We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.
We perform Bell's measurement and perform quantum Fourier transform with the classical vortex beam. The violation of Bell's inequality for such a non-separable classical correlation has been demonstrated experimentally. Based on the classical vortex beam and nonquantum entanglement between the polarization and orbital angular momentum, the Hadamard gates and conditional phase gates have been designed. Furthermore, a quantum Fourier transform has been implemented experimentally, which is the crucial final step in Shor's algorithm
We demonstrate a Fourier Imaging system with centimeter field of view(FOV), and 0.0042°angular resolution at C band, for the entire 180° radiation angular range. To pursue omnidirectional Fourier imaging without aberration, a technique called angular synthetic aperture is employed, by multi-perspective imaging and stitching. The effect of tilting-introduced virtual lens is pointed out and dealt with in our system. For the sake of limited sensor size and aberration spot size, Fourier imaging at each perspective is restricted to angle range smaller than 3°. The imaging system with a 4f demagnifi…
Electron vortex beams have been predicted to enable atomic scale magnetic information measurement, via transfer of orbital angular momentum. Research so far has focussed on developing production techniques and applications of these beams. However, methods to measure the outgoing orbital angular momentum distribution are also a crucial requirement towards this goal. Here, we use a method to obtain the orbital angular momentum decomposition of an electron beam, using a multi-pinhole interferometer. We demonstrate both its ability to accurately measure orbital angular momentum distribution, and i…
We present a scheme to measure the orbital angular momentum spectrum of light using a precisely timed optical loop and quantum non-demolition measurements. We also discuss the influence of imperfect optical components.
The interplay between spin and orbital angular momentum in the up-conversion process allows us to control the macroscopic wave front of high harmonics by manipulating the microscopic polarizations of the driving field. We demonstrate control of orbital angular momentum in high harmonic generation from both solid and gas phase targets using the selection rules of spin angular momentum. The gas phase harmonics extend the control of angular momentum to extreme-ultraviolet wavelength. We also propose a bi-color scheme to produce spectrally separated extreme-ultraviolet radiation carrying orbital a…
Light intensity control of the orbital angular momentum of the fundamental beam in a quadratic nonlinear process is theoretically and numerically presented. In particular we analyzed a seeded second harmonic generation process in presence of orbital angular momentum of the interacting beams due both to on axis and off axis optical vortices. Examples are proposed and discussed.
We investigate the dynamical properties of a type-II optical parametric oscillator pumped by a structured light beam carrying orbital angular momentum. Different dynamical regimes are theoretically derived and experimentally demonstrated, depending on the anisotropy effects imposed by the nonlinear medium. In a weakly anisotropic regime, fine-tuning of the orbital angular momentum transfer is obtained by adjusting the crystal parameters. Under strong anisotropy, orbital angular momentum transfer is not possible and a sharp dynamical behavior is observed, with abrupt switching between different…
Many methods now exist to prepare free electrons into orbital angular momentum states, and the predicted applications of these electron states as probes of materials and scattering processes are numerous. The development of electron orbital angular momentum measurement techniques has lagged behind. We show that coupling between electron orbital angular momentum and a spatially varying magnetic field produces an angular momentum-dependent focusing effect. We propose a design for an orbital angular momentum measurement device built on this principle. As the method of measurement is non-interfero…
The magnitude of the topological charge of the vortex of a ring-shaped pulse is found to be limited by the squared mean frequency of the pulse spectrum at the ring relative to its variance. This limitation implies a upper bound to the orbital angular momentum carried by a pulse, and a lower bound to the duration for a pulse to carry any orbital angular momentum.
We implement an interferometric method using two angular slits to measure the orbital angular momentum (OAM) mode spectrum of a partially coherent field. As the angular separation of the slits changes, an interference pattern for a particular OAM mode is obtained. The visibility of this interference pattern as a function of angular separation is equivalent to the angular correlation function of the field. By Fourier transforming the angular correlation function obtained from the double angular slit interference, we are able to calculate the OAM spectrum of the partially coherent field. This me…
In this letter a general method for expanding paraxial beams into multipolar electromagnetic fields is presented. This method is applied to the expansion of paraxial modes with orbital angular momentum (OAM), showing how the paraxial OAM is related to the general angular momentum of an electromagnetic wave. This method can be extended to quasi-paraxial beams, i.e. highly focused laser beams. Some applications to the control of electronic transitions in atoms are discussed.
