Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866914709627731968 |
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| author | Kukolj, Trivko Čubrović, Mihailo |
| author_facet | Kukolj, Trivko Čubrović, Mihailo |
| contents | 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) $Q$, the initially circular (isotropic) beam acquires the symmetry of a polygon with $Q$, $2Q$ or $3Q$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1812_08805 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials Kukolj, Trivko Čubrović, Mihailo Optics Other Condensed Matter Quantum Physics 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) $Q$, the initially circular (isotropic) beam acquires the symmetry of a polygon with $Q$, $2Q$ or $3Q$ 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. |
| title | Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials |
| topic | Optics Other Condensed Matter Quantum Physics |
| url | https://arxiv.org/abs/1812.08805 |