Radiation Losses of Tapered Dielectric Slab Waveguides

The study of radiation losses of dielectric waveguides, which has been described in three earlier papers, 1-3 has been extended to cover abrupt steps in a single mode waveguide as well as continuous tapers. The mathematical theory of radiation losses caused by a step in the waveguide is used to compute the losses caused by tapers by regarding the taper as a succession of infinitely many infinitesimal steps. This method can also be used to rederive the equations for a dielectric slab waveguide with small wall distortions presented earlier.1 Both the earlier method and the derivation based on small steps lead to identical results. The perturbation theory used in Ref. 1 was not very well suited for calculating the losses of TM modes. The step method is equally applicable to TM and TE modes and allows us to derive for TM modes 273 274 T H E BELL SYSTEM TECHNICAL JOURNAL, FEBRUARY 1970 the corresponding expressions which for TE modes were presented in Ref. 1. The radiation losses of steps and tapers are surprisingly small. A step which changes the thickness of a dominant mode slab waveguide to one half of its original value causes a loss of only about 1 percent for TE modes and about 2 percent for TM modes if operated at favorable frequencies. The losses of tapers are even smaller and can be made as small as desired for sufficiently long tapers. Comparison of the radiation losses of slab waveguides with round and rectangular waveguides (to be published) shows that the slab waveguide losses are exceptionally low.