# Optical momentum and angular momentum in complex media: From the Abraham-Minkowski debate to unusual properties of surface plasmon-polaritons

## TL;DR

This paper investigates the momentum and angular momentum of monochromatic optical fields in complex media, clarifying Abraham and Minkowski approaches, and applies the theory to surface plasmon-polaritons, revealing their unique properties.

## Contribution

It develops a comprehensive theory of optical momentum and angular momentum in dispersive inhomogeneous media, including surface plasmon-polaritons, with both phenomenological and microscopic validation.

## Key findings

- Minkowski-type momentum describes the actual wave momentum with dispersion corrections.
- Surface plasmon-polaritons have a wave vector exceeding that of photons in vacuum.
- Transverse spin of SPP can change sign depending on frequency.

## Abstract

We examine the momentum and angular-momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham- and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and angular momentum carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spin-orbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e., a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which explains the difference between the Abraham and Minkowski momenta.

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Source: https://tomesphere.com/paper/1706.05493