Angular Momentum Spectrum Research Articles

Phase control method for generating orbital angular momentum beams using coherent beam combining based on deep learning

In recent years, orbital angular momentum (OAM) beams have shown great potential for applications in laser communication, laser processing, optical imaging, and detection. For free-space optical communication, high-power, high-quality vortex beams with a high signal-to-noise ratio are critical for long-distance communication. Coherent beam combining (CBC) of vortex beams enables the enhancement of power while maintaining high beam quality. Considering the orbital angular momentum spectrum as a new dimension of optical wave resources, achieving rapid phase locking of specific phases is crucial for increasing communication capacity. Traditional phase control methods based on wavefront intensity distribution face limitations in optimization, particularly for centrosymmetric laser phased arrays. To address this, we propose a deep learning-based method using spiral phase modulation. By designing a loss function that eliminates phase periodicity, we establish a nonlinear mapping between the sub-beam phases and the far-field image. To improve the phase prediction accuracy of the deep learning model, we introduce a power-in-the-bucket (PIB) metric for the vortex beam’s main lobe, which mitigates dynamic phase errors caused by thermal and environmental disturbances. This method holds promise for application in high-power vortex beam optical systems with coherent combining of fiber laser phased arrays.

Precision measurement of the topological charge of a fractional vortex beam based on angular-grating-diffraction OAM spectrum.

Vortex light beams carrying fractional vortices have shown promising applications in many fields such as optical communications, optical encryption, and quantum information processing. Accurate detection of the topological charge of a fractional vortex phase is essential for these applications. In this paper, a simple yet effective method for measuring the fractional topological charge is proposed, which is based on the detection of the orbital angular momentum (OAM) spectrum of a fractional vortex beam diffracted by an angular grating. When the fractional vortex beam passes through an angular grating, the OAM spectrum broadens, increasing the number of detectable OAM components. By applying nonlinear least squares fitting to the broadened spectrum, the topological charge can be detected with high precision. Experimental results demonstrate the detection range for fractional topological charges is from -6 to 6, with a resolution of 0.01 and an error of less than 0.005. Our protocol offers significant potential for high-capacity information transfer.

Universal analyzer for measuring the orbital angular momentum spectrum of a randomly fluctuated beam.

The orbital angular momentum (OAM) of beams provides an additional degree of freedom and has been applied in various scientific and technological fields. Accurate and quantitative measurement of intensity distributions across different OAM modes, referred to as the OAM spectrum of a beam, is crucial. Here, we propose a straightforward and efficient experimental setup for measuring the OAM spectrum of a randomly fluctuating beam. By employing a modal decomposition analyzer, a randomly fluctuating light field can be decomposed into an incoherent superposition of a series of modes, followed by a coordinate transformation to calculate the OAM spectrum. This method is suitable for measuring the OAM spectrum of partially coherent beams and superposition of vortex beams. The experimental results are in good agreement with the theoretical predictions. Precise measurement of the OAM spectrum is critical for various applications in optical communications, quantum optics, and digital imaging.

Measuring the OAM spectrum of a fractional helical beam in a single shot

We propose and experimentally demonstrate a new technique, to our knowledge, to precisely measure the orbital angular momentum (OAM) spectrum of the fractional helical beam in a single shot. This is realized using a single-path interferometer scheme combined with space division multiplexing and polarization phase-shifting. Such a combination enables the single-shot recording of multiple phase-shifted interferograms, which leads to extracting the phase profile of the incident fractional helical beam. Furthermore, by adopting an orthogonal projection method, this measured phase is utilized to evaluate the corresponding OAM spectrum. To test the efficacy, a set of simulations and experiments for different fractional helical beams is demonstrated. The proposed method shows enormous potential to characterize the OAM spectrum in real time.

