Radiation- and Bound-Mode Propagation in Rectangular, Multimode Dielectric, Channel Waveguides With Sidewall Roughness

This paper calculates and displays accurate radiation modes for rectangular, multimode dielectric, channel waveguides, for the first time, and introduces the new semianalytical calculation method used to find them, the radiation-mode Fourier decomposition method (RFDM), which is an extension of the Fourier decomposition method (FDM) for finding bound propagating modes. The optimum choice of non-linear conformal transformation parameters is discussed for achieving highest accuracy. Once the radiation modes are known, the coupling coefficients can be found between the bound and radiation modes, as well as those between the bound modes themselves, andhence, the propagation loss can be found. The paper adapts Marcuse's coupled power theory, for the first time, to enable it to model propagation in rectangular, multimode dielectric, channel waveguides suffering from one dimensional sidewall roughness enabling the equilibrium distance to be calculated, at which rate of loss to radiation modes becomes constant, and to find that equilibrium propagation loss, and the dependence on the statistical properties of the wall roughness. This leads to the conclusion that at sufficient distance there exist two uncoupled modes, a symmetric and an asymmetric lowest order mode.