Radiation Losses of Dielectric Waveguides in Terms of the Power Spectrum of the Wall Distortion Function

Abstract

In an earlier paper I described a perturbation theory of the radiation losses of a dielectric slab waveguide. The statistical treatment of the radiation losses was based on the correlation function of the wall distortion. This paper discusses the results of the radiation loss theory in terms of the power spectrum of the function describing the thickness of the slab. We found that only those mechanical frequencies Θ of the power spectrum contribute to the radiation loss that fall into the range β <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf> - k < Θ < β <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf> + k. (β <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</inf> = propagation constant of guided mode, k = free space propagation constant.) The mechanical frequencies near both end points of this mechanical frequency range contribute more to the radiation loss than the region well inside of this range. We also discuss the far-field radiation pattern caused by a strictly sinusoidal wall distortion.