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.
Highlights
Wave propagation in disordered media can give rise to a variety of interesting physical phenomena such as Anderson localisation and coherent back scattering[1,2,3]
Both oscillatory and monotonically decaying intensity correlation functions have for instance been observed near semi-continuous metal interfaces, where the dominant behaviour is dictated by the degree of surface plasmon-polaritons (SPPs) scattering[28]
Strong near field polarisation effects in the presence of SPPs or surface phonons have for example been predicted[31,32], whereas surface waves excited by thermal emission from a half space have been shown to give rise to long coherence lengths[33]
Summary
In this work fluctuations in the electric field of surface plasmon polaritons undergoing random scattering on a rough metallic surface are considered. Our derivation exploits the known analytic form of the Green’s tensor describing SPP scattering[39] These formulae help generalise and validate the predications of more specialised and approximate treatments given in the literature, which for example either assume the exciting source or surface correlation function is well described by a Dirac delta function (e.g. by considering a thermal source), or factor out slowly varying terms from the full integral representation of the cross-spectral density matrix[31,32,33]. We conclude by using our formulae to study the spatial polarisation and coherence properties of SPP speckle The former is possible since our derivation yields the full correlation matrix, including off-diagonal terms. Such properties can be relevant in, for example, plasmonic interferometry[42,43], plasmonic focusing[44] and leakage radiation microscopy[45,46]
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