### Abstract

*m*are shown to rotate with an angular velocity ω=2

*m/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 −2

*m*/

*R*2≤ω≤2

*m*/

*R*2 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*)/

*R*2, 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=2

*mL,R*/

*R*2 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.

Language | English |
---|---|

Pages | 31273-31289 |

Number of pages | 17 |

Journal | Optics Express |

Volume | 27 |

Issue number | 22 |

DOIs | |

Publication status | Published - 28 Oct 2019 |

### Fingerprint

### Keywords

- beam shaping
- light beams
- vector beams
- Kerr cavities

### Cite this

}

*Optics Express*, vol. 27, no. 22, pp. 31273-31289. https://doi.org/10.1364/OE.27.031273

**Control of spatially rotating structures in diffractive Kerr cavities.** / Yao, Alison M.; Gibson, Christopher J.; Oppo, Gian-Luca.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Control of spatially rotating structures in diffractive Kerr cavities

AU - Yao, Alison M.

AU - Gibson, Christopher J.

AU - Oppo, Gian-Luca

PY - 2019/10/28

Y1 - 2019/10/28

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.

KW - beam shaping

KW - light beams

KW - vector beams

KW - Kerr cavities

U2 - 10.1364/OE.27.031273

DO - 10.1364/OE.27.031273

M3 - Article

VL - 27

SP - 31273

EP - 31289

JO - Optics Express

T2 - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 22

ER -