Superposition Of Beams Research Articles

Spin angular momentum and optical chirality of Poincaré vector vortex beams

Abstract The optical chirality and spin angular momentum of structured scalar vortex beams has been intensively studied in recent years. The pseudoscalar topological charge $\ell$ of these beams is responsible for their unique properties. Constructed from a superposition of scalar vortex beams with topological charges $\ell_\text{A}$ and $\ell_\text{B}$, cylindrical vector vortex beams are higher-order Poincar'e modes which possess a spatially inhomogeneous polarization distribution. Here we highlight the highly tailorable and exotic spatial distributions of the optical spin and chirality densities of these higher-order structured beams under both paraxial (weak focusing) and non-paraxial (tight focusing) conditions. Our analytical theory can yield the spin angular momentum and optical chirality of each point on any higher-order or hybrid-order Poincar'e sphere. It is shown that the tunable Pancharatnam topological charge $\ell_{\text{P}} = (\ell_\text{A} + \ell_\text{B})/2$ and polarization index $m = (\ell_\text{B} -\ell_\text{A})/2$ of the vector vortex beam plays a decisive role in customizing their spin and chirality spatial distributions. We also provide the correct analytical equations to describe a focused, non-paraxial scalar Bessel beam.

Reconfigurable unitary transformations of optical beam arrays

Spatial transformations of light are ubiquitous in optics, with examples ranging from simple imaging with a lens to quantum and classical information processing in waveguide meshes. Multi-plane light converter (MPLC) systems have emerged as a platform that promises completely general spatial transformations, i.e., a universal unitary. However, until now, MPLC systems have demonstrated transformations that are far from general, e.g., converting from a Gaussian to Laguerre-Gauss mode. Here, we demonstrate the promise of an MLPC, the ability to impose an arbitrary unitary transformation that can be reconfigured dynamically. Specifically, we consider transformations on superpositions of parallel free-space beams arranged in an array, which is a common information encoding in photonics. We experimentally test the full gamut of unitary transformations for a system of two parallel beams and make a map of their fidelity. We obtain an average transformation fidelity of 0.85 ± 0.03. This high-fidelity suggests that MPLCs are a useful tool for implementing the unitary transformations that comprise quantum and classical information processing.

High-efficiency generation of long-distance, tunable, high-order nondiffracting beams

Nondiffracting beams (NDBs) have presented significant utility across various fields for their unique properties of self-healing, anti-diffraction, and high-localized intensity distribution. We present a versatile and flexible method for generating high-order nondiffracting beams predicated on the Fourier transformation of polymorphic beams produced by the free lenses with tunable shapes. Based on the tunability of the digital free lenses, we demonstrate the experimental generation of various long-distance nondiffracting beams, including Bessel beams, polymorphic generalized nondiffracting beams, tilted nondiffracting beams, asymmetric nondiffracting beams, and specially structured beams generated by the superposition of Bessel beams. Our method achieves efficiency of up to about seven times compared with complex beam shaping methods. The generated NDBs exhibit characteristics of extended propagation distance and high-quality intensity profiles consistent with the theoretical predictions. The proposed method is anticipated to find applications in laser processing, optical manipulation, and other fields.

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.

A novel multiple-image encryption with multi-petals structured light

The study proposed a novel multiple-image encryption scheme using spatial multiplexing under the illumination of a multi-petals structured light. The security is enhanced through the multi-petals structured light with coherent superposition of several vortex beams with different topological charges. Through the system, an image array is formed behind the sub-petals of the complex structured light. Using Fresnel diffraction, each image is encrypted into the ciphertext by the Fibonacci Lucas transform. The multi-petals structured light with different orbital angular momentum can integrate more system parameters as the additional keys resulting in rich key space with improved security level of the cryptosystem. The feasibility and security of the proposed methods are validated through both numerical simulation and experiments. The research has strong and practical applications for three-dimensional information encryption system.

A Reduction in the Rotational Velocity Measurement Deviation of the Vortex Beam Superposition State for Tilted Object

In measuring object rotational velocity using vortex beam, the incident light on a tilted object causes spectral broadening, which significantly interferes with the identification of the true rotational Doppler shift (RDS) peak. We employed a velocity decomposition method to analyze the relationship between the spectral extremum and the central frequency shift caused by the object tilt. Compared with the linear growth trend observed when calculating the object rotational velocity using the frequency peak with the maximum amplitude, the central frequency calculation method effectively reduced the deviation rate of the RDS and velocity measurement value from the true value, even at large tilt angles. This approach increased the maximum tilt angle for a 1% relative error from 0.221 to 0.287 rad, representing a 29.9% improvement. When the tilt angle was 0.7 rad, the velocity measurement deviation reduction rate can reach 5.85%. Our work provides crucial support for achieving high-precision rotational velocity measurement of tilted object.

