Modes in SAW grating resonators

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Abstract
A Rayleigh wave of finite width, propagating along the surface of an isotropic medium, is shown to obey approximately a paraxial wave equation if the width is large compared with a wavelength. Results of laser wave propagation can be applied to the Rayleigh‐wave case. Furthermore, an equation is derived for the two‐dimensional Rayleigh‐wave propagation underneath a grating surface. A grating of finite width is shown to provide transverse confinement (guidance) of the wave. The mode patterns are obtained of the fundamental and higher‐order guided modes under uniform gratings of finite width. For a grating resonator formed of two uniform gratings separated by a quarter‐wave section, a variational expression is developed for the resonance frequencies. Using a simple mode pattern for the trial solution, the resonance frequencies of the higher‐order modes are evaluated. They all lie on the high side of the Bragg frequency, increasing with increasing mode number.

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