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Quantum Electronics

A study of radiation propagation in a medium with quadratic inhomogeneity

Aleksei A. Pikulev

Published Sep 30, 2001• 0 citations
Publisher

Abstract

The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.

DOI
10.1070/qe2001v031n09abeh002044

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The propagation of Hermitian beams in a medium with a distributed quadratic inhomogeneity is studied and is shown that any solution can be represented as a function of some particular solution. This is accomplished by establishing a one-to-one correspondence between optical fields in a homogeneous medium and in a medium with an arbitrary quadratic inhomogeneity. The stability of optical resonators is studied and the condition for their stability is found. Several solutions are found using the method developed.
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.
Methods of integrals of motion, coherent states, dynamical symmetry group, and density matrix formalism are used to describe the propagation of light in weakly inhomogeneous media, in particular, in a two-dimensional medium having a quadratic transverse distribution of the refractive index and an arbitrarily inhomogeneous longitudinal distribution. Expressions are obtained for the trajectories and widths of the modes and rays. The coefficients of coupling between the modes and rays due to the longitudinal inhomogeneity of the medium and distortion of the axis are discussed. It is shown that, for certain laws of longitudinal inhomogeneity, matching occurs when no energy redistribution takes place between the modes and mismatch is found when all the energy is coupled out of the medium. On the basis of these effects, methods of matched joining of two different graded-index optical waveguides and of coupling light out of a graded-index waveguide are proposed. It is shown that each initial mode of the medium is strongly coupled to three final modes. These results may be used in fiber-optic communication lines.
The choice of the representation (the complete set of functions) is very important for describing a field in many problems of wave propagation. A representation proved to be convenient here depends on excitation conditions and waveguide properties. It was shown [ 1 ] that the coherent states (CS) representation and the integrals of motion method turn to be extremely convenient for investigating Gaussian beam propagation in quadratic-index media. In [ 2 ] the correlated coherent states (CCS) were used to describe arbitrary Gaussian beam propagations in such media. The coherent state representation turns to be also convenient for description of nonparaxial propagation of both coherent and partially coherent radiation in the gradient medium [ 3 , 4 ]. Here we show that CCS turn to be also more convenient representation for investigating wave propagation in optic active quadratic media. CCS in such media describe a Gaussian wave packets with constant parameters during beam propagation. These states permit the concept of geometric ray width and wave front curvature to be introduced by natural manner and the relationship between wave and ray optics description to be clearly visualized for quadratic media with loss or gain.