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<p>A simplified mathematical model is proposed to describe the dynamics of a quasi-monochromatic light wave in the bulk of an effectively isotropic metamaterial with a nearly zero averaged permittivity in the presence of weak spatial inhomogeneity, Kerr nonlinearity, and linear gain under external pumping. The model is based on a general Ginzburg–Landau vector equation with the dominance of the curl–curl term in the dispersion operator and resembles the equation for electromagnetic waves in a plasma [E.A. Kuznetsov, “The Collapse of Electromagnetic Waves in a Plasma,” Sov. Phys. JETP <b>39</b>, 1003 (1975)]. The split step Fourier method is appropriated in the case of purely real Kerr coefficients. This method has made it possible to reveal various variants of non-trivial evolution of both centrosymmetric and toroidal vector wave structures in a parabolic well potential, as well as the nonlinear interaction between longitudinal and transverse waves in the case of a combination of these structures.</p>

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Numerical Simulation of Light Structures in Bulk Epsilon-Near-Zero Media with Kerr Nonlinearity

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  • 发表日期：

    2026年1月1日

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  • V. P. Ruban

摘要

A simplified mathematical model is proposed to describe the dynamics of a quasi-monochromatic light wave in the bulk of an effectively isotropic metamaterial with a nearly zero averaged permittivity in the presence of weak spatial inhomogeneity, Kerr nonlinearity, and linear gain under external pumping. The model is based on a general Ginzburg–Landau vector equation with the dominance of the curl–curl term in the dispersion operator and resembles the equation for electromagnetic waves in a plasma [E.A. Kuznetsov, “The Collapse of Electromagnetic Waves in a Plasma,” Sov. Phys. JETP 39, 1003 (1975)]. The split step Fourier method is appropriated in the case of purely real Kerr coefficients. This method has made it possible to reveal various variants of non-trivial evolution of both centrosymmetric and toroidal vector wave structures in a parabolic well potential, as well as the nonlinear interaction between longitudinal and transverse waves in the case of a combination of these structures.