Topological defects, geometric phases, and the angular momentum of light

Recent reports on the intriguing features of vector vortex bearing beams are analyzed using geometric phases in optics. It is argued that the spin redirection phase induced circular birefringence is the origin of topological phase singularities arising in the inhomogeneous polarization patterns. A unified picture of recent results is presented based on this proposition. Orbital angular momentum (OAM) shift within the light beam has exact equivalence with the angular momentum holonomy associated with the geometric phase consistent with our conjecture.     

Beam moments and angular momentum in non-uniformly polarized beams

The angular momentum of non-uniformly totally polarized beams is investigated using methods from the beam characterization approach. The relationship between the elements of the beam matrix for the two components of the field and the angular momentum is given. The unconventional distribution of the polarization across the beam profile could result in contributions to both the spin and orbital terms of the angular momentum. To illustrate this, a particular example with a vortex beam is considered.     

Spatial-angular Mueller matrices

Arbitrary polarization changing devices are described within paraxial approximation by their action on the spatial angular Stokes parameters associated with the generalized rays of a Wigner formulation of wave optics. This approach leads to the introduction of generalized Mueller matrices being functions of the spatial and angular variables parameterizing generalized rays. We apply this approach to a polarization grating.     

The Imbert-Fedorov shift of paraxial light beams

We present a solution to the problem of reflection and transmission of a polarized paraxial light beam at an interface between two homogeneous media by using a two-form amplitude and an extension matrix to represent the vectorial angular spectrum of a three-dimensional (3D) light beam. We derive general formulas for the Imbert-Fedorov (IF) shift of the reflected and transmitted beams of a polarized paraxial light beam. The IF shift of two different types of polarized beams is calculated, and the influence of the polarization state and the polarization feature of the vectorial angular spectrum on the IF shift is discussed.     

Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle

We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an airglass interface near the Brewster angle.A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle.Using a hybrid angular spectrum representation and vector potential method,the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation.The local energy,momentum,spin,and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach.Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly,and are significantly affected by their topological charge,half-cone angle,and polarization state.The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.     

Reflection of the light beam carrying orbital angular momentum from a lossy medium

It is shown that after reflection from a lossy medium the s- or p-polarized paraxial light beam carrying the orbital angular momentum suffers the 2D shift of the beam's centre of gravity relative the geometric optic axis. The direction as well as the length of the 2D vector, which describes the shift, change smoothly with the change of the angle of incidence.     

Optimal phase steps of multi-level spiral phase plates

We analyze vortex properties of the optical beams generated by a multi-level spiral phase plate (MLSPP) and find that this kind of beams consists of vortex components with topological charges of L − kM, where k is zero or any integer, M is the level number and L is the intrinsic topological charge of the MLSPP. We proved that the orbital angular momentum of the beams generated by a MLSPP reaches its maximum only if the phase steps (or the ratio of M to L) satisfies some special conditions.     

Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam

Orbital angular momentum of the coherent beam has been intensively studied and promises potential applications in free space optical communication. But the orbital angular momentum of partially coherent beam is not well known. In this communication the coherent-mode representation method is adopted to describe the partially coherent beam and the orbital angular momentum spectrum is introduced for the partially coherent beam. The characteristics of the orbital angular momentum spectrum of partially coherent beam are discussed. To study the influence of the partial coherence on the optical link, the channel capacity is studied, with two kinds of available mode separators included.     

Polarization selection rules for the allowed optical transitions in europium-terbium double activated calcium tungstate phosphor

The paper is devoted to the problem of the optical anisotropy of the rare-earth ions occupying low-symmetry positions in crystals. The crystal field multiplets arising from LSJ terms of Eu³⁺ and Tb³⁺ ions in the crystal field of calcium tungstate scheelite (CaWO₄) are analyzed (S₄ point symmetry). The selection rules, in particular, polarization rules for the allowed electric dipole optical transitions in the electronic shells of the Eu³⁺ and Tb³⁺ in CaWO₄ host lattice are discussed. Special attention is paid to the study of the angular (polarization) dependence of the two-photon absorption that seems to be an effective tool for the understanding of the complicated optical pattern. The peculiarities of the anisotropy of the two-photon absorption prove to be specific for each allowed dipole transition in S₄ symmetry center.     

Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum L. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed.     

