Spectral Green’s function for wave excitation and propagation in a piezoelectric, continuously twisted, structurally chiral medium

Abstract

A continuously twisted, structurally chiral medium (CTSCM) is a reciprocal medium whose constitutive properties vary helicoidally along its axis of spirality (say, the $z$ axis), and the corresponding piezoelectric medium is abbreviatedly called the PCTSCM. Very recent progress in thin-film research is presented here to show that technologically significant CTSCM’s and PCTSCM’s are waiting in the wings and calling for theoretical advances in the understanding of wave excitation and propagation in these novel materials. A spectral Green’s function is obtained as a bilinear composition of two matrices, after implementing a spatial Fourier transform in the $\mathrm{xy}$ plane as well as the Oseen transformation. As a result, multilayered media problems as well as grating problems utilizing CTSCM’s and PCTSCM’s become accessible to theoretical exploration leading to novel transducers, sensors, and other devices.