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

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.

5 pages, 10 figures, in Russian

References in corpus (9)

• Realization of an all-dielectric zero-index optical metamaterial
• Non-local effects in effective medium response of nano-layered meta-materials
• Extreme nonlinear electrodynamics in metamaterials with very small linear dielectric permittivity
• Split-step Fourier methods for the Gross-Pitaevskii equation
• Nonlocal homogenization theory in metamaterials: effective electromagnetic spatial dispersion and artificial chirality
• Quantum and classical dynamics of Langmuir wave packets
• Two-peaked and flat-top perfect bright solitons in epsilon-near-zero nonlinear metamaterials: novel Kerr self-trapping mechanisms
• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Gain assisted nanocomposite multilayers with near zero permittivity modulus at visible frequencies