The electronic structure and the ferromagnetic intermolecular interactions in the crystal of TEMPO radicals

Based on the generalized gradient approximation, full potential linearized augmented plane wave (FP-LAPW) calculations have been performed to study the electronic band structure and the intermolecular ferromagnetic (FM) interactions for the two TEMPO radicals 4-Benzylideneamino-2,2,6,6-tetramethylpiperidin-1-oxyl (1) and 4-(2-naphtylmethyleneamino)-2,2,6,6-tetramethylpiperidin-1-oxyl (2). The total and the partial density of states and the atomic spin magnetic moments are calculated and discussed. The calculation revealed that the two TEMPO radicals have the intermolecular FM interactions, and the spontaneous magnetic moment is 1.0 μ_B per molecule of each crystal, which is in good agreement with the experimental value. It is found that the unpaired electrons in these compounds are localized in a molecular orbital constituted primarily of π* (NO) orbital, and the main contribution of the spin magnetic moment comes from the NO-free radical. The origin of FM is also studied in detail.     

Proposals for the generation of angular momentum from non-uniformly polarized beams

Several optical arrangements using non-uniformly polarized fields are proposed for generating beams with spin and/or orbital angular momentum. By choosing adequately the input beam polarization and the characteristics of the different proposed set-ups we can control the overall angular momentum of the output beam at will. The orbital angular momentum is analyzed with the beam moments theory and the spin term is evaluated using the averaged s₃ Stokes parameter.     

Magnetic properties,electronic structure,and optical properties of the filled skutterudite BaFe4Sb12

The magnetic properties, electronic structure, and optical properties of the filled skutterudite BaFe₄Sb₁₂ are calculated by the first-principles full-potential linearized augmented plane wave (FPLAPW) plus local orbital method. It is found that the local spin density approximation (LSDA) method appears more accurate than the generalized gradient approximation (GGA) method in calculating the electronic structures and optical properties of this compound. Furthermore, our calculated lattice constant and spin magnetic moments with the LSDA method are in overall better agreement with experiment. In contrast with recent experiment, our calculations are in good agreement with experimental reflectivity spectra and optical conductivity spectrum.     

Spin-dependent current in resonant tunneling diode with ferromagnetic GaMnN layers

The spin-polarized tunneling current through a double barrier resonant tunneling diode (RTD) with ferromagnetic GaMnN emitter/collector is investigated theoretically. Two distinct spin splitting peaks can be observed at current-voltage (I-V) characteristics at low temperature. The spin polarization decreases with the temperature due to the thermal effect of electron density of states. When charge polarization effect is considered at the heterostructure, the spin polarization is enhanced significantly. A highly spin-polarized current can be obtained depending on the polarization charge density.     

Orbital angular momentum and nonparaxial light beams

The simple relationship between total angular momentum and energy and the seemingly natural separation of the angular momentum into spin and orbital components in the paraxial approximation, are investigated for a general nonparaxial form of monochromatic beam with near cylindrical symmetry.     

The electronic structure and the ferromagnetic properties of the organic radical 4-methacryloyloxy-2,2,6,6-tetramethyl-1-piperidinyloxyl (MOTMP)

The ab initio method of the full potential linearized augmented-plane-wave has been used to study the electronic band structure and the ferromagnetic (FM) properties of the organic radical MOTMP. The total and the partial density of states and the atomic spin magnetic moments are calculated. The calculation revealed that MOTMP has a stable ferromagnetic ground state and the spin magnetic moment is 1.0 μ_B per molecule, which is in good agreement with the experimental value. It is found that the unpaired electrons in this compound are localized in a molecular orbital constituted primarily of π*(NO) orbital and the main contribution of the spin magnetic moment comes from the NO free radical. It is also found that there exists ferromagnetic intermolecular interaction in the compound.     

Analytical characterization of spectral anomalies in polychromatic apertured beams

The power spectrum of polychromatic apertured spherical waves changes strongly in the vicinity of phase singularities. A spectral shift effect is observed and, in some cases, a spectral switch occurs together with a broadening of the power spectrum. Low-order moments of the power spectrum are evaluated in points of the focal volume with spectral anomalies. First-order analytical expressions are proposed for the evaluation of the relative spectral shift and the relative spectral broadening in the transverse focal plane and along the optical axis. The influence of the fractional bandwidth and the selected singularity order is considered.     

A numerical parameter study of chiral metamaterial based on complementary U-shaped structure in infrared region

In this paper, the optical properties of the chiral metamaterial (CMM) with complementary U-shaped structure assembly have been investigated numerically in infrared frequencies. Here, we systematically study the dependence of CMM's optical properties to the structural parameters. The giant optical activity, circular dichroism (CD), and high negative refraction can be obtained by properly selecting the parameters, respectively. CMMs will also lead to many applications in photonic devices due to their strong polarization effect and CD effect.