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Polarization Science and Remote Sensing

The degree of genuine unpolarization

Sethuraj Karimparambil Raju, A. Nick Vamivakas

Published Oct 4, 2023• 0 citations
Publisher

Abstract

An ideal unpolarized light should have random instantaneous polarization states covering the entire Poincare sphere with equal probability. Light beams, which are otherwise known as unpolarized, do not always satisfy this criterion. Wolf’s definition of the degree of polarization cannot account for these differences. Hence, we define the degree of genuine unpolarization (DoGUP)—a metric that assigns a maximum value to the ideal unpolarization and dictates how far an unpolarized field is from the ideal case. To define the DoGUP, we introduce the polarization probability space (PPS) concept and illustrate using a two-mode Fock state.

DOI
10.1117/12.2676911

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An ideal unpolarized light should have random instantaneous polarization states covering the entire Poincare sphere with equal probability. Light beams, which are otherwise known as unpolarized, do not always satisfy this criterion. Wolf’s definition of the degree of polarization cannot account for these differences. Hence, we define the degree of genuine unpolarization (DoGUP)—a metric that assigns a maximum value to the ideal unpolarization and dictates how far an unpolarized field is from the ideal case. To define the DoGUP, we introduce the polarization probability space (PPS) concept and illustrate using a two-mode Fock state.
Quantum optics entails polarization properties that cannot be fully described by the classical Stokes parameters. In this work, we characterize the polarization of classical as well as quantum fields by means of a probability distribution on the Poincar\'e sphere. This serves to define the degree of polarization of a field state as the distance between the corresponding polarization distribution and the uniform distribution representing unpolarized light. We apply this definition to relevant quantum field states such as SU(2) coherent, squeezed, number, and phase states.
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It is well established that unpolarized light is invariant with respect to any SU(2) polarization transformation. This requirement fully characterizes the set of density matrices representing unpolarized states. We introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We use two different candidates of distance, namely the Hilbert-Schmidt and the Bures metric, showing that they induce fundamentally different degrees of polarization. We apply these notions to relevant field states and we demonstrate that they avoid some of the problems arising with the classical definition.
We present a quantum analysis of two-mode single-photon states based on the probability distributions of the optical field strength (or position quadrature) in order to describe their quantum polarization characteristics, where polarization is understood as a significative confinement of the optical field-strength values on determined regions of the two-mode optical field-strength plane. We will show that the mentioned probability distributions along with the values of quantum Stokes parameters allow us to characterize the polarization of a two-mode single-photon state, in an analogous way to the classical case, and to distinguish conceptually between mixture and partially polarized quantum states; in this way, we propose a simple definition of the quantum polarization degree based on the recent concept of distance measure to an unpolarized distribution, which gives rise to a depolarization degree equivalent to an overlapping between the probability distribution of the quantum state and a non-polarized two-mode Gaussian distribution. The work is particularly intended to university physics teachers and graduate students as well as to physicists and specialists concerned with the issue of optical polarization.
We address a quantitative determination of the degree of polarization of type-II unpolarized light via the computation of the distance between the polarization distribution and the uniform distribution associated with fully unpolarized light (i.e., type-I unpolarized light or natural light). We determine the maximum degree of polarization for type-II unpolarized light and the states reaching it. We show that the degree of polarization can be arbitrarily large, approaching complete polarization for increasing mean photon numbers.