Exploiting electro-optic effects in liquid crystals, we achieved real-time control of the retardation of liquid- crystal-based $q$-plates through an externally applied voltage. The newly conceived electro-optic $q$-plates can be operated as electrically driven converters of photon spin into orbital angular momentum, enabling a variation of the orbital angular momentum probabilities of the output photons over a time scale of milliseconds.
We introduce a new method to generate and tune the optical orbital angular momentum of a focused Gaussian beam passing through the optical superlattice under the electro-optic effect. The orbital angular momentum (OAM) arises from the curl of polarization in our calculation. We see that adjusting the external electric field, the beam waist radius and the crystal length provides dramatic variation of OAM of light across the transverse section. It is believed that this invention will find its application in optical manipulation area.
Spatiotemporal optical vortices (STOVs) are a new type of intrinsic optical orbital angular momentum (OAM) structure in which the OAM vector is orthogonal to the propagation direction [Optica 6, 1547, (2019)] and the optical phase circulates in space-time. Here, we experimentally and theoretically demonstrate, for the first time, the generation of the second harmonic of a STOV-carrying pulse along with the conservation of STOV-based OAM. Our experiments verify that individual photons can have intrinsic orbital angular momentum perpendicular to their propagation direction.
It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that originates from the former part is spin, and the angular momentum that originates from the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxial bea…
We theoretically analyze stimulated parametric down conversion as a means to produce dichroism based on the orbital angular momentum (OAM) of an incident signal field. The nonlinear interaction is shown to provide differential gain between signal states of differing OAM, the peak gain occurring at half the OAM of the pump field.
We present a tunable liquid crystal device that converts pure orbital angular momentum eigenmodes of a light beam into equal-weight superpositions of opposite-handed eigenmodes and vice versa. For specific input states, the device may thus simulate the behavior of a π/2 phase retarder in a given two-dimensional orbital angular momentum subspace, analogous to a quarter-wave plate for optical polarization. A variant of the same device generates the same final modes starting from a Gaussian input.
We have theoretically predicted the gigantic spikes of the orbital angular momentum caused by the conversion processes of the centered optical vortex in the circularly polarized components of the elliptic vortex beam propagating perpendicular to the crystal optical axis. We have experimentally observed the conversion process inside the subwave deviations of the crystal length. We have found that the total orbital angular momentum of the wave beam is conserved.
We describe the coupling between orbital angular momentum (OAM) and temporal degrees of freedom in pulsed Laguerre-Gauss beams. The effects of this coupling are to increase significantly the duration of few-cycle pulses when the OAM carried by the pulse is large, and to enhance spatiotemporal couplings. Contrary to other detrimental but retrievable effects such as spatial, group velocity and topological charge dispersions in these pulses, OAM-temporal coupling effects are unavoidable, and have therefore an impact in applications such as OAM-based optical communications, or in the generation of…
A matrix representation is introduced for stationary beam-like light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This Coherence-OAM matrix is a counterpart of the 2 x 2 beam Coherence-polarization matrix in a Cartesian polarization basis or Coherence-spin angular momentum (SAM) matrix in a circular polarization basis. The general properties of the Coherence-OAM matrix are discussed and then the Coherence-SAM-OAM matrix is introduced as a unifying entity for treating beams with any coherence, spin and orbit…
We present and test the integration of a static orbital angular momentum mode multiplexer with a dynamical geometric-phase optical element enabling on-demand spin-controlled angular momentum multiplexing. A diffractive optics multiplexer fabricated with 3D high-resolution electron beam lithography performs a conformal mapping for the conversion from linear to azimuthal phase gradients. The latter is functionalized by a dynamic spin-orbit add-on that consists of a self-engineered electrically-activated liquid crystal optical vortex generator having large clear-aperture and high-resolution. By c…
Starting from covariant expressions, a gauge independent separation of orbital and spin angular momentum for electrodynamics is presented. This results from the non-symmetric canonical energy momentum tensor of the electromagnetic field. The origin of the difficulty is discussed and a covariant gauge invariant spin vector is derived. The paradox concerning the spin angular momentum of a plane wave finds a natural solution.
