Perturbation Theory for Electromagnetic Coupling to Elastic Surface Waves on Piezoelectric Substrates

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Abstract
Starting from the fundamental acoustic and electromagnetic field equations an approximate expression is obtained for the perturbation in propagation wavenumber of a surface acoustic wave in a piezoelectric crystal. The source of perturbation is taken to be a surface spaced an air‐gap distance h above the piezoelectric and is described in terms of an electrical impedance. The resulting perturbation is found in terms of the perturbing electrical impedance, an effective dielectric constant for the piezoelectric, the air‐gap spacing h, and a perturbation coupling constant defined in terms of the unperturbed electric potential at the piezoelectric surface and the average acoustic power flow per unit frequency. The theory is applied to the case of a short‐circuit perturbing surface and found to be in excellent agreement with certain numerical results for Y‐cut Z‐propagating LiNbO3 and several cuts of Bi12 GeO20. In the general case of a complex perturbing impedance, such as that exhibited by a semiconductor, the theory indicates that attenuation or gain and dispersion may be introduced by the perturbation, in close agreement with experimental observations.