Harnessing physics-guided neural networks for tailoring the orbital angular momentum spectrum in second harmonic generation

The management of orbital angular momentum (OAM) in frequency conversion processes is essential for numerous applications such as quantum and classical optical communications. This paper presents a wavefront modulation approach for the fundamental beam in second harmonic generation (SHG) to efficiently control the OAM spectrum. We employ an inverse design method to derive the necessary wavefront shape of the fundamental beam for achieving a desired SHG OAM spectrum. Specifically, we introduce an efficient inverse design technique based on physics-guided neural networks (PGNNs) that incorporates the coupled equations governing SHG, aimed at tailoring the OAM spectrum of SHG. Utilizing the proposed PGNN, we design the phase pattern for a spatial light modulator (SLM) to shape the wavefront of the fundamental beam. Furthermore, we present a novel loss function, to our knowledge, that effectively links the OAM of the SHG spectrum and efficiency to the SLM phase pattern and crystal temperature, independent of empirical weight coefficients. The proposed PGNN facilitates the purification of the SHG OAM spectrum, even when the fundamental beam comprises mixed Laguerre–Gaussian (LG) modes. Additionally, we demonstrate the generation of desired SHG spectra using the proposed PGNN framework. This study introduces what we believe to be a groundbreaking inverse design method for developing photonic devices with customized functionalities, addressing challenges associated with traditional data-driven deep learning techniques.

Evolutions of a ring Airy vortex beam and a ring Pearcey vortex beam in turbulent atmosphere and a comparative analysis of their channel efficiencies and OAM spectra

An optical vortex beam propagating through turbulent atmosphere encounters distortions in the wavefront that result in modal scattering. Abruptly autofocusing (AAF) beams with orbital angular momentum have gained significant attention due to their non-diffracting and self-healing nature. These warrant understanding of the behavior of these beams through turbulent atmosphere absolutely necessary. With this intuition, in the present work we investigate the behavior of two AAF beams, namely the ring Airy vortex beam (RAVB) and ring Pearcey vortex beam (RPVB) through the turbulent atmosphere in two cases—multiplexed and non-multiplexed. We propagate multiplexed as well as non-multiplexed RAVB and RPVB in different levels of turbulent atmosphere. In the non-multiplexed case, channel efficiency declines for both beams with increase in mode numbers. In the multiplexed case, increasing the gap between the mode sets results in a decrease in channel efficiency. We also report that in weak atmospheric turbulence RAVB outperforms RPVB in terms of channel efficiency. We use the optical transformation sorting (log-polar) method to demultiplex the optical beams at the output. Furthermore, we investigate and compare the orbital angular momentum (OAM) spectra of both beams in different levels of atmospheric turbulence and at different propagation distances. The comparison reveals that the spectra of RPVB are more dispersive as compared to those of RAVB.

Propagation dynamics of orbital angular momentum beams under the hazy scattering environment.

The disturbance of the scattering medium, such as hazy, can affect the propagation of vortex beams and induce cross-talk within the orbital angular momentum (OAM) spectrum in optical communications based on vortex beams. This paper first validates the integrated scattering phase screen model through experimental beam phase measurements using a simple interferometer. Then, the influence of macroscopic physical parameters of the scattering medium on the OAM spectrum is investigated based on the hazy scattering phase model. It is demonstrated that the larger particle radius, concentration, and thickness will result in a greater cross-talk of the OAM spectrum. Moreover, the behavior of multiplexed vortex beams influenced by the hazy environment is also studied. The results may be a powerful tool to estimate the effect of the scattering medium on beam quality in optical communication based on vortex beams.

Orbital angular momentum spectrum of model partially coherent beams in turbulence

The use of partial coherence has been extensively studied as a potential solution to mitigate the destructive effects of atmospheric turbulence in optical applications involving the free space propagation of light. However, in OAM-based optical systems, reducing coherence leads to the broadening of the orbital angular momentum (OAM) spectrum, consequently increasing the cross-talk between adjacent modes. In this paper, we have investigated three fundamental classes of partially coherent OAM beams under the influence of turbulence. The aim is to identify a distinct type of partially coherent beam (PCB) in which the reduction in coherence results in higher resistance of the OAM spectrum against atmospheric disturbances. It is demonstrated that, for a specific propagation distance, we can prepare a PCB in which the benefits of reducing coherence outweigh its drawbacks.

