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Optical and Quantum Electronics

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01-11-2018

Vortex dynamics of counterpropagting laser beams in photorefractive materials

Authors: Mihailo Čubrović, Milan Petrović

Published in: Optical and Quantum Electronics | Issue 11/2018

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Abstract

We study vortex patterns of counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two “flavors” because there are two opposite directions of beam propagation. In a certain parameter range, the vortices form stable equilibrium configurations which we study using the methods of statistical field theory and generalize the Berezinsky–Kosterlitz–Thouless transition of the XY model to the “two-flavor” case. In the nonequilibrium regime, the patterns exhibit an Andronov–Hopf bifurcation which may lead to oscillations (limit cycle), chaos or decay to zero intensity due to radiation losses. We show how to identify various pathways toward instability from intensity patterns, i.e. from experiment.

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One might also worry that a realistic crystal is anisotropic, while our equation is isotropic. Nevertheless, comparison to experiment (Neshev et al. 2004; Fleischer et al. 2004; Dreischuh et al. 2002) shows that this model is able to describe actual measurements rather well. Also, the effects of anisotropy can be suppressed in experiment by illuminating the crystal by uniform light for very long times before starting the experiment (Cohen et al. 2002).

There is no difference between upper and lower indices as both flavors always enter the sum with positive sign.

The boldface vectors are the coordinate vectors in the plane.

Negative sign means the fixed point is stable everywhere before the bifurcation and is replaced by a stable limit cycle after the bifurcation (supercritical). Positive sign means the fixed point coexists with the stable limit cycle before the bifurcation and the \((X_1,X_5)\) plane is divided among their attraction regions; after the bifurcation there is no stable solution at all (subcritical). However, one should not take the stability in the whole \((X_1,X_5)\) plane in the supercritical case too seriously. We have expand the equations of motion in the vicinity of the fixed points and the expansion ceases to be valid far away from the origin.

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Title: Vortex dynamics of counterpropagting laser beams in photorefractive materials
Authors: Mihailo Čubrović
Milan Petrović
Publication date: 01-11-2018
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 11/2018
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-018-1667-x

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