Goos-Hänchen and Imbert-Fedorov shifts of vortex beams at air–left-handed-material interfaces

Abstract

In this paper, we present a systematic study of beam shifts and angular momenta of paraxial vortex beams at air-left-handed-material (LHM) interfaces. It is shown that, compared to their counterparts at air-right-handedmaterial (RHM) interfaces, the spatial Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts remain the same, while the angular GH and IF shifts are reversed at air-LHM interfaces. The spatial and angular shifts of paraxial vortex beams have their respective origins in transverse angular momenta and transverse linear momenta. The spatial GH and IF shifts remain unreversed as a result of both reversions of transverse angular momenta and z-component linear momentum, while the angular GH and IF shifts are reversed because the z-component linear momentum is reversed and the transverse linear momenta are unreversed at air-LHM interfaces. In addition, we perform a quantitative analysis on spin-orbit angular momentum conversion and orbit-orbit angular momentum conversion, which further helps us understand the essence of vortex beam shifts at air-LHM interfaces and their fundamental distinctions from those at air-RHM interfaces.

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

“…If the incident beam is a paraxial vortex one, the displacements of the RCP and LCP components of the reflected beam along the x r direction [Eq. ( 2 )] will contain two additional terms resulting respectively from the vortex-induced spatial GH effect and the coupling between the spin dependent out-of-plane angular shifts and the complex vortex structure 1 , 23 . They are both linearly proportional to the vortex charge 23 , 24 .…”

“…( 2 )] will contain two additional terms resulting respectively from the vortex-induced spatial GH effect and the coupling between the spin dependent out-of-plane angular shifts and the complex vortex structure 1 , 23 . They are both linearly proportional to the vortex charge 23 , 24 . The vortex-induced spatial GH shift is spin independent, and thus moves the centroids of the RCP and LCP field components together while not changing the value of the IPSS 23 .…”

“…They are both linearly proportional to the vortex charge 23 , 24 . The vortex-induced spatial GH shift is spin independent, and thus moves the centroids of the RCP and LCP field components together while not changing the value of the IPSS 23 . The additional spin dependent term, however, only exists for total internal reflection, since the spin dependent out-of-plane angular shift vanishes when the Fresnel coefficients for the s and p waves are both real 25 .…”

Impact of Polarization Phase of Incident Light on In-Plane Spin Splitting of Reflected Beam

“…here, σ = ±1 respectively represent the left and right spin components. Substituting (4) into the following centroid formalism [32]:…”

Interference effect on Goos–Hänchen shifts of anisotropic medium interface

“…It affects the modes of optical waveguides and microcavities [9][10][11][12][13], and offers potential for the design of new optical sensors [14,15]. Consequently, understanding the mechanisms underlying GH displacement generation [16][17][18][19][20][21][22][23][24][25][26][27][28] and developing techniques for manipulating GH displacement [29][30][31][32][33][34][35][36] have become significant research pursuits. Some representative work on GH shift is as follows: (1) Li has proposed a unified theory describing the GH and the Imbert-Fedorov (IF) displacement by representing the vector angular spectrum of the three-dimensional beam in terms of two forms of angular spectrum composed of two orthogonal polarization components [17].…”