# Optical Momentum, Spin, and Angular Momentum in Dispersive Media

## TL;DR

This paper develops a comprehensive theory of optical momentum, spin, and angular momentum in dispersive media, resolving longstanding dilemmas and introducing novel canonical quantities with applications to surface plasmon-polaritons.

## Contribution

It introduces new canonical momentum and angular momentum densities for optical fields in dispersive media, clarifying the Abraham-Minkowski dilemma and applying the theory to surface plasmon-polaritons.

## Key findings

- SPPs carry super-momentum proportional to their wave vector
- SPPs exhibit a transverse spin that can change sign with frequency
- The kinetic Abraham momentum describes energy flux and group velocity

## Abstract

We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowsky-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. We apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "super-momentum", proportional to the wave vector $k_{p} > \omega/c$, and a transverse spin, which can change its sign depending on the frequency $\omega$.