The possibility is studied of using a medium inhomogeneous in three dimensions as a kind of open resonator to trap optical waves. The existence of realizable eigenfunctions and eigenvalues suggest the existence of bound electromagnetic wave modes in a toroidal-shaped inhomogeneous medium, the refractive index of which is assumed to decrease monotonically in the radial as well as axial direction. For a general, slowly varying refractive-index profile, the radial variations of the trapped electromagnetic wave are Bessel and Airy integral-type functions, similar to those found in gas-lens studies, whereas axial variations are gaussian–hermite polynomials like those of the open resonators. Expressions for the turning radius and angular propagation constant of the waves have been derived for a general profile, and a few particular cases have been examined in detail. In a summation-type profile, the propagation constant and turning radius are shown to be independent of the axial position, whereas in the product-type profile they become functions of the axial position, so that the electromagnetic wave will propagate around in a spiral fashion.
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