Cross-polarization Characteristics In Photonic Spin Hall Effect

While a linear polarized beam propagates through medium with refractive index gradient, photons with opposite spin direction will drift apart along the direction perpendicular to gradient of refractive index. It leads to the beam splitting into two circularly polarized components with opposite spin direction. Circularly polarized component lay separately on each side of the transfer beam’s cross section. This phenomenon is called the photonic spin Hall effect. Since photonic spin Hall effect can be an analogy of electronic spin Hall effect, and electron spin has been researched and applied in many important fields, the photonic spin Hall effect also gets more and more attention. In this paper, based on the paraxial Gaussian beam transmission model, we analyze characteristic of cross polarization effect’s vector field. Revealing the inner link between cross polarization effect and photonic spin Hall effect, put forward the method of using cross polarization to control the photonic spin Hall effect. Main work done is as follows:First, light polarization theory is the foundation of research in cross polarization. This paper reviews the concept of light polarization and some typical polarization states of light, introduces an optical device for changing the state of light polarization—wave plate. Reviewing the propagation equation of Gaussian beam and physical meanings of its commonly used parameters, and the paraxial Gaussian beam propagation model is introduced. We have a brief introduction about the derivation process of Fresnel formula, in order to facilitate subsequent analysis on Fresnel coefficient’s influence on photonic spin Hall effect.Second, based on paraxial transmission model and the relation between angular spectrum of reflected light and incident light, we deduce the explicit expression of angular spectrum of reflected light under parallel polarized incident light and vertical polarized incident light. We deduce field expression of reflected light through its angular spectrum. We simulate the cross polarization effect of reflected light, and try to explain new ways to regulate the spin Hall effect of reflected light through the cross polarization theory. Results show that either parallel or vertical polarized incident light, reflected light contains cross polarization component, with the incidence angle gradually increases near the Brewster angle, cross polarization effect will gradually strengthen. The cross polarization effect of parallel polarized incident light is much intense than the condition when incident light is with vertical polarization. The cross polarization effect of reflected light is proportional to rs/rp under parallel polarized incident light, cross polarization effect of reflected light is proportional to rp/rs under vertical polarized incident light. Due to the ratio of the reflection coefficient is related to the intensity of spin Hall effect of reflected light, it can be concluded that the cross polarization effect has some internal links with the photonic spin Hall effect. We get enhanced spin splitting and enhanced cross polarization effect by increasing incidence angle, and we have the theory tested with weak measurements.Third, we analyze the vector field of refracted light and its cross polarization effect under the condition of parallel polarized incident light and vertical polarized incident light. Similar to the process of analyzing reflected light, we come to a conclusion that either parallel or vertical polarized incident light, refracted light contains cross polarization component. As the incidence angle increases gradually, cross polarization effect will be gradually strengthened. Due to the spin Hall effect of refracted light is proportional to the cross polarization effect, we can properly increases the incidence angle to enhance cross polarization of refracted light, then obtain enhanced photonic spin Hall effect.