Tailoring nondiffracting fields with a non-Markovian phase imprint.

We experimentally generate nondiffracting speckles that carry non-Markovian properties by encoding the wavefront of a monochromatic laser beam with ring-shaped non-Markovian phases. The resulting non-Markovian nondiffracting fields present a ring-shaped pattern and central dark notches, which are analyzed with an expression of the orbital angular momentum spectra of the wavefront possessing ring-shaped non-Markovian phases. Furthermore, we demonstrate that the intensity profiles of these non-Markovian nondiffracting fields exhibit stability over multiple Rayleigh ranges, and their statistical properties could be controlled with the non-Markovianity of the input phase masks. This work presents an approach for simultaneously tailoring the diffracting property and non-Markovianity of optical fields and provides a deeper understanding of non-Markovian processes.

Turbulence on open string worldsheets under non-integrable boundary conditions

We demonstrate the turbulent dynamics of the Nambu-Goto open string in the AdS3 spacetime. While the motion of a classical closed string in AdS is known to be integrable, the integrability of an open string motion depends on the boundary conditions at the string endpoints. We numerically solve the equations of motion of the open string under the boundary conditions where the endpoints are i) fixed to a finite radial coordinate in AdS, and ii) free. For i), we find turbulence on the string, that shows a cascade in the energy and angular momentum spectra. This result indicates the non-integrability of the open string with this type of boundary conditions. For ii), we find no turbulence. This is consistent with the integrability of the open string with the free boundary conditions.

Metasurface for Engineering Superimposed Ince-Gaussian Beams.

Ince-Gaussian beams (IGBs) are the third complete family of exact and orthogonal solutions of the paraxial wave equation and have been applied in many fields ranging from particle trapping to quantum optics. IGBs play a very important role in optics as they represent the exact and continuous transition modes connecting Laguerre-Gaussian and Hermite-Gaussian beams. The method currently in use suffers from the high cost, complexity, and large volume of the optical system. The superposition of IGBs can generate complicated structured beams with multiple phase and polarization singularities. A metasurface approach is proposed to realizing various superpositions of IGBs without relying on a complicated optical setup. By superimposing IGBs with even and odd modes, multiple phase, and polarization singularities are observed in the resultant beams. The phase and polarization singularities are modulated by setting the initial phase in the design and controlling the incident linear polarization. The compactness of the developed metasurface devices and the unique properties of the generated beams have the potential to impact many practical applications such as particle manipulation, orbital angular momentum spectrum manipulation, and optical communications.

Analytical calculation of beam profile and orbital angular momentum spectrum of Laguerre Gaussian beams reflected from a graphene plasmonic structure.

In this paper, Laguerre Gaussian (LG) beams with different topological charges are used for excitation of surface plasmon polaritons (SPPs) through a graphene layer inserted in the Otto-configuration. By utilizing the angular spectrum representation (ASR) and Lorenz-gauge vector potential, an explicit analytical expression is derived for the electromagnetic fields of the reflected beam. At the optimal excitation state of graphene SPPs, the reflected beam exhibits a distinctive field profile characterized by two identical crescent-shaped lobes separated by a vertical strip with null intensity. Furthermore, in the absence of external magnetic field, the orbital angular momentum (OAM) spectrum of the reflected beam at the optimal excitation of SPPs reveals the annihilation of central OAM mode and the generation of two equal OAM sidebands, regardless of the incident OAM topological charge. Furthermore, the phase distributions of electric field of the reflected beam confirm the existence of OAM sidebands in the vicinity of optimal SPPs excitation. As the system is taken away from the optimal excitation of SPPs by introduction of an external magnetic field or increasing the chemical potential or increasing the incident angle, both central and sideband modes appear in the OAM spectrum of the reflected beam. In this case, when the topological charge of the incident wave increases, the weight of central OAM mode decreases while the weight of sidebands increases. In contrast, in the presence of external magnetic field, at the optimal excitation of SPPs, both central OAM and sidebands modes exist in the reflected beam such that the weight of central modes increases with the external magnetic field. This effect is also confirmed by plotting the phase distributions of the reflected beam at different external magnetic fields and for different incident topological charges. Therefore, the manipulation of graphene plasmons characteristics leads to the control of OAM sideband generation.

