Spin Hall Effect Of Light In A Multilayer-Medium Structure

The spin Hall effect of light (SHEL) is a new optical effect discovered in recentyears, which paves a new way to manipulate photon and has important applications innano-optics, quantum information, and semiconductor physics. The SHEL alsoprovides an indirect evidence of the intrinsic SHE in a diversity of physical systems.Therefore, the SHEL has drawn considerable attention. The effect shows that photonswith opposite spin angular momenta will deviate from each other perpendicular to thedirection of refractive index gradient because of the photon spin-orbit interactions,leading to a spin-dependent splitting. This paper based on the theory of light waves,taking three-layer medium for example, reveals the phenomenon and factors oftransverse shift and the angular shift that resulted from the SHEL in amultilayer-medium structure. The main work is summarized as follows:First, reviewing the light wave propagation characteristics in the medium, weintroduce the reflection and refraction of light beam in layered media, and discuss themonochromatic plane waves of reflection and transmission’s rule in single mediumand multi-layer medium respectively according to the Maxwell’s equations andboundary conditions of the electromagnetic fields. Starting from the plane angularspectrum theory, we build a three dimensional transmission model of the Gaussianbeams passing through a prim-air-prim barrier. It would provide the basis for studyingthe transverse shift and the angular shift of the SHEL in a multilayer-mediumstructure.Second, based on the transmission model of the Gaussian beams in thethree-layer medium, we analyze the transverse shift of the SHEL and reveal thequalitative influence of thickness of the air gap, refractive index gradient, polarizationstate of light and incident angel. The results indicate that the transverse shift increasesalong with the thickness of the air gap in a certain range. It is clear that the SHE in theGaussian beam can be evidently enhanced via multilayer-layer medium. In thereflected light field, the transverse shift of circular polarized light is larger than theother elliptical polarization light, and the transverse shift increases with thepolarization parameters rising, but the refraction of light field is just the opposite. Fora certain circularly polarized component, the magnitude and direction of thetransverse shift can be modulated by altering the refractive index gradient associated with the two prisms and the incident angel. Based on these theories of spin Hall effectof light，it would provide the theoretical basis for regulating and enhancing the spinHall effect of light.Third, we analyze the angular shift of the SHEL and reveal the relation ofpolarization state of light, refractive index gradient, reflection coefficient andrefractive coefficient upon the angular shift. The study shows that for a linearly andelliptically polarized light beam, the centroid exhibits a transverse angular shift in thereflective light field and refraction light field. Whether the angular shift is positive ornegative depends on the reflection coefficient and refractive coefficient. However, thetransverse angular shift would disappear when the incident light beam is circularlypolarized. The refractive index gradient regulating the transverse angular shift shouldbe based on the incident angel. In addition, according to the law of conservation ofenergy, the angular shift and transverse shift are governed by the total linearmomentum conservation law and the total angular momentum conservation law,respectively. Exploring the transverse angular shift will further provide the theoreticalfoundation to amend the reflection law and Snell’s law. And it also provides referencevalue on how to regulate and enhance the spin Hall effect of light.