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

Wenguo Zhu,Zhe Chen,Jianhui Yu,Jun Zhang,Heyuan Guan,Huihui Lu,Jieyuan Tang,Yunhan Luo

doi:10.1038/s41598-017-01323-0

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 w0/2. 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 w0. These findings provide a deeper insight into the optical spin splitting phenomena and thereby facilitate the development of spin-based applications.

Highlights

As is well known, when a light beam is reflected from or transmitted through an interface between two different media, its two opposite spin components may separate in directions parallel and perpendicular to the plane of incidence, i.e., so-called the in-plane and out-of-plane spin splitting (IPSS and OPSS)[1,2,3]
At the Brewster angle, the IPSS can be approximately close to the incident beam waist w0, which is proven to be the upper limit of the IPSS
We further study the IPSSs in two other angular ranges: when the incident angle is either slightly smaller or larger than the critical angle, which is the angle of incidence for which the angle of refraction is 90°

Summary

Introduction

As is well known, when a light beam is reflected from or transmitted through an interface between two different media, its two opposite spin components may separate in directions parallel and perpendicular to the plane of incidence, i.e., so-called the in-plane and out-of-plane spin splitting (IPSS and OPSS)[1,2,3]. It has been demonstrated that the IPSS and OPSS can be considered as analogous but reverse effects[3] Both of them can be rewritten as a combination of a zr- (propagation axis) independent term and a zr-dependent term, which associate with the spatial and angular spin splitting, respectively[1]. The OPSS can be enhanced when a Gaussian beam is reflected by an air-glass interface near the Brewster angle[12, 13]. Large spin splitting and high energy reflectivity can be obtained simultaneously In the latter angular range, asymmetric spin splitting may occur, i.e., the displacement of one of the spin component is relatively small, while the displacement of the other component can be up to w0/2. The schematic of the generation of IPSS is shown, where a Gaussian beam is launched onto the glass-air interface with an incident angle of θi. The relationship between the angular spectra of the reflected and incident beams under the paraxial condition has been derived in ref

Methods

Results

Conclusion