Spin-induced angular momentum switching

Manipulation of optical orbit-induced localized spin angular momentum using the periodic edge dislocation

Orbit-induced localized spin angular momentum (OILS) has recently garnered significant attention. This paper introduces periodic edge dislocation (PED) into the tight focusing system. The study delves into the tight focusing characteristics of the radially polarized vortex plane beam with PED, demonstrating that PED serves as a straightforward and effective means of manipulating OILS, especially when both the orbital angular momentum and the polarization of the incident beam are fixed. Our findings indicate that the longitudinal OILS reaches its maximum when the difference between the period of PED and the vortex topological charge is equal to 1. Conversely, when the difference is 0, the transverse OILS reaches its maximum, while the longitudinal OILS reaches its minimum. Similar patterns are also observed in linearly polarized vortex beams. This research proposes a simple and practical way to control OILS, contributing to our understanding of optical orbit-spin coupling.

Polarization-insensitive wavefront shaping using the Pancharatnam-Berry phase

We discuss a method to achieve a polarization-independent modulation of the electromagnetic wavefront based upon the Pancharatnam-Berry phase. When the length of the twisted anisotropic material is equal to the birefringence length (i.e., full-wave plate length), a phase delay proportional to the squared transverse derivative of the twisting angle appears. Physically, the phase delay is associated with the Kapitza effect applied to the Pancharatnam-Berry phase. Our theoretical results are confirmed by finite-difference time-domain (FDTD)-based numerical simulations.

Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams

Optical spin-orbit interaction has gained much interest recently due to its universality and importance in modern photonics. In this Letter, we theoretically demonstrate that orbit-induced localized spin angular momentum (SAM) conversion can occur in the tight focusing of spin-free linearly polarized vortex beams (LPVBs). By analysis of the polarization states that are associated with the SAM density, we attribute the occurrence of such a conversion to the helical-phase-induced change of local polarization states in the focused field. In the local SAM, density can be further regulated by altering the sign and value of the orbital angular momentum in the incident LPVBs, as well as their polarization orientations. This Letter is expected to advance our understanding of optical spin-orbit coupling and benefit applications of optical microscopy and trapping.

Paraxial light beams in structured anisotropic media

We discuss the paraxial approximation for optical waves propagating in a uniaxial anisotropic medium inhomogeneously twisted on the plane normal to the wave vector, with the latter being parallel to one of the two principal axes normal to the optic axis. Such geometry implies a continuous power transfer between the ordinary and extraordinary components, regardless of the input beam polarization. We pinpoint that this peculiar feature, generalizable to any inhomogeneous linear birefringent material, strongly affects the application of the paraxial approximation due to the simultaneous presence of two different phase velocities. We eventually show that a local coordinate transformation permits a correct application of the paraxial approximation.

Geometric phase Doppler effect: when structured light meets rotating structured materials

We examine the geometric phase Doppler effect that appears when a structured light interacts with a rotating structured material. In our scheme the structured light possesses a vortex phase and the structured material works as an inhomogeneous anisotropic plate. We show that the Doppler effect manifests itself as a frequency shift which can be interpreted in terms of a dynamic evolution of Pancharatnam-Berry phase on the hybrid-order Poincaré sphere. The frequency shift induced by the change rate of Pancharatnam-Berry phase with time is derived from both the Jones matrix calculations and the theory of the hybrid-order Poincaré sphere. Unlike the conventional rotational Doppler effect, the frequency shift is proportional to the variation of total angular momentum of light beam, irrespective of the orbital angular momentum of input beams.

Propagation model for vector beams generated by metasurfaces

A propagation model of vector beams generated by metasurfaces based on vector diffraction theory is established theoretically and verified experimentally. Considering the Pancharatnam-Berry phase introduced by the metasurface, analytical forms of vector beams for arbitrary incident polarization and topological charge of metasurfaces are found in the Fresnel and Fraunhofer diffraction regions, respectively. The complex amplitude of the resultant vector beam can be described in terms of a confluent hypergeometric function, with an intensity profile that manifests concentric rings in the Fresnel region and a single ring in the Fraunhofer one. Fraunhofer diffraction provides a method to create vector beams with simultaneously high purity and modal power. Further experiments verify the theoretical results.

Spin-orbit interactions of a Gaussian light propagating in biaxial crystals

Based on the plane-wave angular spectrum representation, we derive a formal expression for any light fields propagating in biaxial crystals, and particularly, present an effective numerical method to investigate the propagation behavior for a Gaussian light beam. Unlike uniaxial crystals, we observe the intriguing formation, repulsion and disappearance of vortex pairs, as the refractive indices deviate slightly and gradually from the uniaxial limit. In the Minkowski angular momentum picture, we also investigate the orbital angular momentum dynamics for both left- and right-handed circularly polarized components. Of further interest is the revelation of nonconservation of the angular momentum within the light field during the spin-orbit interactions, and the optical torque per photon that the light exerts on the biaxial crystal is quantified. We interpret these interesting phenomena by the weakly broken rotational invariance of biaxial crystals. The self-consistency of our theory is confirmed by the balance equation describing the conservation law of total angular momentum of filed and crystal in the Minkowski picture.

Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems

We present a general theory of spin-to-orbital angular momentum (AM) conversion of light in focusing, scattering, and imaging optical systems. Our theory employs universal geometric transformations of non-paraxial optical fields in such systems and allows for direct calculation and comparison of the AM conversion efficiency in different physical settings. Observations of the AM conversions using local intensity distributions and far-field polarimetric measurements are discussed.

Optical nanoprobing via spin-orbit interaction of light

We show, both theoretically and experimentally, that high-numerical-aperture (NA) optical microscopy is accompanied by strong spin-orbit interaction of light, which translates fine information about the specimen to the polarization degrees of freedom of light. An 80 nm gold nanoparticle scattering the light in the focus of a high-NA objective generates angular momentum conversion, which is seen as a nonuniform polarization distribution at the exit pupil. We demonstrate remarkable sensitivity of the effect to the position of the nanoparticle: Its subwavelength displacement produces the giant spin-Hall effect, i.e., macroseparation of spins in the outgoing light. This brings forth a far-field optical nanoprobing technique based on the spin-orbit interaction of light.

Structure of the dielectric tensor in nematic liquid crystals with topological charge

A q-plate is a stratified medium composed of a uniaxial nematic liquid crystal with an inhomogeneous orientation of the optical axis possessing a topological charge q, which looks promising as a switching device. This work reports an approach to diagonalizing the dielectric tensor in q-plates, giving a detailed study of nontrivial tensor coordinate transformations. The relationship between the diagonal dielectric tensor and the topological charge of the plate is established. From that, the dielectric tensor for a given q-plate can be explicitly calculated in a convenient frame, and hence the field propagation equations can be derived. These studies establish a theoretical basis that could further deepen the research on these particular structures for nonconventional manipulation of the light.

Nondiffracting wave properties in radially and azimuthally symmetric optical axis phase plates

A wave propagation analysis carried out in two kinds of q-plates having topological unit charge (1-plates), one plate with a radial orientation of the optical axis and the other with an azimuthal one, reveals that these devices admit nondiffracting Bessel beams as exact solutions of the vector Helmholtz's equation. The phase shifts between the ordinary and the extraordinary waves in both structures were found to be different. The polarization-scrambling term in the Helmholtz equation is responsible for such differences, emphasizing that this term cannot be dropped in radial plates, contrary to the azimuthal case. A phase shift analysis suggests that these plates are relevant for the control of nonconventional polarization states of light. In this way, a novel redistribution of the spin-orbital angular momentum of these nondiffracting beams passing by the 1-plate is demonstrated, which could be useful for applications in classic and quantum regimes.

Polarization control of single photon quantum orbital angular momentum states

The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum m degree of freedom within the subspaces of |m| = 2h and |m| = 4h per photon.

Quantum information transfer from spin to orbital angular momentum of photons

The optical "spin-orbit" coupling occurring in a suitably patterned nonuniform birefringent plate known as a "q plate" allows entangling the polarization of a single photon with its orbital angular momentum (OAM). This process, in turn, can be exploited for building a bidirectional "spin-OAM interface," capable of transposing the quantum information from the spin to the OAM degree of freedom of photons and vice versa. Here, we experimentally demonstrate this process by single-photon quantum tomographic analysis. Moreover, we show that two-photon quantum correlations such as those resulting from coalescence interference can be successfully transferred into the OAM degree of freedom.

Light propagation in a birefringent plate with topological charge

We calculated the Fresnel paraxial propagator in a birefringent plate having topological charge q at its center, named "q-plate." We studied the change of the beam transverse profile when it traverses the plate. An analytical closed form of the beam profile propagating in the q-plate can be found for many important specific input beam profiles. We paid particular attention to the plate having a topological unit charge and found that if small losses due to reflection, absorption, and scattering are neglected, the plate can convert the photon spin into orbital angular momentum with up to 100% efficiency provided the thickness of the plate is less than the Rayleigh range of the incident beam.

Electrically tunable and spin-dependent integer or noninteger orbital angular momentum generator

We propose an orbital angular momentum (OAM) generator consisting of two conjugated electro-optic spiral phase plates with two longitudinal electrodes, which enables us to realize the electrically tunable generation of integer or noninteger optical vortices according to the input photon's polarization. We demonstrate that such an OAM generator allows the electro-optic management of the multidimensional OAM vector states, and it would have potential applications in quantum information processing system.

Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam

We demonstrate that the conversion of spin-to-orbital angular momentum in a focused vectorial light beam can be forbidden or enhanced by the electric-field-erased or increased spatial anisotropy of a uniaxial crystal undergoing the Pockels effect. A focused right-handed circularly polarized quasi-Gaussian beam incident on an electro-optic crystal strontium barium niobate is taken to illustrate the effect, and a conversion-forbidden electric field E(0)=-16.87 kV/cm is found. Of special interest is that single photons generated in this effect exhibit an entanglement of 2 deg of freedom of spin and orbital angular momentum, and it is electro-optically controllable.