Evolution of C-point singularities and polarization coverage of Poincaré–Bessel beam in self-healing process

As a vector version of scalar Bessel beams, Poincaré–Bessel beams (PBBs) have attracted a great deal of attention due to their non-diffracting and self-healing properties as well as the presence of polarization singularities. Previous studies of PBBs have focused on cases that consist of a superposition of Bessel beams in orthogonal circular polarization states; here, we present a theoretical and experimental study of PBBs for which the polarization states are taken to be linear, which we call a linear PBB. Using a mode transformation of a full Poincaré beam constructed from linear polarization states, we observe the linear PBB as providing an in-principle infinite number of covers of the Poincaré sphere in the transverse plane and with an infinite number of C-points with positive and negative topological indices. We also study the dynamics of C-point singularities in a linear PBB in the process of self-healing after being obstructed by an obstacle, providing insight into “Hilbert Hotel” style evolution of singularities in light beams. The present study can be useful for imaging in the presence of depolarizing surroundings, studying turbulent atmospheric channels, and exploring the rich mathematical concepts of transfinite numbers.

Recognizing OAM mode of high-order radial vortex beam superposition states employing convolutional neural network

Recognizing OAM mode of high-order radial vortex beam superposition states employing convolutional neural network

Investigation of the Effect of Defocusing on Interference Patterns Obtained in X-Ray Three-Block Interferometers

The results of studying the effect of defocusing on interference patterns obtained in X-ray three-block interferometers are presented. Three-block defocused interferometers without a thick block analyzer, with a thick block analyzer and with a separate thick block (enlarger) are designed, manufactured and tested. It is shown that fine structures of interference patterns obtained from three-block defocused interferometers are observed in cases when the interferometer analyzer block is thick or an enlarger is used (fourth thick block). Theoretical calculations show that in the presence of defocusing, as a result of superposition of beams on the input surface of the interferometer analyzer, an interference pattern is formed in the form of parallel fringes (lines) lying in the scattering plane. The coordinates of the maxima of the interference fringes (lines) and the period of the fringes are calculated in the cases without a thick crystal and in its presence, as well as the magnification factor. It has been experimentally proved that a thick crystal (enlarger crystal) does not introduce new information into the interference pattern, but only increases its size in the scattering plane.

Distortion and Compensation of Doppler Shift Characteristics of Vortex Beam Superposition Due to Rotating Rough Surfaces and Occlusion

Distortion and Compensation of Doppler Shift Characteristics of Vortex Beam Superposition Due to Rotating Rough Surfaces and Occlusion

Tunable multifunctional terahertz metasurface based on an indium antimonide medium

Active adjustable terahertz multifunctional devices are crucial for the application of terahertz technology. In this paper, we propose a composite metasurface structure based on an indium antimonide metal octagonal pattern, which achieves different functional switching by controlling the phase state of indium antimonide material under different ambient temperatures. When indium antimonide exhibits in the dielectric state, by stacking and encoding the unit cell, the designed metasurface has the functions of two-beam splitting beam superposition, vortex beam and quarter beam superposition, and dual vortex beam superposition for circularly polarized and linearly polarized wave incidence. When indium antimonide appears in the metallic state, the encoding metasurface alters the modulation function of incident circularly polarized and linearly polarized terahertz waves. This terahertz metasurface provides a new approach for the design of multifunctional devices that can flexibly regulate terahertz wave metasurfaces.

Multi-dimensional tunable arbitrary shape beams with engineered axial profile

Bessel beams, as one type of special light field, would significantly do benefit to several applications such as light-sheet microscopy, particle manipulation and free-space optical communications. In this paper, we investigate the generation of multi-dimensional tunable arbitrary shape beams with engineered axial profile based on the superposition of zero-order Bessel beams by designing the angular spectrum, providing a universal method to manipulate arbitrary shape beams in terms of longitudinal intensity, transverse wavevector distribution and transverse field shape. Through angular spectral analysis, we demonstrate the shape-invariant axial engineering of circle, ellipse, parabolic, and epicycloid-shaped beams, as well as shape-variant axial engineering such as self-acceleration, self-rotation, and self-mode conversion, from both theoretical and experimental perspectives. Our work provides a deep insight into the fundamental properties of arbitrary shape light with engineered axial profile and paves new way toward exploiting more dimensions for its future applications.

Intrinsic dichroism in amorphous and crystalline solids with helical light

Amorphous solids do not exhibit long-range order due to the disordered arrangement of atoms. They lack translational and rotational symmetry on a macroscopic scale and are therefore isotropic. As a result, differential absorption of polarized light, called dichroism, is not known to exist in amorphous solids. Using helical light beams that carry orbital angular momentum as a probe, we demonstrate that dichroism is intrinsic to both amorphous and crystalline solids. We show that in the nonlinear regime, helical dichroism is responsive to the short-range order and its origin is explained in terms of interband multiphoton assisted tunneling. We also demonstrate that the helical dichroism signal is sensitive to chirality and its strength can be controlled and tuned using a superposition of OAM and Gaussian beams. Our research challenges the conventional knowledge that dichroism does not exist in amorphous solids and enables to manipulate the optical properties of solids.

Deep learning-assisted light sheet holography.

