Modes of grating waveguide

Starting with the coupled-paraxial-wave equations for Rayleigh waves propagating under a SAW grating, modes are derived with characteristic transverse-mode patterns. Modes exist below the first-order Bragg frequency both within a passband (real propagation constant) and a stop band (imaginary propagation constant). Cutoff (disappearance of guided mode solutions) is reached within the stop band above the Bragg frequency. No passband is found immediately above the stop band. Guidance of the waves by the grating is due to reflection at the grating edges and not due to a velocity difference of the Rayleigh waves between the regions outside the grating and underneath the grating. We take up the study of the effect of the velocity difference and find enhancement of guidance (as expected) when the outside region has a higher Rayleigh velocity. When the outside region has a smaller velocity, guided modes do not necessarily disappear. In fact, some guidance is provided by the velocity discontinuity.