Vorticity cutoff in nonlinear photonic crystals

Abstract

Using group theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the non-linearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.

4 pages, 5 figures; minor changes in address and references

References in corpus (5)

• Observation of discrete vortex solitons in optically-induced photonic lattices
• Fundamental and vortex solitons in a two-dimensional optical lattice
• Asymmetric vortex solitons in nonlinear periodic lattices
• Vortex solitons in photonic crystal fibers
• Nodal solitons and the nonlinear breaking of discrete symmetry

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• Angular Pseudomomentum Theory for the Generalized Nonlinear Schrödinger Equation in Discrete Rotational Symmetry Media
• Symmetry-assisted vorticity control in Bose-Einstein condensates
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• Soliton shape and mobility control in optical lattices
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