Decoupling the energy and momentum of photons in the quasistatic limit

TL;DR

This paper demonstrates that in certain photonic crystals, at low frequencies, photon energy and momentum can be decoupled, allowing light to propagate with zero energy but nonzero momentum, challenging traditional assumptions.

Contribution

It provides a rigorous theoretical framework and closed-form conditions for decoupling photon energy and momentum in photonic crystals, including novel insights into light cone origins.

Findings

Light cones can originate away from the origin in k-space.

First bands can start from arbitrary Bloch coordinates.

Photon energy and momentum can be decoupled at low frequencies.

Abstract

We theoretically show that the frequency and momentum of a photon are not necessarily proportional to one another at low frequencies in photonic crystals comprising materials with positive- and negative-valued material properties. We rigorously determine closed-form conditions for the light cone to emanate from points other than the origin of $k$ space, ultimately decoupling the first band from the origin and demonstrating light propagation at zero energy with nonzero crystal momentum. We also numerically show that first bands can originate from an arbitrary Bloch coordinate as well as from multiple coordinates simultaneously.