Breaking the symmetric spiral spectrum distribution of a Laguerre-Gaussian beam propagating in moderate-to-strong isotropic atmospheric turbulence.

We demonstrate that the spiral spectrum (also known as orbital angular momentum spectrum) of a Laguerre-Gaussian (LG) beam with topological charge (TC) l is asymmetrically broadened propagating through moderate-to-strong atmospheric turbulence, even the statistics of turbulence is isotropic. This phenomenon is quite different from that predicted in weak turbulence where the spiral spectrum of a disturbed LG beam is symmetric with respect to its TC number l. An explicit analytical expression of the spiral spectrum of the LG beam with l = 1 is derived based on the extend Huygens-Fresnel integral and quadratic approximation, which is used to illustrate the transition scenarios of the spiral spectrum from symmetry to asymmetry in weak-to-strong turbulence. The physical mechanism for the asymmetric spiral spectrum in moderate-to-strong turbulence is thoroughly discussed. Our results are confirmed by the multi-phase screen numerical simulations and are consistent with the experimental results reported in Phys. Rev. A105, 053513 (2022)10.1103/PhysRevA.105.053513 and Opt. Lett.38, 4062 (2013)10.1364/OL.38.004062.

Photon sphere and quasinormal modes in AdS/CFT

Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large angular momentum analysis owes to an analogue to solvable Schrödinger equations such as an inverted harmonic oscillator and the Pöschl-Teller model, with a Dirichlet boundary condition. Through the AdS/CFT dictionary, it predicts the existence of a peculiar subsector in the large angular momentum spectrum of thermal holographic CFTs on a sphere.

Spin angular momentum and angular harmonics spectrum of two-order polarization vortices at the tight focus

We investigate the spin angular momentum (SAM) of two-order cylindrical vector beams at the tight focus. Such beams are a generalization of the conventional cylindrical vector beams since the transverse field components on the Cartesian axes have different polarization orders. Using the Richards-Wolf approximation, we derive an expression for the longitudinal component of the SAM density distribution. We show that if the polarization indices are of different parity then, an optical spin Hall effect arises at the tight focus, meaning that alternating areas with positive and negative SAM are originated although the initial light field is linearly polarized. We study the angular harmonics spectrum of all the components of the focused light field and determine the predominant angular harmonics. Then, neglecting the insignificant harmonics, we define the shape of the longitudinal component of the SAM density distribution and demonstrate the possibility of generating a focal SAM distribution where the areas with positive and negative SAM reside on a circle as alternating pairs or separated into different half-circles.

Single-shot Kramers–Kronig complex orbital angular momentum spectrum retrieval

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few shots. Yet, its single-shot retrieval remains elusive, due to the signal–signal beat interference inherent in the measurement. Here, we introduce the concept of Kramers–Kronig (KK) receiver in coherent communications to the OAM domain, enabling rigorous, single-shot OAM spectrum measurement. We explain in detail the working principle and the requirement of the KK method and then apply the technique to precisely measure various characteristic OAM states. In addition, we discuss the effects of the carrier-to-signal power ratio and the number of sampling points essential for rigorous retrieval and evaluate the performance on a large set of random OAM spectra and high-dimensional spaces. Single-shot KK interferometry shows enormous potential for characterizing complex OAM states in real time.

