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Soviet Journal of Quantum Electronics

Deflection of a light beam in an inhomogeneously amplifying medium

V P Konarev, I. N. Matveev, Vladimir Protopopov

Published Apr 30, 1977• 0 citations
Publisher

Abstract

A theoretical analysis is made of the propagation of a monochromatic beam of arbitrary form through an amplifying medium with a coordinate-dependent gain. The Fourier transformation is used to obtain a system of integrodifferential equations for the Fourier components of the field. The results of numerical calculations are given for one specific case.

DOI
10.1070/qe1977v007n04abeh009753

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A theoretical analysis is made of the propagation of a monochromatic beam of arbitrary form through an amplifying medium with a coordinate-dependent gain. The Fourier transformation is used to obtain a system of integrodifferential equations for the Fourier components of the field. The results of numerical calculations are given for one specific case.
We study optical wave deflection in a three-level active Raman gain medium using a spatially inhomogeneous pump field. Using the eikonal approximation, we derive an analytical expression for the deflection angle and demonstrate more than an order of magnitude increase in deflection when compared to the electromagnetically induced transparency method. Numerical simulations have shown excellent agreement with semi-classical theoretical predictions. We further discuss the concept of light-beam-deflection-based wavelength division multiplexing which may have important applications in integrated circuits for optical telecommunications.
The analysis of wave propagation in linear, passive media is usually done by considering a single real frequency (the monochromatic limit) and also often a single plane-wave component (plane-wave limit). For gain media, we demonstrate that these two limits generally do not commute; for example, one order may lead to a diverging field, while the other order leads to a finite field. Moreover, the plane-wave limit may be dependent on whether it is realized with a finite-support excitation or Gaussian excitation, eventually of infinite widths. We consider wave propagation in gain media by a Fourier-Laplace integral in space and time, and demonstrate how the correct monochromatic limit or plane-wave limit can be taken, by deforming the integration surface in complex frequency--complex wave-number space. We also give the most general criterion for absolute instabilities. The general theory is applied in several cases, and is used to predict media with novel properties. In particular, we show the existence of isotropic media which in principle exhibit simultaneous refraction, meaning that they refract positively and negatively at the same time.
Based on the equation for the second-order coherence function, the propagation of partially coherent radiation is studied under the combined action of diffraction and refraction caused by the inhomogeneous distribution of the real and imaginary parts of the perturbation of the permittivity of a medium in the case of inhomogeneous absorption (amplification). The limits of application of the method of geometrical optics for inhomogeneously absorbing (amplifying) media are studied, as well as of the methods that neglect refraction caused by the inhomogeneous distribution of the imaginary part of the permittivity of the medium.