Vortex generation in the spin-orbit interaction of a light beam propagating inside a uniaxial medium: origin and efficiency

Role of beam parameters in the spin-orbit interactions of light

We employ a full-wave theory to systematically investigate two types of spin-orbit interactions and their topological phase transitions for various light beams (e.g., Laguerre-Gaussian, Bessel, and Bessel-Gaussian beams) at optical interfaces, and explore the influence of beam parameters on the spin-Hall shift. It is demonstrated that at small-angle incidence, the beam profile and spin-Hall shift are significantly affected by the beam parameters (e.g., waist radius, radial index, azimuthal index, and cone angle), whereas at large-angle incidence, only the azimuthal index has a salient influence on them. We further find that the Bessel beam and the Gaussian-modulated ones (i.e., Laguerre-Gaussian and Bessel-Gaussian beams) have similar topological phase transition phenomena but different shifts. Quantitative dependences of beam parameters, such as waist radius, radial index, azimuthal index, and cone angle, on the shift are also presented. Our findings offer alternative degrees of freedom in controlling the topological phase transitions of light, and suggest a valuable insight for exploring the applications of SOIs of diverse light fields.

Separating radial and azimuthal polarizations of circular Airy vortex beam via uniaxial crystal

Since Ciattoni A. et al. found that a particular circularly polarized beam propagating along the optical axis in a uniaxial crystal can generate a vortex with a reversed circular polarization, numerous studies of spin-orbit coupling in this polarization conversion process have been carried out. In this paper, from another perspective rather than the circular polarization conversion, for the first time we find that radial- and azimuthal-polarization components will be separated and finally focus on two separated focus points when circular Airy vortex beams propagate in a uniaxial crystal. Both the separation of the radial- and azimuthal-polarization components in positive and negative uniaxial crystals are investigated, and the physical mechanism of this phenomenon is explained in details. Moreover, the influences of the crystal length and birefringence on the separation of the radial- and azimuthal-polarization components are also discussed. Our results could offer deeper understanding of the propagation of light beam in uniaxial crystal and facilitate the flexible applications of circular Airy vortex beams.

Controlling the spin Hall effect of grafted vortex beams propagating in uniaxial crystal

Though numerous studies of spin-orbit interaction (SOI) of light beams propagating along the optic axis of uniaxial crystals have been carried out, in previous studies, the initial input beams have cylindrical symmetry. In this case, the total system preserves cylindrical symmetry so that the output light after passing through the uniaxial crystal doesn't exhibit spin dependent symmetry breaking. Therefore, no spin Hall effect (SHE) occurs. In this paper, we investigate the SOI of a kind of novel structured light beam, grafted vortex beam (GVB) in uniaxial crystal. The cylindrical symmetry of the system is broken by the spatial phase structure of the GVB. As a result, a SHE determined by the spatial phase structure emerges. It is found that the SHE and evolution of the local angular momentum are controllable both by changing the grafted topological charge of the GVB and by employing linear electro-optic effect of the uniaxial crystal. This can open a new perspective to investigate the SHE of light beams in uniaxial crystals via constructing and manipulating the spatial structure of the input beams artificially, hence offers novel regulation capabilities of spin photon.

Enhancement of the conversion efficiency of optical spin-orbit interactions in PT symmetric systems

The optical spin-orbit interaction (SOI) caused by momentum-dependent Pancharatnam-Berry phase (PB) provides new opportunities in the development of spin-optical devices, but the relatively low conversion efficiency limits its application. Here, through rigorous full-wave analyses on it in a parity-time (PT) symmetric system with thickness less than a wavelength, we find that the conversion efficiency of the SOI can be enhanced in both transmission and reflection in a wide range of incidence angles. When the parameters of the PT symmetric system meet the requirement of coherent perfect absorbers-laser mode, the effective anisotropy between the TM and TE components (e.g., a difference of their Fresnel coefficients) within the beam will be amplified dramatically, which results in significantly enhanced conversion efficiency of SOIs (up to 10⁶). These findings offer an effective way to modulate the SOIs with an ultra-thin PT symmetric system, and may exhibit applications in spin-orbit optical devices.

