Constituent Beams Research Articles

Energy rule for enhancing the spin Hall effect in superposition of axisymmetric beams with cylindrical and linear polarization

We study the spin angular momentum of a superposition of two vector light beams radial symmetry, one has cylindrical polarization and another – linear. Both beams can have an arbitrary radial shape. An analytical expression is obtained for the spin angular momentum and two its properties are proven. The first one is that changing weight coefficients of the superposition does not changes the shape of the spin angular momentum density distribution, whereas the intensity shape can change. The second property is that the maximal spin angular momentum density is achieved when both constituent beams in the superposition have equal energy.

Interference of high-order perfect optical vortex beams

We investigate the interference of high-order perfect optical vortex (POV) beams with different topological charges. Through numerical simulations, we reveal a remarkable phenomenon: keeping the beam width, and beam radius fixed while changing the topological charge, the splitting of the composite POV beam into two distinct individual perfect vortices occurs exactly at the same inter-axial separation. The observed interference pattern exhibits pronounced sensitivity to factors such as axial separation, phase shift, beam radius, and topological charges of the constituent beams. Notably, our findings are contrasted with the interference of high-order Laguerre-Gauss (LG) beams, highlighting that the splitting of composite vortices into their individual components is more rapid in the case of LG beams. We also investigate the evolution of the interference pattern for both POV, and LG beams along the propagation direction in free-space. Our research provides significant insights into the distinct interference properties of high-order POV beams, presenting potential applications in the fields of optical manipulation and communication systems.

Optical spin and orbital Hall effects at the tight focus of the superposition of two coaxial cylindrical vector beams with different-parity numbers

We study properties of a light field at the tight focus of the superposition of two different-order cylindrical vector beams (CVBs). In the source plane, this superposition has a polarization singularity index amounting to the half-sum of the numbers of two constituent CVBs, while having neither spin angular momentum (SAM) nor transverse energy flow. We show that if the constituent CVBs have different-parity numbers, in the focal plane there occur areas that have opposite-sign longitudinal SAM projections, alongside areas of opposite-handed energy flows rotating on closed paths (clockwise and anticlockwise). The observed phenomena indicate that longitudinal optical spin/orbital Hall effects occur in the focal plane. It is found that if the two constituent CVBs have the same-parity numbers, in the focal plane the light field is inhomogeneously linearly polarized and the energy flow (Umov-Poytning vector) has just a longitudinal component. It is also shown that in the focal plane, the intensity of the on-axis superposition of two opposite-parity CVBs is defined by the sum of the constituent beams’ intensities, as though the two beams would be orthogonally polarized. Meanwhile, in the source plane, the beams under study are not orthogonally polarized and the relation for the intensity contains an interference term.

Size dependent scaling law of plastic flow in FCC nanolattices: A dislocation dynamics study

Micro- and nanolattices can achieve simultaneously both lightweight and ultra-high strength due to a combination of resilient architecture and enhanced mechanical properties of small-scale unit constituents. However, understanding the fundamental deformation mechanism for these novel materials remains intriguing due to the intricate interplay of various geometric characteristics and intrinsic microscopic defects. Here, we investigate the fundamental mechanism of plastic deformation in terms of dynamic evolution of defects and corresponding mechanical responses in aluminum nanolattices using a mesoscale defect dynamics model which couples three-dimensional dislocation dynamics and finite element method. Our concurrently coupled model could capture detailed dislocation motion under complex loading conditions and predict the plastic flow stress of the nanolattices. We demonstrate that the size of individual constituent beam plays a critical role in the properties of nanolattices through small-scale strengthening, showing the strength of the nanolattices increases with decreasing beam size with the scaling law of σ∝db−0.89. As a result, the scaling law of plastic yielding with material density drastically increases from the continuum prediction. In addition, our modeling could allow us to study the geometric effect with various nanolattices. These findings establish a foundation for the fundamental understanding of the governing mechanism of plastic deformation, allowing access to a new regime in designing optimal structures using nanolattices.

Controlling the Spin Hall Effect in the Sharp Focus of an Axial Superposition of Two Optical Vortices with Left- and Right-Handed Circular Polarization

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus.

