Purity of 3D polarization

Abstract

Measures of purity for 3D partially polarized fields, and in particular, the separation into circularly and linearly polarized contributions, are reexamined, and a new degree of total linear polarization introduced. Explicit expressions for the characteristic decomposition in terms of coherency matrix elements are presented, including the special case of an intrinsic coherency matrix. Parameterization of the coherency matrix in terms of ellipticity, and the directions of the ellipse normal and major axis are investigated. Phase consistency is discussed. A comprehensive collection of results regarding intrinsic polarization properties is presented.

Dual Approaches to Express the Generalized Degree of Polarimetric Purity

“…Therefore, P 3s provides fractional contributions from both P l and P d (i.e., polarization fraction due to mixed states), whereas P 2s provides pure contribution from P l . Using the derivation proposed in Sheppard et al, [17], we can show that,…”

“…One can show that P ns is invariant under unitary transformation. In particular, P 3s can be considered as the degree of polarization of the real part of the partially polarized 3 × 3 intrinsic coherency matrix, Re(Φ) [17]. Moreover, it is interesting to note that we can relate the degree of shearing to the component of polarimetric purity (CPP) proposed by Gil [18,19] i.e., the degree of linear polarization, P l , for 2D and 3D cases, and the degree of directionality, P d , for the 3D case as,…”

“…where P L is defined in [17] as the degree of total linear polarization, i.e., the contribution from both the purely polarized and mixed state. Now, expanding P ns , and P c in the expression of P nD given in equation (16) in terms of the Frobenius norm and the matrix trace, we find that,…”

Correlation Optics, Coherence and Optical Singularities: Basic Concepts and Practical Applications

“…Recent advances in the areas of nanophotonics and near-field optics stipulate growing interest to the polarimetric structure of 3D light fields [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. An interesting fact is that any state of polarization of the 3D fields can be represented in terms of regular and irregular components [34][35][36].…”

“…An extension of this approach involves the assessment of purity for partially polarized fields in three dimensions [37] with separation of the circularly-and linearly-polarized contributions, which is proposed to be described via the coherency-matrix elements parameterized in terms of polarization ellipticity, regarding the intrinsic polarization properties of the field. The similar concepts appear to be fruitful for purposeful formation of complex optical fields with inhomogeneous 3D polarization structures [38,39].…”