The excitation of soliton states in optical layers exhibiting Kerr nonlinearities is theoretically investigated. The optical transmission coefficient is obtained as a function of the intensity of an incident light beam. The incident electromagnetic wave is considered to be monochromatic and linearly polarized in the transverse electric configuration. In materials exhibiting self-defocusing nonlinearity, soliton excitations are not observed if the product of the nonlinear dielectric coefficient of the slab and the absolute square of the incident electric-field amplitude is below a well-defined value. At such a limit, a soliton excitation with a position-independent electric field amplitude is observed within the nonlinear layer, regardless of the frequency value of the incident wave.
A theoretical study of the optical properties of a relativistic Fermi gas at a finite temperature is performed. The results are obtained from Maxwell’s equations, assuming bianisotropic constitutive relations for the relativistic gas. The longitudinal and transverse spatial directions are defined according to the properties of the electric permittivity tensor. The electromagnetic modes and the refractive index of the relativistic gas are calculated along such directions. The longitudinal and transverse group velocities corresponding to the respective propagation modes are also obtained. No typical characteristics of metamaterials are observed, neither in the refractive index nor in the group velocities corresponding to the transverse modes. However, in the case of longitudinal modes, negative values of the group velocity are observed in a region of the reciprocal space where particle–antiparticle excitations can occur.
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