Asymmetric spin splitting of Laguerre-Gaussian beams in chiral PT-symmetric metamaterials

We systematically study the spin Hall effect of light (SHEL) in chiral PT-symmetric metamaterials when Laguerre Gaussian beams (LG beams) are incident and discover that cross-polarization (r_{s p}, r_{p s}) and intrinsic orbital angular momentum (IOAM) result in an asymmetric splitting of left-spin circularly polarized (LCP) light and right-spin circularly polarized (RCP) light. Additionally, there are spin Hall shift peaks near |r_pp | ≪ |r_ss | (r_{s s} and r_{p p} are Fresnel reflection coefficients). Altering the topological charge number ℓ, the chiral parameter κ, the dimensionless frequency M, and the incident angle θ may also influence the asymmetric spin splitting and displacement peak. We believe that this research will provide new ways to manipulate and enhance the asymmetric spin splitting of light and provide new applications for spin photonic devices.

Spin-orbit coupling mediated transverse spin mode rotation in a uniaxial crystal

We demonstrate topological features in a spin-orbit coupled inhomogeneously polarized beam of light due to propagation of a linearly polarized focused Gaussian beam through a tilted-rotated (θ-ϕ) quartz crystal plate. The crystal plate is kept in a polarization interferometer, and transverse and longitudinal phase difference is introduced between the o- and e-wave-beams via (θ-ϕ) variation. The curvature in the phase difference, originating at a phase saddle, at the stem of an intensity forklet pattern, enables continuous rotation of the output two-lobe intensity pattern as a function of (θ-ϕ). The transverse spin-shift of the rotating output beam shows variation in both magnitude and slope. Such a study of exploring topological features arising due to spin-orbit coupling in simple optical systems is of fundamental interest and is expected to open up potential applications in the investigation of material anisotropy and polarization-sensitive sensing.

Propagation Characteristics of Circular Airy Vortex Beams in a Uniaxial Crystal along the Optical Axis

Circular airy vortex beams (CAVBs) have attracted much attention due to their “abruptly autofocusing” effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB’s profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane.

Tunable optical differential operation based on the cross-polarization effect at the optical interface

To achieve optical differential operation based on the cross-polarization effect at the optical interface, one just needs an optical interface composed of two uniform media with different refractive indices. When certain conditions are satisfied, the reflection co-efficient of the light field at the interface conforms to the form of the spatial spectrum transfer function required by the spatial differentiation, the spatial analog operation can be achieved with a single interface. In this paper, based on the optical differentiation of Brewster effect, we propose a tunable optical differentiation based on the cross-polarization effect at the optical interface. We theoretically derive the tunable optical differentiation and then conduct an experiment to demonstrate theoretical results. It is found that the differentiator can achieve the tunable optical differentiation by adjusting the polarization of output beam. While getting the clear edge of the object, we can also observe the imaging of the middle part to different degrees, which realizes the multi-degree of freedom imaging for the measured target. This provides a potential way to develop devices more suitable for microscopic imaging and target detection.

Spin-orbit interactions in a nonlinear medium due to a nonlinear-induced geometric phase

In general, a spin-polarized light beam cannot couple its spin angular momentum (SAM) with intrinsic orbital angular momentum (IOAM) without spin reversal. Here we find that nonlinear media can give the spin-polarized photon an IOAM, as they travel in the media due to the nonlinear susceptibility along the transmission direction, which does not require spin reversal. To characterize this SAM-to-IOAM conversion process, we establish an evolution ray equation for photons carrying IOAM by reference to the Schrödinger equation. We further reveal the inherent physics of such a phenomenon from a full-wave perspective and find that the vortex generation originates from the nonlinear-induced geometric phase.