Comparing Mechanical Neural-Network Learning Algorithms

Abstract The purpose of this work is to compare learning algorithms to identify which is the fastest and most accurate for training mechanical neural networks (MNNs). MNNs are a unique class of lattice-based artificial intelligence (AI) architected materials that learn their mechanical behaviors with repeated exposure to external loads. They can learn multiple behaviors simultaneously in situ and re-learn desired behaviors after being damaged or cut into new shapes. MNNs learn by tuning the stiffnesses of their constituent beams similar to how artificial neural networks (ANNs) learn by tuning their weights. In this work, we compare the performance of six algorithms (i.e., genetic algorithm, full pattern search, partial pattern search, interior point, sequential quadratic progression, and Nelder–Mead) applied to MNN leaning. A computational model was created to simulate MNN learning using these algorithms with experimentally measured noise included. A total of 3900 runs were simulated. The results were validated using experimentally collected data from a physical MNN. We identify algorithms like Nelder–Mead that are both fast and able to reject noise. Additionally, we provide insights into selecting learning algorithms based on the desired balance between accuracy and speed, as well as the general characteristics that are favorable for training MNNs. These insights will promote more efficient MNN learning and will provide a foundation for future algorithm development.

Analytical solutions for Bloch waves in resonant phononic crystals: deep-subwavelength energy splitting and mode steering between topologically protected interfacial and edge states

Summary We derive analytical solutions based on singular Green’s functions, which enable efficient computations of scattering simulations or Floquet–Bloch dispersion relations for waves propagating through an elastic plate, whose surface is patterned by periodic arrays of elastic beams. Our methodology is versatile and allows us to solve a range of problems regarding arrangements of multiple beams per primitive cell, over Bragg to deep-subwavelength scales; we cross-verify against finite element numerical simulations to gain further confidence in our approach, which relies upon the hypothesis of Euler–Bernoulli beam theory considerably simplifying continuity conditions such that each beam can be replaced by point forces and moments applied to the neutral plane of the plate. The representations of Green’s functions by Fourier series or Fourier transforms readily follows, yielding rapid and accurate analytical schemes. The accuracy and flexibility of our solutions are demonstrated by engineering topologically non-trivial states, from primitive cells with broken spatial symmetries, following the phononic analogue of the Quantum Valley Hall Effect. Topologically protected states are produced and coexist along: interfaces between adjoining chiral-mirrored bulk media, and edges between one such chiral bulk and the surrounding bare elastic plate, allowing topological circuits to be designed with robust waveguiding. Our topologically protected interfacial states correspond to zero-line modes, and our topological edgestates are produced in accordance with the bulk-edge correspondence. These topologically non-trivial states exist within near flexural resonances of the constituent beams of the phononic crystal and hence can be tuned into a deep-subwavelength regime.

The mechanics and optimal design of micro-architectured stepped hexagonal lattices

This paper conceptualises and analyses a new class of stepped hexagonal lattice achieved through modifying the cross-section of the constituent beams in a controlled manner. The main idea lies in the redistribution of the mass of the constituent beam to obtain a range of equivalent elastic properties, which is not possible within the scope of regular hexagonal lattices. The mass of the stepped lattices is kept the same as the regular hexagonal lattices with equivalent geometry. The in-plane mechanics of such mass-conserved hexagonal lattices are investigated, considering stepped beams as constituent members. The mechanics of a unit cell is exploited to derive the closed-form analytical expressions of equivalent elastic properties of the lattice. The derivation utilises the stiffness elements of the constituent stepped beam members. The stiffness matrices are obtained using two different approaches. They include a semi-analytical condensed stiffness matrix approach based on static substructuring and an analytical method based Castigliano’s energy formulation. Both of these approaches are general and can handle arbitrary geometry for the constituent beams. New closed-form analytical expressions of equivalent elastic properties of the lattice are derived. The optimum geometric parameters are obtained by formulating an analytical optimisation problem. It is shown that a unique solution is possible by solving two simultaneous nonlinear equations. The general closed-form expressions of the equivalent elastic properties can be considered benchmark solutions. In the particular case of the regular lattice, they reduce to the well-known classical expressions. Numerical results show that the values of equivalent elastic properties of the lattice can change significantly by redistributing the mass of the constituent beams. It is demonstrated that up to a 37% increase in the equivalent elastic modulus can be achieved compared to the regular lattice by optimally choosing a stepped profile of the constituent elements.

Using binary-stiffness beams within mechanical neural-network metamaterials to learn

This work introduces the concept of applying binary-stiffness beams within a lattice to achieve a mechanical neural-network (MNN) metamaterial that learns its behaviors and properties with prolonged exposure to unanticipated ambient loading scenarios. Applying such beams to MNN metamaterials greatly increases their learning speed and simplifies the actuation demands, control circuitry, and optimization algorithms required by previously proposed concepts. A binary-stiffness beam design is proposed that uses principles of constraint manipulation and stiffness cancelation to achieve two switchable and discrete states of stiffness (i.e. binary stiffness) along its axis. The beam achieves a near-zero low-stiffness state and a large difference in stiffness between its high and low-stiffness states, which are both shown to be desirable attributes for learning mechanical behaviors. Simulations are conducted to characterize the effect of lattice size, the difference in stiffness between the constituent beam’s high and low-stiffness states, the magnitude of its low-stiffness state, and the number of simultaneously learned behaviors on MNN learning using binary-stiffness beams. Thus, this work provides a necessary step toward enabling practical artificial intelligent metamaterials.

