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arXiv · 2510.21400

Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity

Victor P. Ruban
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Abstract

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.

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Victor P. Ruban. 2025-10-24. Numerical simulation of light structures in bulk ENZ media with Kerr nonlinearity. https://doi.org/10.1134/s0021364025609650

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