Geometric phase in optics and angular momentum of light

Abstract

The Physical mechanism of the geometric phase in terms of angular momentum exchange is elucidated. It is argued that the geometric phase arising out of the cyclic changes in the transverse mode space of Gaussian light beams is a manifestation of the cycles in the momentum space of the light. The apparent non-conservation of orbital angular momentum in the spontaneous parametric down conversion for the classical light beams is proposed to be related to the geometric phase.     

The angular momentum of light inside a dielectric

Abstract

We consider whether or not a short pulse of light carrying angular momentum will exert a torque when propagating through a transparent disc. The approach is based on the “Einstein-box” argument which we apply to discuss linear optical momentum in a medium. Two competing theories due to Minkowski and Abraham, at least superficially, suggest that the disc will not or will rotate. Our analysis suggests that the disc will rotate and that an experiment using optical tweezers should be able to detect the rotation.     

Angular momentum of the fields of a few-mode waveguide: Conversion of the angular momentum

An analysis is made of the transformation of the angular momentum density in the field of an unstable IV vortex of a few-mode optical fiber. It is shown that the effect of mode dispersion of IV vortices is observed as the conversion of the polarization and orbital components of the electrodynamic angular momentum. The angular momentum defect may be recorded experimentally as a mechanical twist of the optical few-mode fiber. Formally the dispersion process resembles the conversion of the signs of the orbital and polarization components of the angular momentum density. A complex pseudopotential, whose real and imaginary parts characterize the field lines and lines of equal pseudopotential, is introduced to describe the energy flux density of the fiber vortex. The conversion of field states with equivalent partial ê ⁺ F ₁(R)exp{−iφ} and ê2⁻ F ₁(R)exp{+iφ} vortices was investigated experimentally. Pis#x2019;ma Zh. Tekh. Fiz. 23, 58–65 (November 26, 1997)     

Macroscopic jumps of the axial angular momentum variance of a bidimensionally trapped ion

Abstract

The time evolution of the axial angular momentum [Lcirc] _z of an ion confined in a bidimensional trap is investigated. We find that, under suitable initial conditions, the interaction of the ion with two properly configured classical laser beams induces a peculiar dynamical behaviour of the axial angular momentum fluctuations. We show, in fact, that there exists an instant of time at which the variance of [Lcirc] _z undergoes variations proportional to N ² further to a change of one quantum only in the initial total number N ? 1 of vibrational quanta. The non-classical origin of these macroscopic jumps is brought to the light and carefully discussed.     

Generation and selection of laser beams represented by a superposition of two angular harmonics

Abstract

The properties of fields generated by diffractive phase-only optical elements that generate combinations of two angular harmonic fields with different harmonic indices in Fraunhofer and Fresnel regions are investigated theoretically and experimentally. Camomile shaped diffraction patterns are predicted and observed. It is shown that multi-order diffractive phase elements can be used to both generate these beams and to identify the weights of different angular harmonics in a given incident laser beam.     

Coupling a small torsional oscillator to large optical angular momentum

Abstract

We propose a new configuration for realizing torsional optomechanics: an optically trapped windmill-shaped dielectric interacting with Laguerre–Gaussian cavity modes containing both angular and radial nodes. In contrast to existing schemes, our method can couple mechanical oscillators smaller than the optical beam waist to the in-principle unlimited orbital angular momentum that can be carried by a single photon, and thus generate substantial optomechanical interactions. Combining the advantages of small mass, large coupling, and low clamping losses, our work conceptually opens the way for the observation of quantum effects in torsional optomechanics. 10.1080/09500340.2013.778341-SUP0001 Supplementary data      

Efficiency of electrooptic spin-to-orbital angular momentum conversion in crystals

We introduce a figure of merit for the photon spin-to-orbital angular momentum conversion via electrooptic (EO) Pockels effect in single crystals. Relations for the effective EO coefficients are derived for different symmetry groups. We show that Bi₁₂TiO₂₀ crystals reveal the highest figure of merit among well studied crystalline EO materials. The efficiency of the spin-to-orbital angular momentum conversion is measured experimentally for a number of single crystals.     

Commutation Rules and Eigenvalues of Spin and Orbital Angular Momentum of Radiation Fields

Abstract

We investigate the separation of the total angular momentum J of the electromagnetic field into a ‘spin’ part S and an ‘orbital’ part L. We show that both ‘spin’ and ‘orbital’ angular momentum are observables. However, the transversality of the radiation field affects the commutation relations for the associated quantum operators. This implies that neither S nor L are angular momentum operators. Moreover their eigenvalues are not discrete. We construct field modes such that each mode excitation (photon) is in a simultaneous eigenstate of S _z and L _z. We consider the interaction of such a photon with an atom and the resulting effect on the internal and external part of the atomic angular momentum.     

Optical angular correlation in fourier domain

Abstract

The angular correlation of Fourier spectra is optically implemented by means of a single Fourier transformer. Fourier-domain-based angular correlation, which is a technique specific to periodic pattern recognition and characterization, is efficiently applied in real time to ordinary textile structures. By introducing scale corrections, either isomorphic or anamorphic, the optical system is capable of recognizing different structures of the same sort of fabric even when the fundamental frequencies—or thread densities—do not coincide. Two possible methods to introduce the information into the input image of the optical angular correlator are considered: an opto-mechanical rotator containing a transparency with the input sample image; and an electronic addressed spatial light modulator that displays the input sample image controlled by computer. Experimental results of both possibilities are presented and discussed.     

