Mode Conversion Caused by Surface Imperfections of a Dielectric Slab Waveguide

This paper contains a perturbation theory which is applicable to the scattering losses suffered by guided modes of a dielectric slab waveguide as a consequence of imperfections of the waveguide wall. The development of the theory occupies the bulk of the paper. Numerical results appear in Sections VI and VIII to which a reader less interested in the theory is referred. The theory allows us to conclude that random deviations of the waveguide wall in the order of 1 percent, for guides designed to guide an optical wave of Λo= 1μ wavelength, can cause scattering losses of 10 percent per centimeter or 0.46 dB per centimeter. A systematic sinusoidal deviation of the waveguide wall can cause total exchange of energy from the lowest order to the first order guided mode in a distance of approximately 1 cm if the amplitude of the sinusoidal deviation from perfect straightness is only 0.5 percent of the thickness of the guide. An rms deviation of one of the waveguide walls of 9Å causes a radiation loss of 10 dB per kilometer (index difference 1 percent, guide width 2.5μ).