Degree of Polarization in Quantum Optics through second generalization of Intensity

TL;DR

This paper introduces a new quantum definition of the degree of polarization that resolves inaccuracies in previous definitions, especially for intense optical fields, and shows its dependence on photon number.

Contribution

It proposes a second generalization of intensity to define quantum polarization, improving accuracy for various optical fields and establishing its relation to traditional measures.

Findings

New definition aligns with traditional degree for weak fields

Disagrees significantly for intense fields

Polarization depends on average photon number

Abstract

Classical definition of degree of polarization is expressed in quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as first generalization of Intensity. This definition assigns inaccurately the unpolarized status to some typical optical fields such as amplitude coherent phase randomized and hidden polarized, which are not truly unpolarized light. The apparent paradoxical trait is circumvented by proposing a new definition of degree of polarization in Quantum Optics through second generalization of Intensity. The correspondence of new degree of polarization to usual degree of polarization in Quantum Optics is established. It is seen that the two definitions disagree significantly for intense optical fields but coincides for weak light (thermal light) or for optical fields in which occupancy of photons in orthogonal mode is very feeble. Our proposed definition of degree of polarization, similar to other proposals in literature, reveals an interesting feature that states of polarization of optical quantum fields depend upon the average photons (intensity) present therein.