Propagation of electromagnetic waves through weakly nonuniform media as described in terms of the quantum mechanical analogy

Abstract

The propagation of light through weekly nonuniform media is described in the paraxial approximation by the Schrödinger equation. The problem may thus be treated in terms of quantum mechanics. The paths and widths of wave beams are defined as corresponding values, averaged over coherent states. It is shown that the beam path may be found by solving a closed equation with the initial altitude and inclination aws variables. The wave effects are due to higher-order derivatives appearing in the equation. A medium is considered whose refractive index is nearly parabolic. The problem is similar to that of the time evolution of a quantum mechanical anharmonic oscillator. It is shown that the anharmonicity present in the refractive index results in a space modulation of the light beam, which is pure wave nature. A similar effect occurs if the weakly nonparaxial character of light propagation is taken into account. The spatial stochastic resonance in a randomly nonuniform medium associated with the wave nature of light is studied. The propagation of light through media with a rapidly oscillating refractive index is also discussed.