Unified treatment for classical waves in two-dimensional media

TL;DR

This paper presents a unified theoretical framework for analyzing four types of classical waves in two-dimensional media, deriving a common wave equation, energy expressions, and offering insights for device design.

Contribution

It introduces a universal wave equation and energy expressions for multiple wave types in 2D media, unifying their treatment and aiding in understanding and device development.

Findings

Derived a universal wave equation for four wave types.

Provided universal energy density and flow expressions.

Offered insights for photonic and sonic device design.

Abstract

A unified treatment for the propagation of classical waves in inhhomogeneous media is proposed. We deal with four kinds of waves, they are the acoustic wave in fluid, the elastic shear wave in two diemnsional solid, and the E- and H-polarized electromagnetic waves in two diemnsional lossless medium. We first show that a universal wave equation governing the wave motion of all these four kinds of waves can be derived. We then introduce an auxiliary field, and give the universal expressions for the energy densities and energy flows of these waves. This unified treatment provides intuitive insights, which may be helpful in understanding the essential physics of various wave phenomena, or useful for designing new photonic and sonic devices.