Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials
arXiv:1812.08805 · doi:10.1103/PhysRevA.100.053853
Abstract
We explore numerically and analytically the pattern formation and symmetry breaking of beams propagating through left-handed (negative) nonlinear metamaterials. When the input beam is a vortex with topological charge (winding number) , the initially circular (isotropic) beam acquires the symmetry of a polygon with , or sides, depending on the details of the response functions of the material. Within an effective field-theory model, this phenomenon turns out to be a case of spontaneous dynamical symmetry breaking described by a Landau-Ginzburg functional. Complex nonlinear dependence of the magnetic permittivity on the magnetic field of the beam plays a central role, as it introduces branch cuts in the mean-field solution, and permutations among different branches give rise to discrete symmetries of the patterns. By considering loop corrections in the effective Landau-Ginzburg field theory we obtain reasonably accurate predictions of the numerical results.
19 pages, 7 figures; this version: corrected typos, added discussion on the role of magnetic field and on experimental verification; journal reference added
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