Complex field manipulation based on OAM spectrum analysis with an arbitrarily distributed antenna array

In the next generation multiple-input multiple-output (MIMO) communication system, a higher effective degree of freedom (EDoF) is desired to increase the channel capacity. Hence, complex field manipulation, which enriches the diversity of the amplitude and phase distribution, is necessary for an antenna array. In this paper, the complex field manipulation (CFM) scheme based on an arbitrarily distributed antenna array is proposed, which takes the orbital angular momentum (OAM) spectrum analysis as the bridge. Whether the antenna element transformation states are fixed or flexible, the CFM can be achieved with different schemes. This work may promote the application of OAM spectrum analysis and the development of complex field manipulation in the high-EDoF MIMO communication system.

The study of angular momentum on the fusion of [formula omitted]Si+[formula omitted]Si, using SEDF in semiclassical extended Thomas-Fermi approach

The total fusion cross-sections are calculated for energies both above and below the potential barrier by using the properties of the interaction potential in Hill-Wheeler approximation for a positive Q-value system 1428Si+1428Si. The Coulomb and centrifugal parts of the potentials are added directly to the nuclear proximity potential to calculate the total interaction potential, where nuclear proximity potential is obtained in semiclassical extended Thomas-Fermi approach of Skyrme energy density formalism for Skyrme SIV parametrization. The angular momentum spectrum of total cross sections is obtained and calculated by using angular momentum dependent properties of the total interaction potential. The properties of total interaction potential, which are usually treated as independent of angular momentum, i.e. barrier height, barrier position and its width are calculated and found to depend sharply on the angular momentum value at a fixed center of mass energy. It effect the fusion cross-section sufficiently above the barrier energy. However at energies below the barrier energy the addition of large angular momentum values have negligible effects on fusion cross-section. Further, the maximum in fusion cross-section is observed at a particular value of angular momentum, which is not equal to the maximum value of angular momentum.

Distortion Compensation for Orbital Angular Momentum Beams: From Probing to Deep Learning

Beams carrying orbital angular momentum (OAM), has attracted wide interests recently, due to their favorable potential in communications, optical tweezers, remote detection, etc. However, distortion will come once OAM beams propagate through inhomogeneous media like atmospheric turbulence. Such distortion will broaden the orbital angular momentum spectrum, thus introduce interchannel crosstalk. These phenomena will adversely affect practical applications, for instance, the rising bit-error-rate in OAM-based data transmission. Therefore, distortion correction for OAM beams, an important means to improve the robustness of OAM beams when propagating in atmospheric turbulence, must be developed. In this paper, we overview recent advances on distortion compensation of OAM beams, including the influence of atmospheric turbulence on OAM beams, and multiple wavefront correction schemes. In addition, toward the engineering realization of OAM based free space data-transmission, we propose to apply TSVMD-AR model to predict atmospheric turbulence, and expect to further improve the distortion correction efficiency.

Scattering characteristics of electrically large arbitrarily shaped targets illuminated by an off-axis vortex electromagnetic beam

For the application of vortex electromagnetic (EM) beams in practical detection scenes, the scattering characteristics of electrically large arbitrarily shaped targets illuminated by an off-axis Laguerre–Gaussian (LG) vortex beam are investigated and compared to the on-axis incidence case. The vector potential method is used to extract the electric and magnetic field components of the LG beam in different polarization states. The physical optics algorithm is adopted to calculate the scattering fields of four typical targets with the shape of a sphere, NASA almond, blunt cone, and blade model. The results revealed that as the beam center offset and the topological charge of the incident vortex beam increase, the scattering field distorts, and the obvious orbital angular momentum (OAM) spectrum mixing occurs. In addition, OAM spectrum aliasing occurs for asymmetric targets, even at on-axis incidence. These results elucidate the mechanism of vortex EM scattering and provide a reference for applying vortex beams for target detection and recognition.