
counters
trapping
radii
predictions

Keywords

  • beam shaping
  • light beams
  • vector beams
  • Kerr cavities

Cite this

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title = "Control of spatially rotating structures in diffractive Kerr cavities",
abstract = "Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) m are shown to rotate with an angular velocity ω=2m/R2 on rings of radii R. We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range −2m/R2≤ω≤2m/R2 is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM. Using Poincar{\'e} beams that consist of orthogonally polarized eigenmodes with different magnitudes of OAM, the resultant angular velocity is ω=(mL+mR)/R2, where mL,mR are the OAMs of the eigenmodes, assuming good overlap between the eigenmodes. If there is no, or very little, overlap between the modes then concentric Turing pattern rings, each with angular velocity ω=2mL,R/R2 will result. This can lead to, for example, concentric, counter-rotating Turing patterns creating an optical peppermill-type structure. Full control over the speeds of multiple rings has potential applications in particle manipulation and stretching, atom trapping, and circular transport of cold atoms and BEC wavepackets.",
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author = "Yao, {Alison M.} and Gibson, {Christopher J.} and Gian-Luca Oppo",
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Control of spatially rotating structures in diffractive Kerr cavities. / Yao, Alison M.; Gibson, Christopher J.; Oppo, Gian-Luca.

In: Optics Express, Vol. 27, No. 22, 28.10.2019, p. 31273-31289.

Research output: Contribution to journalArticle

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N2 - Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) m are shown to rotate with an angular velocity ω=2m/R2 on rings of radii R. We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range −2m/R2≤ω≤2m/R2 is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM. Using Poincaré beams that consist of orthogonally polarized eigenmodes with different magnitudes of OAM, the resultant angular velocity is ω=(mL+mR)/R2, where mL,mR are the OAMs of the eigenmodes, assuming good overlap between the eigenmodes. If there is no, or very little, overlap between the modes then concentric Turing pattern rings, each with angular velocity ω=2mL,R/R2 will result. This can lead to, for example, concentric, counter-rotating Turing patterns creating an optical peppermill-type structure. Full control over the speeds of multiple rings has potential applications in particle manipulation and stretching, atom trapping, and circular transport of cold atoms and BEC wavepackets.

AB - Turing patterns in self-focussing nonlinear optical cavities pumped by beams carrying orbital angular momentum (OAM) m are shown to rotate with an angular velocity ω=2m/R2 on rings of radii R. We verify this prediction in 1D models on a ring and for 2D Laguerre-Gaussian and top-hat pumps with OAM. Full control over the angular velocity of the pattern in the range −2m/R2≤ω≤2m/R2 is obtained by using cylindrical vector beam pumps that consist of orthogonally polarized eigenmodes with equal and opposite OAM. Using Poincaré beams that consist of orthogonally polarized eigenmodes with different magnitudes of OAM, the resultant angular velocity is ω=(mL+mR)/R2, where mL,mR are the OAMs of the eigenmodes, assuming good overlap between the eigenmodes. If there is no, or very little, overlap between the modes then concentric Turing pattern rings, each with angular velocity ω=2mL,R/R2 will result. This can lead to, for example, concentric, counter-rotating Turing patterns creating an optical peppermill-type structure. Full control over the speeds of multiple rings has potential applications in particle manipulation and stretching, atom trapping, and circular transport of cold atoms and BEC wavepackets.

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