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, some models are based on scalar waveguide theory. These models consider that a device can be described as being made of several layers having different velocities. On the other hand, Haus et al. developed an extension of the COM taking into account the transverse dimension. This paraxial COM predicts that guiding is possible even when there is no velocity difference inside and outside the grating. The guiding is only due to differences in reflectivity between the different regions. A new approach is developed: guided modes and the continuum of radiating modes are first determined. At each period, reflections are then 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 all modes. Dispersion curves very similar to those shown by Haus are obtained by this method. They show in particular the existence of guided modes even with identical velocities in all regions. This model can be used to more easily analyze practical devices and exhibits a good agreement with experimental results.