Generalized coupled mode theory in phononic slab waveguides

We develop the generalized coupled mode theory for the phononic slab waveguides, including core and cladding regions. At first, the eigenfrequency analysis is performed to obtain the dispersion curves for shear (SH) and Rayleigh-Lamb (RL) modes that are the orthogonal modes of slab waveguide. Secondly, the coupled mode equations (CMEs) are introduced for SH and RL modes, separately. Then CMEs are utilized to study transferring elastic energy between two coupled waveguides. We also analytically investigate the coupling of SH modes between nonparallel waveguides through calculating the coupling coefficients for small angles between them. Finally, the coupling of non-parallel waveguides in two different situations is demonstrated, when they are getting away from each other, and vice versa.