A P-matrix based model for SAW grating waveguides taking into account modes conversion at the reflection

Several models exist for analyzing the wave-guiding effect of a reflective grating. On the one hand, there are models based on scalar waveguide theory. These models consider that a device can be described as being made of several regions having different velocities. On the other hand, an extension of the coupling of modes (COM) model taking into account the transverse dimension has been developed. This paraxial COM model predicts that guidance is possible even when there is no velocity difference between the interior and the exterior of the grating region. Guidance, under such circumstances, is due only to differences in reflectivity between regions. Following from this insight, a new approach has been developed: guided modes and the continuum of radiating modes are first determined. At each period, reflections then are considered as occurring only in the reflective regions, so that the modes are truncated. Thus, at each reflection (and transmission), each mode is converted into a distribution of all modes. Dispersion curves very similar to those shown by other researchers are obtained by this method. They show, in particular, the existence of guided modes even when the wave velocity in all regions is identical. This model can be used to more easily analyze practical devices and exhibits a good agreement with experimental results.