How the electromagnetic field evolves in the presence of a mobile membrane

TL;DR

This paper derives simple analytic formulas describing how the electromagnetic field in a one-dimensional cavity evolves when a mobile membrane moves slowly, accounting for position, velocity, and acceleration, and identifies conditions for single-mode approximation.

Contribution

It provides new analytic formulas for electromagnetic field evolution in a cavity with a moving membrane, valid for large displacements and slow membrane motion.

Findings

Formulas accurately describe field evolution with membrane motion.

Conditions for single-mode approximation are established.

Formulas incorporate position, velocity, and acceleration of the membrane.

Abstract

We consider a one-dimensional cavity composed of two perfect, fixed mirrors and a mobile membrane in between. Assuming that the membrane starts to move from rest and that the membrane moves appreciably in a time-scale much larger than the time-scale in which the cavity electromagnetic field evolves appreciably, we derive simple analytic formulas that describe to good approximation the evolution of the field and that provide an intuitive physical picture. These formulas take into account the position, velocity, and acceleration of the membrane and are valid for arbitrarily large displacements of the membrane along the cavity axis. Also, we deduce the conditions under which the field can be described to good approximation by a single instantaneous mode.