Consistency of certain constitutive relations with quantum electromagnetism

TL;DR

This paper extends a Lagrangian framework for quantizing electromagnetic fields to complex media, revealing consistency constraints on constitutive relations and highlighting fundamental differences between moving media and stationary magnetoelectrics.

Contribution

It generalizes the Lagrangian quantization approach to reciprocal and non-reciprocal magnetoelectric media, identifying restrictions on constitutive relations for consistent quantization.

Findings

Some constitutive relations are incompatible with a real Lagrangian.

Restrictions on the magnitude of magnetoelectric coupling are established.

Moving media differ fundamentally from stationary magnetoelectrics in quantization.

Abstract

Recent work by Philbin [1] has provided a Lagrangian theory that establishes a general method for the canonical quantization of the electromagnetic field in any dispersive, lossy, linear dielectric. Working from this theory, we extend the Lagrangian description to reciprocal and non- reciprocal magnetoelectric (bi-anisotropic) media, showing that some versions of the constitutive relations are inconsistent with a real Lagrangian, and hence with quantization. This amounts to a restriction on the magnitude of the magnetoelectric coupling. Moreover from the point of view of quantization, moving media are shown to be fundamentally different from stationary magnetoelectrics, despite the formal similarity in the constitutive relations.