Degree of Polarization in Near Fields of Thermal Sources: Effects of Surface Waves

Abstract

We introduce the concept of degree of polarization for electromagnetic near fields. The approach is based on the generalized Stokes parameters that appear as expansion coefficients of the 3 x 3 coherence matrix in terms of the Gell-Mann matrices. The formalism is applied to optical near fields of thermally fluctuating half-space sources with particular interest in fields that are strongly polarized owing to resonant surface plasmons or phonons. This novel method is particularly useful when assessing the full vectorial characteristics of random evanescent fields, e.g., for near-field spectroscopy and polarization microscopy.

Classical distinguishability as an operational measure of polarization

“…Although this question has been considered for many years, no satisfactory solution has thus far been found. Indeed, there are several contradictory claims made in the literature on this subject [6][7][8][9][10][11][12][13][14][15]. The divergences occur because notions that are equivalent for the 2D case lead to different definitions when extrapolated to the 3D limit.…”

Nanoscale Thermal Transfer – An Invitation to Fluctuation Electrodynamics

“…1 Equation (18) arises from [62,63], which coincide in the present situation. They do not do so in the general case, because of different ways the three field components have been taken into account to define degrees of polarisation.…”

Dimensionality of random light fields

“…Optical fields can thereby be classified into one-dimensional (1D), two-dimensional (2D), or three-dimensional (3D) light, depending on the minimum number of orthogonal coordinate axes required to represent them. The dimensional nature of light plays an essential role in addressing polarization characteristics of complex-structured light fields, e.g., electromagnetic near and surface fields [3][4][5] as well as tightly focused optical beams [6][7][8][9], which are frequently exploited in near-field probing [10], singlemolecule detection [11], particle trapping [12], among other polarization-sensitive applications. Yet, no systematic theory has so far been developed which provides rigorous means to categorize and to characterize the dimensionality of light.…”