Singular value representation of the coherence Poincaré sphere

Abstract

The so-called coherence Poincaré sphere was recently introduced for geometrical visualization of the state of two-point spatial coherence of a random electromagnetic beam. The formalism and its interpretation strongly utilized a specific decomposition of the Gram matrix of the cross-spectral density (CSD) matrix. In this work, we show that the interpretation of the coherence Poincaré sphere is obtained exclusively and straightforwardly via the singular value decomposition of the CSD matrix.

Keywords

• electromagnetic beams
• optical coherence
• polarization