# Field Correlations in Surface Plasmon Speckle

## TL;DR

This paper derives a comprehensive analytical model for second-order correlations in surface plasmon speckle patterns caused by scattering on rough metallic surfaces, accounting for dissipation and partial coherence.

## Contribution

It provides the first rigorous closed-form expression for plasmon speckle correlations, including effects of dissipation and partial coherence, advancing understanding of surface plasmon fluctuations.

## Key findings

- Derived explicit correlation expressions for surface plasmon speckle patterns
- Analyzed the impact of dissipation on correlation behavior
- Extended the framework to partially coherent sources

## Abstract

In this work fluctuations in the electric field of surface plasmon polaritons undergoing random scattering on a rough metallic surface are considered. A rigorous closed form analytic expression is derived describing second order correlations in the resulting plasmon speckle pattern assuming statistically stationary and isotropic roughness. Partially coherent planar Schell-model source fields can also be described within the developed framework. Behaviour of the three-dimensional degree of cross polarisation and spectral degree of coherence is also discussed. Expressions derived take full account of dissipation in the metal with non-universal behaviour exhibited within the correlation length of the surface and source fields.