Arbitrary Angular Momentum Research Articles

Generation of arbitrary vector orbital angular momentum beams on higher-order Poincaré spheres based on an all-dielectric metasurface with complex amplitude modulation

Vector orbital angular momentum (OAM) beams, described by higher-order Poincaré (HOP) sphere, are generalized forms of waves carrying OAM with an inhomogeneous polarization of wavefronts. We construct all-dielectric metasurfaces with adjustable amplitude, polarization, and phase to generate arbitrary vector OAM beams. The metasurface is composed of two pairs of silicon nanopillars arranged alternately. Using the interference effect of the four meta-atoms related to the circular polarization, combined with the propagation and geometric phases, two OAM beams with controlled amplitude, phase, and equal topological charge but opposite signs can be obtained under the incidence of orthogonally circularly polarized lights. For the x linearly polarized light, arbitrary vector OAM beams on the HOP sphere are generated via the superposition of the above OAM beams. Additionally, the evolution process of the beam on the longitude and latitude of the Poincaré sphere is revealed by changing the amplitude and phase of the two OAM beams. This work provides a simple, effective, and flexible method for realizing vector OAM beams while having potential implications for the generation and manipulation of vectorial light fields at the micro-nano scale.

Optical vortex ladder via Sisyphus pumping of Pseudospin

Robust high-order optical vortices are much in demand for applications in optical manipulation, optical communications, quantum entanglement and quantum computing. However, in numerous experimental settings, a controlled generation of optical vortices with arbitrary orbital angular momentum remains a challenge. Here, we present a concept of “optical vortex ladder” for the stepwise generation of optical vortices through Sisyphus pumping of pseudospin modes in photonic graphene. The ladder is applicable in various lattices with Dirac-like structures. Instead of conical diffraction and incomplete pseudospin conversion under conventional Gaussian beam excitations, the vortices produced in the ladder arise from non-trivial topology and feature diffraction-free Bessel profiles, thanks to the refined excitation of the ring spectrum around the Dirac cones. By employing a periodic “kick” to the photonic graphene, effectively inducing the Sisyphus pumping, the ladder enables tunable generation of optical vortices of any order even when the initial excitation does not involve any orbital angular momentum. The optical vortex ladder stands out as an intriguing non-Hermitian dynamical system, and, among other possibilities, opens a pathway for applications of topological singularities in beam shaping and wavefront engineering.

Accelerating Relativistic Exact-Two-Component Density Functional Theory Calculations with Graphical Processing Units.

Numerical integration of the exchange-correlation potential is an inherently parallel problem that can be significantly accelerated by graphical processing units (GPUs). In this Letter, we present the first implementation of GPU-accelerated exchange-correlation potential in the GauXC library for relativistic, 2-component density functional theory. By benchmarking against copper, silver, and gold coinage metal clusters, we demonstrate the speed and efficiency of our implementation, achieving significant speedup compared to CPU-based calculations. One GPU card provides computational power equivalent to roughly 400 CPU cores in the context of this work. The speedup further increases for larger systems, highlighting the potential of our approach for future, more computationally demanding simulations. Our implementation supports arbitrary angular momentum basis functions, enabling the simulation of systems with heavy elements and providing substantial speedup to relativistic electronic structure calculations. This advancement paves the way for more efficient and extensive computational studies in the field of density functional theory.

Efficient approach for generating vortex sources with arbitrary orbital angular momentum in acoustic experiments

Abstract In theoretical research framework of acoustics or optics, how to provide stable and efficient experimental vortex sources with arbitrary orbital angular momentum (OAM) (especially with larger OAM) is a highly challenging research topic. Here, we propose and demonstrate the general principle of two different methods to generate vortex sources with arbitrary OAM, based on the point-sources array and acoustic metamaterials, respectively. Specifically, the general synthetic law is summarized from the analytical perspective behind generating two-dimensional vortex waves using different point sources with different phases, and the design flexibility of acoustic metamaterials is also utilized to provide an ideal solution for generating vortex sources with larger OAM. Besides, we qualitatively and quantitatively determine the OAM of generated vortex waves through simple formulas, and briefly discuss the applicability and stability of two different methods with complementary advantages. The principles of vortex sources generation revealed in this work provide direct theoretical support for the experimental exploration of interactions between multiphysics fields and complex media, with potential applications in vortex fields manipulation and OAM detection.

A semi-analytic approximation for a single-particle continuum wavefunction

A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.

Analytical Solutions of the D-dimensional Klein-Gordon equation with q-deformed modified P¨oschl-Teller Potential

In this article, the D-dimensional Klein-Gordon equation within the framework of Greene-Aldrich approximations scheme for q-deformed modified P¨oschl-Teller Potential is solved for s-wave and arbitrary angular momenta. The energy eigenvalues and corresponding wave functions are obtained in an exact analytical manner via the Nikiforov-Uvarov (N-U) method. Further, it is shown that in the non-relativistic limit, the energy eigenvalues reduce to that of Schrodinger equations for the potential. It is also shown that, the obtained results lead to the solutions of the same problem for modified P¨oschl-Teller potential for \(q = 1\).