In a novel approach to layer-based holography, we propose a machine learning-assisted light sheet holography-an optimized holography technique which projects a target scene onto sheets of light along the longitudinal planes (i.e. planes perpendicular to the plane of the hologram). Using a convolutional neural network in conjunction with superposition of Bessel beams, we generate high-definition images which can be stacked in parallel onto longitudinal planes with very high fidelity. Our holography system provides high axial resolution and excellent control over the light intensity along the optical path, which is suitable for augmented reality and/or virtual reality applications.

Lissajous singularities in Young's interference experiment.

We explore the interference of two bichromatic vector beams in Young's interference experiment. Our analysis focuses on determining the conditions under which the superposition of such beams, emerging from the pinholes, can give rise to Lissajous-type polarization singularities on the observation screen. Two independent sufficiency conditions are derived. This analysis aids in comprehending the inherent characteristics of Lissajous singularities. To the best of our knowledge, this is the first demonstration of the singular behavior of polarization in a two-frequency field in Young's interference experiment.

Exact analytical solutions for micrometer structured vortex beams with applications to optical tweezers

Bessel beams are widely known by their non-diffracting properties, i.e. beams that sustain their transverse profile along the propagation. It is also well known that by a suitable superposition of Bessel beams of the same frequency, but different longitudinal wave numbers, amplitudes and phases, it is possible to obtain a resulting beam whose longitudinal intensity pattern can be shaped along the propagation z-axis. Such approach, named Frozen Wave method, can be implemented through discrete or continuous superposition, the latter being more appropriate for obtaining spatially structured beams in micrometer domains. In previous studies, authors constructed analytical solutions for micrometer zero-order (i.e., null topological charge) Frozen Wave and, thereafter, of order one and two, by making use of a topological charge raising operator. In this paper, we present an analytical closed solution for the general case where the topological charge raising operator is applied an arbitrary number of times to a micrometer zero-order Frozen Wave beam, thus generating one of arbitrary topological charge. We also apply the new solutions to model optical tweezers (in Rayleigh regime) considering different light polarizations.

Differentiated tactile effects of vibration modal superposition considering the time course

Several theoretical studies on modal superposition methods to achieve tactile differentiation have been reported. However, there is still a lack of in-depth analysis and understanding of the regularity of the superposition of vibration modes and the resulting differences in tactile sensation. The touch beam vibrations are no longer in the form of standing waves after the modal superposition. The vibration points on the touch beam will present a periodic motion over time, instead of simply moving harmonically. The vibration response of the touch beam at high frequency, gave subjects a dramatically different tactile perception from that of a single inherent mode. Therefore, this paper reshapes the modal superposition theory of the haptic feedback technique to classify the vibration modes generated by the modal superposition of touch beams showing differences in tactile sensations considering the time course. The analysis and tactile texture prediction theories are improved compared to previous studies. The tactile sensation generated by the vibration patterns of left-right sway were found in the touch beam. Finally, the correctness of the tactile differentiation achieved by the modal superposition method was demonstrated by psychophysical assessment for different finger conditions.

A Simulation Study of the Dynamical Control of Optical Skyrmion Lattices through the Superposition of Optical Vortex Beams

Optical skyrmion lattices play an important role in photonic system design and have potential applications in optical transmission and storage. In this study, we propose a novel metasurface approach to calculating the dependence of the multi-beam interference principle and the angular momentum action in the spin–orbit interaction. The metasurface consists of nanopore structures, which are used to generate an optical skyrmion lattice. The superposition of optical vortex beams with circular polarization states is used to evaluate the evolution of the shape of the topological domain walls of the hexagonal skyrmion lattice. Our results show that the distribution of the skyrmion spin vector can be controlled by changing the lattice arrangement from triangular to hexagonal shapes. The distribution of skyrmion number at the microscale is further calculated. Our work has significant implications for the regulation of the shape of topological domain walls of skyrmion lattices, with potential applications in polarization sensing, nanopositioning, and super-resolution microimaging.

High-order optical Hall effect at the tight focus of laser radiation

In this work, by the Richards-Wolf method, which describes the behavior of electromagnetic radiation at the tight focus, it is shown that high-order spin and orbital Hall effects take place in the focal plane. It is shown that when focusing a linearly polarized optical vortex with unit topological charge, four local subwavelength regions are formed in the focal plane, in which directions of the longitudinal projection of the spin angular momentum are opposite in the neighboring regions. That is, photons falling into neighboring regions in the focus have the opposite spin. This is the spin Hall effect of the 2nd order. It is also shown that when tightly focusing of superposition of cylindrical vector beams of the m-th order and zero order, 2m subwavelength regions are formed in the plane of tight focus, in which directions of the longitudinal projection of the orbital angular momentum are opposite in the neighboring regions. That is, photons falling into the neighboring regions at the focus have the opposite-sign on-axis projections of the orbital angular momentum. This is the orbital Hall effect of the m-th order.

Localization of a Dielectric Spherical Nanoparticle Under the Action of a Gradient Force in an Interference Field Formed by the Superposition of Oncoming Laser Beams

Localization of a Dielectric Spherical Nanoparticle Under the Action of a Gradient Force in an Interference Field Formed by the Superposition of Oncoming Laser Beams