Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915829516337152 |
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| author | Ruban, Victor P. |
| author_facet | Ruban, Victor P. |
| contents | A simplified mathematical model is suggested to describe the dynamics of a quasi-monochromatic optical wave in the bulk of an effectively isotropic metamaterial with averaged dielectrical permittivity near zero (ENZ medium), in the presence of a weak spatial nonuniformity, Kerr nonlinearity as well as linear gain due to external pumping. The model is a vector Ginzburg-Landau equation of the general kind, with the dominating curl-curl term in the dispersive operator, and it resembles the equation for electromagnetic waves in plasma [E. A. Kuznetsov, 1974]. In the case of purely real Kerr coefficients, a split-step Fourier method is appropriate for numerical simulations. It makes possible to observe various variants of nontrivial evolution of both central-symmetric and toroidal vector wave structures trapped by a quadratic potential well, as well as nonlinear interaction between the longitudinal and transverse waves in the case of their combination. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity Ruban, Victor P. Optics Pattern Formation and Solitons A simplified mathematical model is suggested to describe the dynamics of a quasi-monochromatic optical wave in the bulk of an effectively isotropic metamaterial with averaged dielectrical permittivity near zero (ENZ medium), in the presence of a weak spatial nonuniformity, Kerr nonlinearity as well as linear gain due to external pumping. The model is a vector Ginzburg-Landau equation of the general kind, with the dominating curl-curl term in the dispersive operator, and it resembles the equation for electromagnetic waves in plasma [E. A. Kuznetsov, 1974]. In the case of purely real Kerr coefficients, a split-step Fourier method is appropriate for numerical simulations. It makes possible to observe various variants of nontrivial evolution of both central-symmetric and toroidal vector wave structures trapped by a quadratic potential well, as well as nonlinear interaction between the longitudinal and transverse waves in the case of their combination. |
| title | Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity |
| topic | Optics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2510.21400 |