Spin-orbital angular momentum degeneracy breaking in nanoplasmonic metachain.

The spin and orbital angular momentum (namely SAM and OAM) mode division provides a promising solution to surmount exhausted available degrees of freedom in conventional optical communications. Nevertheless, SAM and OAM are often subjected to the degeneracy of total angular momentum (AM) because they both have integer variables of quantum eigenstates, which inevitably brings about the shortcomings specific to limited signal channels and multiplexing cross talk. Herein, we present a nanoplasmonic metachain that can discriminatively couple any input SAM and OAM components to an extrinsic orbital AM, corresponding to the chirality and topological charge of incident light. Importantly, the unambiguous measurement has a prominent advantage of detecting the arbitrary AM component rather than the total AM. The miniature metadevice offers the possibility of harnessing AM division on chip or in fiber and holds great promise to delve the spin-orbit interactions for topological photonics and quantum cryptography.

Asymmetric conversion of arbitrary vortex fields via acoustic metasurface

Asymmetric manipulation of acoustic waves has gained significant attention due to its rich physical properties and potential application prospects. In this study, we design and demonstrate a planar acoustic metasurface (AM) that enables asymmetric conversion for vortex fields with arbitrary orbital angular momentum (OAM) to different plane waves by placing the same vortex source at different focusing points of above and below. This asymmetric effect is caused by the spatial asymmetry of vortex wave, and AM achieves the conversion of two types of waves through directional compensation of phases. Numerical demonstrations and acoustic experiments further validate this asymmetric phenomenon, and the deflection angle of converted plane waves is qualitatively and quantitatively confirmed by a more general formula. Our work enriches the research meta-system of acoustic wave physics and holds potential applications in underwater acoustic communication and OAM-based devices.

Terahertz metasurface for independent modulation of amplitude and phase in multi-channels

It is necessary to achieve simultaneous and independent modulation of the amplitude, polarization and phase of lights utilizing metasurface, which is also a great challenge. In this paper, an all-dielectric metasurface is proposed for simultaneously controlling the amplitude and phase of orthogonal linearly polarized lights in multi-channels. Three pairs of complex amplitude information are encoded in three independent channels by elaborately selecting and combining the meta-atoms. To verify the performance of proposed metasurface in the terahertz (THz) band, three examples are designed, including producing multiple vortex beams and arbitrary orbital angular momentum (OAM) superposition states, producing multiple foci with controllable intensity ratios, and producing multiple foci with controllable intensity ratios and focal lengths. The simulative results agree with experimental results. The proposed design based on single-layer structure has advantages of controllable focusing, compact structure, and simple fabrication, providing an alternative way for the preparation of integrated multifunctional and miniaturized optical devices.

A hybrid CPU/GPU method for Hartree-Fock self-consistent-field calculation.

The calculation of two-electron repulsion integrals (ERIs) is a crucial aspect of Hartree-Fock calculations. In computing the ERIs of varying angular momentum, both the central processing unit (CPU) and the graphics processing unit (GPU) have their respective advantages. To accelerate the ERI evaluation and Fock matrix generation, a hybrid CPU/GPU method has been proposed to maximize the computational power of both CPU and GPU while overlapping the CPU and GPU computations. This method employs a task queue where each task corresponds to ERIs with the same angular momentum. The queue begins with ERIs of low angular momentum, which are computationally efficient on GPUs, and ends with ERIs of high angular momentum, which are better suited for CPU computation. CPUs and GPUs dynamically grab and complete tasks from the start and end of the queue using OpenMP dynamic scheduling until all tasks are finished. The hybrid CPU/GPU computation offers the advantage of enabling calculations with arbitrary angular momentum. Test calculations showed that the hybrid CPU/GPU algorithm is more efficient than "GPU-only" when using a single GPU. However, as more GPUs are involved, the advantage diminishes or disappears. The scaling exponents of the hybrid method were slightly higher than "GPU-only," but the pre-exponent factor was significantly lower, making the hybrid method more effective overall.

Low-energy scattering parameters: A theoretical derivation of the effective range and scattering length for arbitrary angular momentum

The most important parameters in the study of low-energy scattering are the s-wave and p-wave scattering lengths and the s-wave effective range. We solve the scattering problem and find two useful formulas for the scattering length and the effective range for any angular momentum, as long as the Wigner threshold law holds. Using that formalism, we obtain a set of useful formulas for the angular-momentum scattering parameters of four different model potentials: hard-sphere, soft-sphere, spherical well, and well-barrier potentials. The behavior of the scattering parameters close to Feshbach resonances is also analyzed. Our derivations can be useful as hands-on activities for learning scattering theory.

