Two methods for modeling the propagation of the coherence and polarization properties of nonparaxial fields

Multipolar hierarchy of efficient quantum polarization measures

“…However, the necessity of addressing new issues, such as highly nonparaxial fields [2], narrow-band imaging systems [3], and the recognition of associated propagation questions [4], has brought about significant modifications of this simple classical picture [5][6][7][8][9][10][11][12][13].…”

Generalized phase space representations in classical optics

“…On the other hand, for higher-dimensional problems where g spans not a curve but a surface or some higher order manifold, the condition in Eq. (15) is not sufficient to find a unique change of variables, i.e. a unique definition of the generalized Wigner function with the desired properties.…”

“…13 These functions have been shown to constitute an efficient computational scheme for the propagation of the intensity, flux, and polarization of partially coherent nonparaxial fields, 14,15 given the numerical advantages outlined in Section 6.1. Further, in addition to the local properties mentioned earlier, these generalized Wigner functions can also be used to model the propagation of the cross-spectral density.…”

Polarimetric purity and the concept of degree of polarization

“…Furthermore, P 1 takes its minimum P 1 = 0 for states whose characteristic decomposition R = I [P 2Rm + (1 − P 2 )R u−3D ] lacks the pure componentR p , whileR m retains some contribution P 2 to polarimetric purity, so that the value P 1 = 0 is not reached exclusively by fully random states (R u−3D ). It should be noted that the properties of P 1 and P 3D as candidates for the 3D degree of polarization have been studied in [7,32], while an interesting comparative study of the role of the source coherence length on the properties of P 1 and P 3D has been performed in [33].…”

“…Concerning P 3D , it contains all contributions (linear, circular, directional) to polarimetric purity and can thus be considered a proper degree of polarimetric purity. The fact that the inequality P 3D 1/2 holds for 2D states [2,8,32] is nothing else than a natural consequence of the fact that they are characterized by P d = 1. Obviously, when assumed that a given polarization state is a 2D state (P d = 1), the conventional 2D degree of polarization P 1 = P e = P 2D is a consistent and appropriate measure of the contributions to polarimetric purity, beyond the one due to the deterministic directionality.…”