The upper limit of the in-plane spin splitting of Gaussian beam reflected from a glass-air interface

Abstract

Optical spin splitting has a promising prospect in quantum information and precision metrology. Since it is typically small, many efforts have been devoted to its enhancement. However, the upper limit of optical spin splitting remains uninvestigated. Here, we investigate systematically the in-plane spin splitting of a Gaussian beam reflected from a glass-air interface and find that the spin splitting can be enhanced in three different incident angular ranges: around the Brewster angle, slightly smaller than and larger than the critical angle for total reflection. Within the first angular range, the reflected beam can undergo giant spin splitting but suffers from low energy reflectivity. In the second range, however, a large spin splitting and high energy reflectivity can be achieved simultaneously. The spin splitting becomes asymmetrical within the last angular range, and the displacement of one spin component can be up to half of incident beam waist w 0/2. Of all the incident angles, the spin splitting reaches its maximum at Brewster angle. This maximum splitting increases with the refractive index of the “glass” prism, eventually approaching an upper limit of w 0. These findings provide a deeper insight into the optical spin splitting phenomena and thereby facilitate the development of spin-based applications.

Spin Hall effect of light under arbitrarily polarized and unpolarized light

“…Another important attribute of the SHEL that originates from r s = r p is that the splitting occurs symmetrically in shift (|δ + | = |δ − |) under an arbitrarily polarized incidence. This result is opposed to the conventional wisdom that a circularly or elliptically polarized incidence is split asymmetrically into LCP and RCP [26][27][28][29][30] .…”

“…A variety of nanophotonic devices and metamaterials have been proposed to enlarge the spin-dependent shift [11][12][13][14][15][16][17][18] , to increase the efficiency 19 , and to exploit the SHEL to identify geometric parameters 20,21 , electric and magnetic properties 22,23 , and chemical reactions 24,25 with high precision. Except for the studies of asymmetric SHEL, in which the magnitude of the shift is spin-dependent [26][27][28][29][30] , most previous studies have focused only on horizontally or vertically polarized incidence. By symmetry, a horizontally or vertically polarized light is split at the optical interface into equal amplitudes of left circularly polarized (LCP) and right circularly polarized (RCP) beams, which shift by the same magnitude but with opposite signs 6 .…”

Spin Hall Effect under Arbitrarily Polarized or Unpolarized Light

“…This result is opposed to the conventional wisdom that a circularly or elliptically polarized incidence is split asymmetrically into LCP and RCP. [ 27–31 ]…”

“…This result is opposed to the conventional wisdom that a circularly or elliptically polarized incidence is split asymmetrically into LCP and RCP. [27][28][29][30][31] Although the condition of r s = r p seems to imply the polarization-independent reflection, it is not true. Instead, r s = r p is associated with the 𝜋 phase shift between the electric fields of sand p-polarized reflected beam because of the sign convention.…”

“…A variety of nanophotonic devices and metamaterials have been proposed to enlarge the spindependent shift, [11][12][13][14][15][16][17][18] to increase the efficiency, [19] and to exploit the SHEL to identify geometric, [20,21] electric, [22] and magnetic [23] parameters and chemical reactions [24][25][26] with high precision. Except for the studies of asymmetric SHEL, [27][28][29][30][31] most previous studies have focused only on horizontally or vertically polarized incidence. By symmetry, a horizontally or vertically polarized light is split at the optical interface into equal amplitudes of left circularly polarized (LCP) and right circularly polarized (RCP) beams, which shift by the same magnitude but with opposite signs.…”