Spectral theory for IDTs

Interdigital transducers may consist of thousands of periodic metal strips. This allows us to apply an approximation that the surface acoustic wave is excited, propagates, and is detected in an infinite periodic system of strips. This key approximation, and known Blortekjaer´s theory, are both the foundation of a spectral theory for IDT presented in 1976. The theory has been further developed (J. Acoust. Soc. Am., 1993) to account for the metal strip elasticity, which is important in analyzing unidirectional transducers exploiting both electric, and mechanical interactions of the surface acoustic wave with transducer fingers. Most important steps and results of the theory are presented, primarily the closed form, analytical solution for scattering matrix (P-matrix) of uniform and potentially unidirectional transducers. Some new applications of the theory are presented and the relation of spectral theory to the COM (coupling-of-modes) model is discussed