Exact solutions for the electromagnetic fields of a flying focus

The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwell's equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. The approach combines the complex source-point method, which transforms multipole solutions into beam-like solutions, with the Lorentz invariance of Maxwell's equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus.

The spin-one DKP oscillator with an extra spin–orbit coupling

We consider a generalization of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons, built by implementing an extra spin–orbit coupling (SOC) into the standard DKPO equation. This model meets the requirements of Lorentz covariance as well as the existence of a conserved four-current, and is found to be exactly solvable for both natural and unnatural parity states and for an arbitrary total angular momentum number. The obtained energy eigenvalues show that the additional SOC brings about radical modifications in the spectroscopy of the DKPO. Notably, the spin–orbit splitting of the energy levels becomes controllably independent from oscillator shells. Moreover, interesting particular cases of the model as well as its non-relativistic limit are discussed.

Two particles interacting via a contact interaction on S^2

We consider two particles interacting via a contact interaction that are constrained to a sphere, or S^2. We determine their spectrum to arbitrary precision and for arbitrary angular momentum. We show how the non-inertial frame leads to non-trivial solutions for different angular momenta. Our results represent an extension of the finite-volume Lüscher formulas but now to a non-trivial geometry. We apply our results to predict the spectrum of select two-nucleon halo nuclei and compare with experimental results.

The use of photoionization cross section for evaluating contribution of continuum to the blackbody radiation induced shift and broadening of Rydberg-state energy levels of group IIb ions

General properties of n-dependence at the threshold and regularities of above-threshold ionization cross sections for states with high principal quantum numbers n and arbitrary angular momenta l are determined and used for evaluating the blackbody-radiation(BBR)-induced ionization broadening of nS, nP, nD and nF Rydberg-state energy levels of the group IIb ions Zn+, Cd+, Hg+ at temperatures from T=100 K to T=3000 K. The contributions to the energy level shifts from transitions into continuum are also determined with the use of the ionization cross sections. The single-electron quantum defect method (QDM) was used, which appears rather precise and suitable for calculating the amplitudes of radiation transitions from Rydberg states, and specifically for summation of matrix-element-dependent terms over infinite number of discrete states. The dependencies on temperature and binding energy are determined and approximate analytic equations are proposed for simplified evaluations of the BBR-induced ionization broadening and shifts. Numerical parameters of approximate equations are tabulated for S, P, D and F Rydberg states of the group IIb ions.

High‐Efficiency Phase and Polarization Modulation Metasurfaces

Use of metasurfaces to control the characteristics of electromagnetic waves is an emerging trend at present. Multifunctional metasurfaces, which can modulate multiple wave parameters, greatly reduce the complexity and enrich the functionality of optical systems. Herein, a high‐efficiency multifunctional metasurface for operation in the terahertz band is proposed and demonstrated. Use of a trilayer structure allows the working efficiency to reach 85% at the designed operating frequency. The phase and polarization states of the transmitted waves are modulated individually via subtle adjustment of the geometric parameters of each layer. Two terahertz‐band vector beam generators are demonstrated based on the proposed metasurface. The two devices individually generate radial and azimuthal terahertz vortex beams that can carry arbitrary orbital angular momentum. The experimental results demonstrate the validity of the proposed approach. This method represents a route toward easy fabrication of high‐performance phase and polarization modulation metasurfaces that can improve the information‐carrying capabilities of terahertz systems and offers benefits for structured light generation, optical information security, and optical communication applications.

Arbitrary polarization and orbital angular momentum generation based on spontaneously broken degeneracy in helically twisted ring-core photonic crystal fibers.

Using orbital angular momentum (OAM) as a spatial information channel attracts a lot of attention due to its infinite multiplexing capability. The research on OAM carrying fibers is intensively studied and ring-core fibers are promising candidates for them. At the same time, generating OAM modes in those fibers are also important topic. Here, the evolutions of polarization states including OAM of light in helically twisted ring-core photonic crystal fibers (PCFs) are investigated for generating OAM states. The degeneracy of some of the mode sets is spontaneously broken, and the birefringence cause a geometric phase (GP) in the twisted PCFs while preserving the vectorial nature of the modes. It is demonstrated that an arbitrary polarization and OAM state can be generated by using the GP in uniformly twisted and twisted PCFs with periodical inversion. In the ring-core PCF presented in this paper, the degeneracy of HE31 and EH31 mode sets are broken, and OAM light with the topological charge of 2 and 4 can be generated. The wavelength dependence is very small compared with that of OAM generators based on long-period gratings (LPGs). Furthermore, by properly setting the period of the inversion, OAM light with different topological charges can be simultaneously generated with the same fiber structure. These results indicate that the proposed approach is effective for the generation of OAM modes with the conventional fiber modes.

ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL

In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics

Bound State Solutions of the Hua Potential within the Framework of Two Approximations Scheme

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

Consistent Theory of Alpha-Decay

In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.