Strong-field ionization of heteronuclear diatomic molecules in circularly polarized laser fields

Abstract

We theoretically investigate the strong-field ionization of heteronuclear diatomic molecules, CO and NO, by calculating the photoelectron angular distribution and the photoelectron momentum distribution in circularly polarized fields. We find that the photoelectron angular distribution and the photoelectron momentum distribution of CO are inversion asymmetric, but symmetric about the molecular axis, most of the photoelectrons are ejected from the neighborhood of the C core. In contrast, for NO the photoelectron angular distribution and photoelectron momentum distribution are nearly fourfold symmetric about the molecular axis and its vertical axis, which means that the photoelectrons are equally ejected from the neighborhood of the N and O cores. By our results, the photoelectron angular distribution and photoelectron momentum distribution can be used to imprint the molecular orbitals.     

Spin-to-orbit conversion at acousto-optic diffraction of light: conservation of optical angular momentum

Acousto-optic diffraction of light in optically active cubic crystals is analyzed from the viewpoint of conservation of optical angular momentum. It is shown that the availability of angular momentum in the diffracted optical beam can be necessarily inferred from the requirements of angular momentum conservation law. As follows from our analysis, a circularly polarized diffracted wave should bear an orbital angular momentum. The efficiency of the spin-to-orbit momentum conversion is governed by the efficiency of acousto-optic diffraction.     

Equivalent geometric transformations for spin and orbital angular momentum of light

We consider the analogous geometric transformations for spin and orbital angular momentum states of light. Spin angular momentum is manifested as polarization and its possible transformations are typified by those introduced by waveplates and the rotation associated with optical activity. Orbital angular momentum is associated with the mode structure of the beam and, while the action of a waveplate is similar to that of a mode converter, the equivalent analogue of optical activity is not obvious. We reason that the equivalent is a rotation of the transmitted image. We consider the extent to which an image orientation of this type might be achieved by a coherent fibre bundle, twisted around its central axis. The possibility of equivalents to the Kerr, Pockels and Faraday electro-optic effects for orbital angular momentum is raised.     

Angular Momentum Balance on Light Reflection

Abstract

It was pointed out by Holbourn in 1936 that there is an apparent breakdown of angular momentum conservation on reflection of circularly polarized light at the plane interface between two lossless dielectrics. The analysis presented in this paper shows that this discrepancy does not arise provided that: (a) the intensities of the incident, reflected, and transmitted beams vanish at large distances from their axes, and (b) the angular momentum of each beam is calculated from first principles.     

Preparation of macroscopically distinguishable superpositions of circular or linear oscillatory states of a bidimensionally trapped ion

Abstract

A simple scheme for the generation of two different classes of bidimensional vibrational Schrödinger cat-like states of an isotropically trapped ion is presented. We show that by appropriately adjusting an easily controllable parameter having a clear physical meaning, the states prepared by our procedure are quantum superpositions of either vibrational axial angular momentum eigenstates or Fock states along two orthogonal directions.     

Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation

We derive a full field solution for Laguerre-Gaussian beams consistent with the Helmholtz equation using the angular spectrum method. Field components are presented as an order expansion in the ratio of the wavelength to the beam waist, f=λ/(2πw?), which is typically small. The result is then generalized to a beam of arbitrary polarization. This result is then used to reproduce the signature angular momentum properties of Laguerre-Gaussian beams in the paraxial limit. The subsequent higher-order term is similarly obtained, which does not display a clear separation of orbital and spin angular momentum components.     

Quantisation of the free electromagnetic field implies quantisation of its angular momentum

It is shown that when the gauge-invariant Bohr–Rosenfeld commutators of the free electromagnetic field are applied to the expressions for the linear and angular momentum of the electromagnetic field interpreted as operators then, in the absence of electric and magnetic charge densities, these operators satisfy the canonical commutation relations for momentum and angular momentum. This confirms their validity as operators that can be used in quantum mechanical calculations of angular momentum.     

Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP₁₁ mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γ _b =±δβ ₂₁ z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV⁺ and IV⁻ modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP₁₁ mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber. Pis’ma Zh. Tekh. Fiz. 23, 59–67 (December 12, 1997)     

Transfer of orbital angular momentum from a stressed fiber-optic waveguide to a light beam

A stressed fiber-optic waveguide is used to impart orbital angular momentum to a Hermite-Gaussian (HG(10)) laser mode. The transmitted beam has an annular intensity profile and a well-defined azimuthal phase dependence. We confirm the phase structure of the beam by observing the interference pattern produced between it and a plane wave. The transfer of the angular momentum to the light occurs because of a difference in phase velocity within the fiber for two orthogonal modes that comprise the input beam. This represents a mechanism for the transfer of orbital angular momentum to a light beam that has not hitherto been identified.     

Optical tweezers and optical spanners with Laguerre–Gaussian modes

Abstract

We numerically model the axial trapping forces within optical tweezers arising from Laguerre–Gaussian laser modes. For an 8 μm diameter sphere suspended in water, the higher-order modes produce an axial trapping force several times larger than that of the fundamental. Partial absorption results in a transfer of the orbital angular momentum from the Laguerre–Gaussian mode to the trapped particle. This results in the rotation of the particle by what may be called an optical spanner (wrench). For an absorption coefficient of α = 5700 m^?1 and a laser power of 10 mW, we find that an 8 μm diameter sphere would acquire an angular acceleration of 10 × 10⁴ rad s^?2 and a limiting angular velocity of 0.2 rad s^?1.