We present an easy, efficient and fast method to generate arbitrary linear combinations of light orbital angular momentum eigenstates $\ell=\pm 2$ starting from a linearly polarized TEM$_{00}$ laser beam. The method exploits the spin-to-orbital angular momentum conversion capability of a liquid-crystal-based $q$-plate and a Dove prism inserted in a Sagnac polarizing interferometer. The nominal generation efficiency is 100\%, being limited only by reflection and scattering losses in the optical components. When closed paths are followed on the polarization Poincaré sphere of the input beam, the…
We consider the effect of orbital angular momentum (OAM) on localized waves in optical fibers using theory and numerical simulations, focusing on splash pulses and focus wave modes. For splash pulses, our results show that they may carry OAM only up to a certain maximal value. We also examine how one can optically excite these OAM-carrying modes, and discuss potential applications in communications, sensing, and signal filtering.
We experimentally study the behavior of orbital angular momentum (OAM) of light in a noncollinear second harmonic generation (SHG) process. The experiment is performed by using a type I BBO crystal under phase matching conditions with femtosecond pumping fields at 830 nm. Two specular off-axis vortex beams carrying fractional orbital angular momentum at the fundamental frequency (FF) are used. We analyze the behavior of the OAM of the SH signal when the optical vortex of each input field at the FF is displaced from the beam's axis. We obtain different spatial configurations of the SH field, al…
We calculate analytically the spin-orbital decomposition of the angular momentum using completely non-paraxial fields that have certain degree of linkage of electric and magnetic lines. The split of the angular momentum into spin-orbital components is worked out for non-null knotted electromagnetic fields. The relation between magnetic and electric helicities and spin-orbital decomposition of the angular momentum is considered. We demonstrate that even if the total angular momentum and the values of the spin and orbital momentum are the same, the behaviour of the local angular momentum density…
We present the results of numerical analysis of Gauss-Bessel beam reflection from a dielectric film under different angles of incidence. A transverse shift of the beam under the orbital momentum sign change is observed. The value of the shift is independent of the polarization state of the incident beam.
We propose two schemes for achieving continuous and complete orbital angular momentum tuning using a simple device based on a phase only parallel aligned liquid crystal on silicon display, where the tuning is managed by changing the input beam state of polarization. We use an optical tweezers toolbox to simulate the optical force field of the tuned beams applied to dielectric spherical particles in order to prove the applicability of the method.
It is well known that reflection of a Gaussian light beam ($\text{TEM}_{00}$) by a planar dielectric interface leads to four beam shifts when compared to the geometrical-optics prediction. These are the spatial Goos-Hänchen (GH) shift, the angular GH shift, the spatial Imbert-Fedorov (IF) shift and the angular IF shift. We report here, theoretically and experimentally, that endowing the beam with Orbital Angular Momentum (OAM) leads to coupling of these four shifts; this is described by a $4 \times 4$ mixing matrix.
The transverse beam pattern, usually observed in experiment, is a result of averaging the optical-frequency oscillations of the electromagnetic field distributed over the beam cross section. An analytical criterion is derived that these oscillations are coupled with a sort of rotation around the beam axis. This criterion appears to be in direct relation with the usual definition of the beam orbital angular momentum.
We show that a high-order Bessel beam propagating in a medium with nonlinear absorption is not completely absorbed, but survives in the form of a new propagation invariant vortex beam in which the beam energy and orbital angular momentum are permanently transferred to matter and at the same time refueled by spiral inward currents of energy and angular momentum. Unlike vortex solitons and dissipative vortex solitons, these vortex beams are not supported by specific dispersive nonlinearities (self-focusing or self-defocusing) and do not require gain. Propagation invariance in presence of multipl…
We investigate the second harmonic generation of light field carrying orbital angular momentum in bulk $χ^{(2)}$ material. We show that due to conservation of energy and momentum, the frequency doubled beam light has a modified spatial distribution and mode characteristics. Through rigorous phase matching conditions, we demonstrate efficient mode and frequency conversion based on three wave nonlinear optical mixing.
