Harmonic admittance and dispersion equations - the theorem

The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface-acoustic waves in periodic electrode arrays. In particular, the dispersion relations for open- and short-circuited systems can be reconstructed from the zeros and poles of the harmonic admittance. Here we show that a strict reverse relationship also exists: the harmonic admittance may always be expressed as the ratio of two determinants, specifically constructed to define the eigenmodes of the open- and short-circuited systems. There is no need to solve dispersion equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus (1985) and was recently used to model surface transverse waves, but a rigorous mathematical proof was only found later by Biryukov (2000). Here we reproduce this theorem in detail, and discuss some of its consequences