Study Of Photonic Orbital Hall Effect Of Vortex Beam

The reflection of light beam at a plane dielectric interface is one of the most important optical processes.The interaction of light beam with an interface is usually described by the Snell's law and Fresnel formulae,which is belong to the geometrical-optics.However,the real optical beam which has a finite width can be seen as the superposition of many plane-wave components with different propagation direction.That is to say,the real beam contains some finite spectral components corresponding to the different reflection coefficients.Therefore,there exists some tiny shifts called spatial and angular displacements in reflection.The transverse and in-plane displacements are Imbert-Fedorov and Goos-Hanchen shifts,respectively.The photonic spin Hall effect(SHE)can be regarded as a direct optical analogy of the SHE in electronic systems where the spin electrons and electric potential are replaced by the spin photon and refractive index gradient,respectively.The photonic SHE manifests itself as the transverse spin-dependent splitting when the linear polarization beam(consists of left-and right-hand circular polarization components)incidents at the medium interface.In fact,the photonic SHE is sometimes referred to the Imbert-Fedorov shifts which consider the incident beam with circular polarization.As we all know,the basic reason of the photonic SHE is spin-orbit interaction.It is also important to consider the photonic SHE of high-order beam with intrinsic orbital angular momentum(OAM),which will bring the orbital-dependent spatial shifts called the photonic orbital Hall effect(OHE).Vortex beam itself carries the spiral phase and has an unique optical field distribution.The special of vortex beam are the phase wave front structure and the OAM 1h.The special phase wave front structure has great significance in investigating the generated,propagation,interaction of vortex beam,which has potential application.As a degree of freedom,the OAM has application value in optical manipulation,high-resolution imaging,communications,quantum information and so on.With deep research,its importance will be widely expanded to the other areas.This paper has investigated the photonic OHE of vortex beam carrying intrinsic OAM.Our innovations are described as follows:(i)Based on the angular spectrum theory,we establish a propagation model for vortex beam in reflection at an air-glass interface in the paraxial approximation,and investigate the cross polarization effects.When the horizontal polarization vortex beam is incident at different angles,the cross polarization component of the reflected beam shows a double-peak intensity distribution which is similar to the first-order Hermite-Gaussian mode.The distribution of horizontal polarization component is similar to that of the incident beam,and will show a double-peak intensity distribution which is perpendicular to the distribution of cross polarization components at the Brewster incidence.For the incident beam with arbitrary linear polarizations,we find that the polarized direction of cross polarization component is not perpendicular to the incident polarized direction,but exhibits an interesting rotational characteristic.The physical nature of this phenomenon is attributed to the different reflection coefficients of parallel and perpendicular polarizations.Experimental results agree well with our theoretical analysis.(?)Basing on the angular spectrum theory,we study that the OAM steer asymmetric splitting in photonic SHE.Taking the beam reflection at an air-glass interface for example,a propagation model describing the SHE of vortex beam is established,which clearly shows that the transverse displacements of left-handed and right-handed circular polarization components are asymmetric with regard to the incident plane.Particularly,the displacement magnitudes and directions of the two spin components are significantly affected by the topological charge of vortex beam.The asymmetric splitting is steered by the OAM which can be regarded as integral transverse shifts of two spin components for the incident plane,this integral transverse shifts corresponds to Imbert-Fedorov effects of linear polarization vortex beam.The physics nature of these phenomenon are attributable to the spin-orbit interaction and orbit-orbit conversion at the interface,and this is little different from its symmetric counterpart for Gauss beams.The results suggest that the OAM of light provides an alternative degree of freedom for tuning the photonic SHE.(?)We examine the orbit-orbit interaction when a paraxial beam with intrinsic OAM reflects at an air-glass interface.The orbital-dependent splitting of the beam intensity distribution arises due to the interaction between intrinsic OAM and extrinsic OAM.In addition,we find that the beam centroid shows an orbital-dependent rotation when seen along the propagation axis.However,the motion of beam centroid related to orbit-orbit interaction undergoes a straight line trajectory with a small angle inclining from the propagation axis.Similarly to the developed earlier spin-dependent splitting in photonic SHE,the orbital-dependent splitting would leads to the photonic OHE.