Orbital angular momentum associated with the helical phase-front of optical beams provides an unbounded \qo{space} for both classical and quantum communications. Among the different approaches to generate and manipulate orbital angular momentum states of light, coupling between spin and orbital angular momentum allows a faster manipulation of orbital angular momentum states because it depends on manipulating the polarisation state of light, which is simpler and generally faster than manipulating conventional orbital angular momentum generators. In this work, we design and fabricate an ultra-th…
A light beam with phase singularity (PS) characterized with azimuthally symmetric angular positions (APs) can be constructed by the rotationally symmetric superposition of n (n is N) fractional vortex light beams with identical charges. The profile of this light beam deforms after propagation owing to its orbital angular momentum (OAM) noneigenvalue, and the deformation degree can be evaluated by the degree of phase dislocation associated with the PS. The expectation value of the mean deviation of its OAM from its characteristic charge value and the variation of the degree of phase dislocation…
We identify a class of modal solutions for spatio-temporal optical vortex (STOV) electromagnetic pulses propagating in dispersive media with orbital angular momentum (OAM) orthogonal to propagation. We find that symmetric STOVs in vacuum can carry half-integer intrinsic orbital angular momentum (OAM); for general asymmetric STOVs in a dispersive medium, the OAM is quantized in integer multiples of a parameter that depends on the STOV symmetry and the group velocity dispersion. Our results suggest that STOVs propagating in dispersive media are accompanied by a polariton-like quasiparticle. The …
Recent experiments in orbital angular momentum multiplexing have demonstrated its potential for improving the link capacity in optical interconnection networks. Meanwhile, compact photonic integrated orbital angular momentum (de-)multiplexing devices are needed to address requirements such as high scalability, fast configurability, low cost and low power consumption. Here we report on a large-scale integrated tunable orbital angular momentum mode multiplexer, which supports up to 20 multiplexed orbital angular momentum modes over 16 wavelength channels with 30 GHz channel spacing. A testbed of…
It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.
As a new degree of freedom for optical manipulation, recently spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentums have been experimentally demonstrated with pulse shapers. Here a spatiotemporal differentiator is proposed to generate STOVs with transverse orbital angular momentum. In order to create phase singularity in the spatiotemporal domain, the spatiotemporal differentiator is designed by breaking spatial mirror symmetry. In contrast to pulse shapers, the device proposed here is a simple one-dimensional periodic nanostructure and thus it is much more comp…
In light beams with circular or elliptic polarization, the transverse energy flow consists of the "spin" and "orbital" parts. Both of them can induce the orbital motion of microparticles suspended within the field of a light beam, and this should be taken into account in experiments on the spin-to-orbital angular momentum conversion. The character of the spin, orbital and total transverse energy flows in circular Laguerre-Gaussian beams is studied analytically; graphical representations of the flows in the beam cross section (flow maps) are calculated and analyzed. The spin circulatory flow ca…
We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic TE/TM polarization modes. We show that the superposition of non-paraxial vectorial beams with axial symmetry can provide a well defined orbital angular momentum and that the modes superposition affects the angular momentum flux density. The results are illustrated and analyzed for Bessel beams.
We demonstrate the spin to orbital angular momentum transfer in the nonlinear mixing of structured light beams. A vector vortex is coupled to a circularly polarized Gaussian beam in noncollinear second harmonic generation under type-II phase match. The second harmonic beam inherits the Hermite-Gaussian components of the vector vortex, however, the relative phase between them is determined by the polarization state of the Gaussian beam. This effect creates an interesting crosstalk between spin and orbital degrees of freedom, allowing the angular momentum transfer between them. Our experimental …
We investigate the non linear mixing of orbital angular momentum in type II second harmonic generation with arbitrary topological charges imprinted on two orthogonally polarized beams. Starting from the basic nonlinear equations for the interacting fields, we derive the selection rules determining the set of paraxial modes taking part in the interaction. Conservation of orbital angular momentum naturally appears as the topological charge selection rule. However, a less intuitive rule applies to the radial orders when modes carrying opposite helicities are combined in the nonlinear crystal, an …
It is shown that the momentum density of free electromagnetic field splits into two parts. One has no contribution to the net momentum due to the transversality condition. The other yields all the momentum. The angular momentum that is associated with the former part is spin, and the angular momentum that is associated with the latter part is orbital angular momentum. Expressions for the spin and orbital angular momentum are given in terms of the electric vector in reciprocal space. The spin and orbital angular momentum defined this way are used to investigate the angular momentum of nonparaxi…
