Dimensionality of random light fields

Abstract

Background:The spectral polarization state and dimensionality of random light are important concepts in modern optical physics and photonics. Methods: By use of space-frequency domain coherence theory, we establish a rigorous classification for the electricfield vector to oscillate in one, two, or three spatial dimensions. Results: We also introduce a new measure, the polarimetric dimension, to quantify the dimensional character of light. The formalism is utilized to show that polarized three-dimensional light does not exist, while an evanescent wave generated in total internal reflection generally is a genuine three-dimensional light field. Conclusions:The framework we construct advances the polarization theory of random light and it could be beneficial for near-field optics and polarization-sensitive applications involving complex-structured light fields.

Polarimetric nonregularity of evanescent waves

“…The rapid progress in nano-optics [1] and ever-growing interest toward complex structured light [2] have witnessed the need for a full three-dimensional (3D) treatment of polarization [3][4][5][6][7][8][9][10]. In particular, whereas for two-dimensional (2D) light, such as directional beams, the polarization ellipse is restricted to a plane, evanescent waves [11,12], optical surface fields [13,14], and tightly focused light [15][16][17] encompass 3D polarization states with the electric field fluctuating in three orthogonal directions.…”

“…The incoming wave, carrying both an s-polarized and a p-polarized part, hits the boundary at the angle of incidence θ. The electric field of the transmitted wave in medium 2 then reads, in Cartesian coordinates, as [9,11,12] Er, ω…”

Sets of orthogonal three-dimensional polarization states and their physical interpretation

“…By analyzing Eqs. (20) and (13), it turns out that a = 0 corresponds either to (1) |χ 1 | = π/4 (η 1 circularly polarized, should be analyzed separately); (2) |θ i | = π/2 and t 2 χ i = −1 (unphysical), or (3) φ i = 0, π (already studied). Thus, for the sake of consistency of Eq.…”

“…Polarization is a fundamental property of light and plays a vital role in understanding and exploiting electromagnetic interactions of diverse physical nature [1,2]. The polarization properties of random light fields, in their most general threedimensional (3D) representation, have lately been a subject of increasing interest within modern optical physics because of the rapid progress in nonparaxial optics and nanophotonics [3][4][5][6][7][8][9][10][11][12][13]. The 3D character of random light is especially encountered in the context of high numerical aperture systems [14,15], optical evanescent waves [16,17], and plasmonic surface fields [18,19], highlighting the necessity to develop appropriate theoretical methods for the treatment and physical interpretation of general 3D states of polarization.…”

Measurement of intensity and polarization beatings in the interference of independent optical fields

“…The traditional concepts cover the Jones vector, Stokes parameters, Poincaré sphere, Mueller matrices, and degree of polarization, for instance [3,4]. Concerning the highly nonparaxial fields, possibly with an evanescent-wave contribution, several novel polarimetric descriptors such as the polarimetric dimension [5], degree of intensity anisotropy [6], and nonregularity [7] have recently been introduced. Interference is another fundamental attribute of light with important applications, e.g., in optical communication and information processing [3], laser cavity design [8], correlation imaging [9], spectroscopy [10], and metrology [11].…”