Vorticity cutoff in nonlinear photonic crystals

Details Vorticity cutoff in nonlinear photonic crystals Vorticity cutoff in nonlinear photonic crystals

2004-11-02

arxiv.org/abs/nlin/0411005v2

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1103/PhysRevLett.95.043901

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.

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