Green's functions, propagation invariants, reciprocity theorems, wave-field representations and propagator matrices in 2D time-dependent materials

TL;DR

This paper explores fundamental aspects of 2D electromagnetic and acoustic wave propagation in time-dependent materials, including Green's functions, reciprocity, and propagator matrices, advancing understanding of wave behavior in dynamic media.

Contribution

It provides a comprehensive analysis of wave propagation in 2D time-dependent materials, including new expressions for Green's function retrieval and insights into propagator matrix properties.

Findings

Derived an expression for Green's function retrieval in time-dependent materials.

Discussed symmetry properties of Green's functions and propagator matrices.

Analyzed wave transmission, reflection, and invariants in 2D time-dependent media.

Abstract

The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent materials, this relation is less straightforward for multi-dimensional materials. This paper discusses fundamental aspects of 2D electromagnetic and acoustic wave propagation and scattering in homogeneous, time-dependent materials. This encompasses a review of transmission and reflection at a single time boundary, a discussion of the Green's function and its symmetry properties in a piecewise continuous time-dependent material, a discussion of propagation invariants (including the net field-momentum density), general reciprocity theorems, and wave field representations. Analogous to the well-known expression for Green's function retrieval by time-correlation of passive measurements in a space-dependent material, an expression is derived for Green's function retrieval by space-correlation of passive measurements in a time-dependent material. The paper concludes with the discussion of the propagator matrix for a piecewise continuous time-dependent material, its symmetry properties and its relation with the Green's function.