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

In an earlier paper I developed a perturbation theory of the mode conversion effects between guided modes and of the radiation losses of a given guided mode caused by deviations from perfect straightness of the waveguide wall.1 For simplicity, the discussion had been limited to a waveguide in the form of an infinitely extended dielectric slab. The statistical discussion had been based on the description of the wall distortion by means of a correlation function. In Ref. 1 an exponential correlation function had beeii assumed. However, it has been established that the shape of the correlation function has little influence on the radiation losses. It is possible to base the discussion of radiation losses not on correlation functions, but on the mechanical power spectrum of the wall distortion function. This study provides information as to how the various 3233 3234 T H E BELL SYSTEM TECHNICAL JOURNAL, DECEMBER 1969 mechanical frequencies of the wall distortion function contribute to the radiation losses. The analysis of Ref. 1 was based on the use of radiation modes of the dielectric slab which represent standing waves in directions transverse to the propagation direction of the guided modes. The question naturally arises how a superposition of these standing waves can result in radiation flowing away from the rod. This question is answered by examining the far field radiation pattern caused by a sinusoidal distortion of one wall of the dielectric waveguide. This paper gives the relation between the length of the mechanical period, the wavelength of the guided mode, and the direction of the main lobe of the radiation.