We present a quantum mechanical analysis of the orbital angular momentum of a class of recently discovered elliptically-symmetric stable light fields --- the so-called Ince-Gauss modes. We study, in a fully quantum formalism, how the orbital angular momentum of these beams varies with their ellipticity and discover several compelling features, including: non-monotonic behavior, stable beams with real continuous (non-integer) orbital angular momenta, and orthogonal modes with the same orbital angular momenta. We explore, and explain in detail, the reasons for this behavior. These features may h…
We propose to use an acoustic surface wave as a memory for a photon carrying orbital angular momentum. We clarify the physical mechanism that enables the transfer of information, derive the angular momentum selection rule that must be obeyed in the process, and show how to optimize the optoacoustic coupling. We theoretically demonstrate that high fidelities can be achieved, using realistic parameters, for the transfer of a coherent optical Laguerre-Gaussian state, associated with large angular momentum, to a mechanical shear mode. Our results add a significant possibility to the ongoing effort…
From the viewpoint of classical electrodynamics, we identify the role of spin-to-orbital angular momentum conversion in spin Hall effect of light (SHE). We introduce a distinct separation between spin and orbital angular momenta to clarify the spin-orbital interaction in the SHE of light. We demonstrate that the refractive index gradient can enhance or suppress the spin-to-orbital angular momentum conversion, and thus can control the SHE of light in conventional beam refraction. We suggest that the metamaterial whose refractive index can be tailored arbitrarily may become a good candidate for …
A decomposition of the angular momentum of the classical electromagnetic field into orbital and spin components that is manifestly gauge invariant and general has been obtained. This is done by decomposing the electric field into its longitudinal and transverse parts by means of the Helmholtz theorem. The orbital and spin components of the angular momentum of any specified electromagnetic field can be found from this prescription.
The expression for the total angular momentum carried by a laser optical vortex beam, splits, in the paraxial approximation, into two terms which seem to represent orbital and spin angular momentum respectively. There are, however, two very different competing versions of the formula for the spin angular momentum, one based on the use of the Poynting vector, as in classical electrodynamics, the other related to the canonical expression for the angular momentum which occurs in Quantum Electrodynamic. I analyze the possibility that a sufficiently sensitive optical measurement could decide which …
We present an optomechanical device designed to allow optical transduction of orbital angular momentum of light. An optically induced twist imparted on the device by light is detected using an integrated cavity optomechanical system based on a nanobeam slot-mode photonic crystal cavity. This device could allow measurement of the orbital angular momentum of light when photons are absorbed by the mechanical element, or detection of the presence of photons when they are scattered into new orbital angular momentum states by a sub-wavelength grating patterned on the device. Such a system allows det…
We present a complete and consistent quantum theory of generalised X waves with orbital angular momentum (OAM) in dispersive media. We show that the resulting quantised light pulses are affected by neither dispersion nor diffraction and are therefore resilient against external perturbations. The nonlinear interaction of quantised X waves in quadratic and Kerr nonlinear media is also presented and studied in detail.
We compare three attempts that have been made to decompose the angular momentum of the electromagnetic field into components of an "orbital" and "spin" nature. All three expressions are different and it appears, on the basis of classical electrodynamics, that there is no preferred way of decomposing the angular momentum of the electromagnetic field into orbital and spin components, even in an inertial frame.
Magnetostatic modes supported by a ferromagnetic sphere have been known as the Walker modes, each of which possesses an orbital angular momentum as well as a spin angular momentum along a static magnetic field. The Walker modes with non-zero orbital angular momenta exhibit topologically non-trivial spin textures, which we call \textit{magnetic quasi-vortices}. Photons in optical whispering gallery modes supported by a dielectric sphere possess orbital and spin angular momenta forming \textit{optical vortices}. Within a ferromagnetic, as well as dielectric, sphere, two forms of vortices interac…
The effect of the transversality condition on the quantization of the photon orbital angular momentum is studied. The quantum gauge that is deduced from the transversality condition is shown to be a Berry gauge. It determines a helicity-dependent reference point relative to which the position is canonically conjugate to the momentum. As a result, the photon orbital angular momentum about the origin of the laboratory reference system split into two parts. One is the orbital angular momentum of the photon about the reference point, which is canonical. The other is the orbital angular momentum of…
