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Journal of Physics D Applied Physics

Interference characteristic features of the transmission of opposing waves through layers with a complex refractive index

Dmitrii I. Sementsov, В. В. Ефимов

Published Jun 14, 1995• 8 citations
Publisher

Abstract

The interference of two opposing coherent waves in a thin layer was studied. Expressions for energy fluxes outside and inside the layer are obtained for normal incidence. It is shown that the interference flux, whose magnitude and direction vary markedly with layer parameters, amplitude and phase of incident waves may be derived together with incident, transmitted and reflected wave fluxes. The distribution of the total energy flux by thickness inside absorbing and amplifying layers was examined for single incident wave. The dependence of transmission and reflection energy coefficients, T and R, on the thickness of a layer with negative absorption has been studied numerically in detail for the case of normal incidence.

DOI
10.1088/0022-3727/28/6/027

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The interference of two opposing coherent waves in a thin layer was studied. Expressions for energy fluxes outside and inside the layer are obtained for normal incidence. It is shown that the interference flux, whose magnitude and direction vary markedly with layer parameters, amplitude and phase of incident waves may be derived together with incident, transmitted and reflected wave fluxes. The distribution of the total energy flux by thickness inside absorbing and amplifying layers was examined for single incident wave. The dependence of transmission and reflection energy coefficients, T and R, on the thickness of a layer with negative absorption has been studied numerically in detail for the case of normal incidence.
An investigation is made of the reflection of light from a nonlinear pile of thick plates. Assuming a small difference between the refractive indices of neighboring plates Δn/n<1, an analytic solution is found in the approximation of a continuous number of plates. It is shown that beginning with a certain intensity, the transmission regime becomes multivalued. At a moderate intensity, high reflection changes to transmission. Numerical calculations are made for the case Δn/n~1. It is found that the qualitative behavior of the transmission coefficient as a function of the incident radiation intensity is similar in both cases.
The coherent, radiative excitation modes of a resonant medium lend a resonant character to the amplitudes for reflection and transmission of light. For a plane wave incident upon a slab-shaped medium of two-level atoms, the reflection and transmission coefficients exhibit sharp peaks and dips as a function of the detuning of the wave from the central atomic resonance frequency. The locations and widths of these resonant features for a normally incident plane wave correspond to the imaginary and real parts, respectively, of the radiative decay constants of the coherent excitation modes of the medium discussed in the preceding paper [Phys. Rev. A 61, 063814 (2000)]. For the case of oblique incidence, generalizations of the modes discussed in the preceding paper are required. The richly detailed, resonant frequency dependence of the reflected and transmitted intensities is shown to depend significantly on the angle of incidence and the polarization of the incident light.
A medium described by an imaginary potential (or imaginary (refractive index) ), that varies sinusoidally in one direction, acts as a volume grating for plane waves incident on it obliquely or normally. Two peculiar features are identified. First, if the potential is weak, so that there are only two significant diffracted beams near the Bragg angle, and three for normal incidence, diffraction is strongly affected by degeneracies of the non-Hermitian matrix generating the `Bloch waves' in the grating; the effect of these degeneracies is very different from that of the Hermitian degeneracies for transparent gratings. Second, if the potential is strong and the grating thick, the asymptotic distribution of intensities among the diffracted beams (momentum distribution) is a rather narrow Gaussian, and dominated by a single set of complex rays; this is very different from the semiclassical limit for transparent gratings, where the rays form families of caustics proliferating with thickness, and with a wider momentum distribution.
We present a theoretical discussion of the optical reflectivity and transmissivity of a dielectric slab of arbitrary thickness, with index of refraction that contains a term proportional to the intensity of the optical wave in the slab. An exact solution is found for the problem, in terms of a single parameter whose value is determined through a straightforward numerical search procedure. We present numerical studies of the power dependence of the transmissivity, with emphasis on bistability, and the multivalued behavior of the transmissivity considered as a function of incident power.
Optical phase conjugation by four-wave mixing is examined in detail. The Fresnel coefficients for reflection and transmission of a plane wave irradiating the surface of the phase conjugator are calculated. It appears that for normal incidence and a weak nonlinear interaction the device produces the phase-conjugated beam with respect to the incoming beam. For finite angles of incidence or stronger nonlinearities in the crystal, the generated wave deviates from the ideal conjugated wave, and also a second, specularly reflected, wave appears.