Spin Hall Effect under Arbitrarily Polarized or Unpolarized Light

Abstract

The spin Hall effect of light (SHEL), which refers to a spin-dependent and transverse splitting of refraction and reflection phenomena, inherently depends on the polarization states of incidence. Most previous research has focused on horizontally or vertically polarized incidence, in which the analytic expressions of the shift are well-formulated and the SHEL appears symmetrically in both shift and intensity. However, the SHEL under arbitrarily polarized or unpolarized incidence has remained largely unexplored. Here, it is proved analytically and numerically that the SHEL is independent of the incident polarization and is symmetrical in shift if the two linear polarization states have the same Fresnel coefficients. Moreover, under an unpolarized incidence composed of a large number of completely random polarization states, the reflected beam is split in half into two circularly polarized components that undergo the same amount of splitting but in opposite directions. This result demonstrates that under unpolarized incidence, the SHEL occurs exactly as it does under horizontally or vertically polarized incidence. It is believed that the incident-polarization-independent SHEL can broaden the applicability of the SHEL to cover optical systems in which the polarization is unspecified.

Tunable metasurfaces towards versatile metalenses and metaholograms: a review

“…10,11 Resonant effects such as plasmonic resonance, [12][13][14][15] Mie resonance, 16,17 and Fabry-Pérot resonance 18,19 have also been exploited. By exploiting these resources, optical elements can be highly miniaturized and various optical applications have been implemented, such as beam splitters, [20][21][22] absorbers, [23][24][25][26][27][28][29] metalenses, 30,31 metaholograms, [32][33][34][35][36][37][38][39][40] selective thermal emitters, [41][42][43] detecting devices, [44][45][46] and structural color. [47][48][49][50][51][52] The functionality and efficiency of metasurfaces have been continuously increased by improving the methods to design meta-atoms, and the development of their material composition.…”

Three-dimensional artificial chirality towards low-cost and ultra-sensitive enantioselective sensing

“…91 These applications can be further improved by analysis of current metasurface and metamaterials that use various optical responses such as Mie-resonance, 92–96 geometric phases, 97,98 nanogap plasmonics, 99,100 nonlinear optics, 101 Bragg-reflection, 102,103 and spin Hall effect. 104–108 Future research could also focus on how tuneable chirality and controllable chiroptical properties can be produced so that the chiral structure is not fixed and the degrees of freedom can be increased. 109,110…”

Incident‐Polarization‐Independent Spin Hall Effect of Light Reaching Half Beam Waist

“…Whereas the previous condition of r s = r p is obtained under the assumption that the wave vector deflections are much smaller than the wave number (k x,y ≪ k 0 ) and is valid under the large beam waist condition (Equation (1)), [10] the only assumption underlying the theoretical proof here is the first-order Taylor expansion (Equation ( 4)). Given that the higher-order terms (n ≥ 2) in Equation ( 4) are on the order of (k 0 w 0 ) −2n and the minimum k 0 w 0 is ≈ 1.22 × 2𝜋 because of the diffraction limit, the higher-order terms have negligible effects (< 2.9 × 10 −4 ) on the SHEL, regardless of the properties of incident light.…”

“…Thus, a medium that supports 𝜀 2x 𝜀 2y = 𝜀 2 1 satisfies r s = r p under normal incidence, regardless of 𝜀 2z (Figure 2c,d). Second, taking the first-order derivative of Equation (10) with respect to 𝜃 i proves that ̇rs = ̇rp = 0 for any permittivity at 𝜃 i = 0 • . Thus, ̇rs = ̇rp holds automatically under normal incidence, which is also confirmed by numerical results (Figure 2e,f).…”

“…It has been reported recently that an interface that has the same reflection coefficients, that is, r s = r p , where subscripts "s" and "p" denote incident polarization states, supports the incident-polarization-independent SHEL for the reflected beam, or equivalently transmission coefficients t s = −t p for the refracted beam. [10] The spin Hall shifts at such an interface are degenerate under incidences that have any polarization state (Figure 1a,b). One assumption that underlies the theoretical demonstration is that the beam waist w 0 is much larger than wavelength 𝜆, satisfying…”