Polarization purity and cross-channel intensity correlations

Document Type

Article

Publication Date

8-1-2025

Department

Department of Physics

Abstract

We consider the question of monitoring polarization purity, that is, measuring deviations from orthogonality δτ and δε of an ostensibly orthogonal polarization basis with a reference channel of ellipticity ε and tilt τ. A simple result was recently derived for a phase-sensitive receiver observing unpolarized radiation [IEEE Trans. Geosci. Remote Sens. 62, 2003610 (2024)]: with ρ(1) denoting the Pearson complex correlation coefficient between channel complex fields, it states that ∓ cos(2ε)δτ ± iδε ≈ ρ(1) when δτ,ε 1. However, phase-sensitive (in-phase and quadrature) data are seldom available at optical frequencies. To that end, here we generalize the result by deriving a new equation for the polarization “alignment” error: cos2(2ε)δτ2 + δε2 ≈ ρ(2), where ρ(2) is the intensity cross-correlation coefficient. Only the measurement of the (real) intensity cross-correlation coefficient is needed when observing unpolarized light. For the special case of a linearly polarized basis, the tilt error is simply δτ ≈ pρ(2), and for the circular basis case, with ellipticity deviation δε from circular helicity π/4 (the reference channel of opposite helicity), δε ≈ pρ(2). These results provide simple means to gauge the quality of polarimeters and depolarizers.

Publication Title

Journal of the Optical Society of America A Optics and Image Science and Vision

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