Wave scattering and guidance by dielectric waveguides with periodic surfaces

Stratified media with periodic surfaces have been used in waveguide-input and waveguide-output couplers and distributed-feedback lasers. We apply the extended-boundary-condition approach to treat the problem of scattering and guidance by stratified media with period surfaces for both the TE and TM polarizations in a unified manner with the use of a transition matrix. Theoretical results are shown to compare well with the experimental data for metallic gratings with surface-plasmon excitations. The anomalous behavior of the diffraction efficiencies is explained with the evanescent Floquet waves, which are excited with incidence angles corresponding to the locations of the dips in the total reflected efficiency plots. Diffraction efficiencies are plotted for wave scattering from corrugated thin-film waveguides with an angle of incidence near that for the waveguide-mode excitation. The guiding constants are also calculated and compared with the results obtained by other numerical methods. The origins of the imaginary parts in the guiding constants are discussed in light of the nonevanscent waves excited in the substrate.