Machine learning for predicting mechanical behavior of concrete beams with 3D printed TPMS

Bioinspired structures are remarkable porous structures with great strength-to-weight ratios. Hence, they have been applied in various fields including biomedical, transportation, and aerospace materials, etc. Recent studies have shown the significant impact of the plastic 3D printed triply periodic minimal surfaces (TPMS) structure on the cement beam including increasing the peak load, reducing the deflection, and improving the ductility. In this study, a machine learning (ML) surrogate model has been conducted to predict the beam behavior under static bending load. At first, various combinations of plastic volume fractions and numbers of core layers have been adopted to reinforce the constituent beam. The finite element method (FEM) was implemented to investigate the influences of these reinforcement strategies. Next, the above data were employed to create the ML model. A three-process assessment was proposed to achieve the most suitable model for the present problem, these processes were the model hyperparameter tuning, the performance assessment, and the handling overfitting with deep learning (DL) techniques. Consequently, both beam peak loads and maximum deflections were proportional to the volume fraction. The increment in TPMS layers could lead to the enhancement in both traits but with a nonlinear relationship. Furthermore, each trait may be a ceiling value that could not be exceeded with a specific volume fraction despite any number of layers. This conclusion was indicated by the surrogate model predictions. The final model in this study could deal with noisy data from FEM and with the support of a new early stopping condition, excellent performance could be found on both train and test data. The maximum deviations of 2.5% and 3.5% for peak loads and maximum midpoint displacements, respectively, have verified the robustness of the present surrogate model.

The long view of triadic resonance instability in finite-width internal gravity wave beams

This article presents our exploration into how a finite-width internal gravity wave beam is modified by triadic resonance instability. We present both experimental and weakly nonlinear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability evolves over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly nonlinear theory, we find that the wave does not monotonically approach a saturated equilibrium of triadic interactions; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour, we develop a weakly nonlinear approach to account for the spatiotemporal evolution of the amplitudes and structures of the beams over slow time scales and long distances, and explore the consequences using a numerical scheme to solve the resulting equations. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatiotemporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

Mechanical neural networks: Architected materials that learn behaviors.

Aside from some living tissues, few materials can autonomously learn to exhibit desired behaviors as a consequence of prolonged exposure to unanticipated ambient loading scenarios. Still fewer materials can continue to exhibit previously learned behaviors in the midst of changing conditions (e.g., rising levels of internal damage, varying fixturing scenarios, and fluctuating external loads) while also acquiring new behaviors best suited for the situation at hand. Here, we describe a class of architected materials, called mechanical neural networks (MNNs), that achieve such learning capabilities by tuning the stiffness of their constituent beams similar to how artificial neural networks (ANNs) tune their weights. An example lattice was fabricated to demonstrate its ability to learn multiple mechanical behaviors simultaneously, and a study was conducted to determine the effect of lattice size, packing configuration, algorithm type, behavior number, and linear-versus-nonlinear stiffness tunability on MNN learning as proposed. Thus, this work lays the foundation for artificial-intelligent (AI) materials that can learn behaviors and properties.

Singular-value decomposition and electromagnetic coherence of optical beams.

We investigate the implications of the singular-value decomposition of the cross-spectral density (CSD) matrix to the description of electromagnetic spectral spatial coherence of stationary light beams. We show that in a transverse plane any CSD matrix can be expressed as a mixture of two CSD matrices corresponding to beams which are fully polarized but in general spatially partially coherent. The polarization and coherence structures of these constituent beams are specified, respectively, by the singular vectors and singular values of the full CSD matrix. It follows that vector-beam coherence, including the coherence Stokes parameters and the degree of coherence, can be formulated in terms of only two correlation functions. We further establish two-point analogs of the spectral and characteristic decompositions of the polarization matrix and show that in the case of a Hermitian CSD matrix their composition is specified by the so-called degree of cross-polarization.

Configuring Polarization Singularity Array Composed of C-Point Pairs

The generation and topological configuration of double-layered polarization singularity array (PSA) having paired C-points of opposite topological index through superposing three Laguerre-Gaussian (LG) component beams with orthogonal linear polarization states are demonstrated. The generated PSA beam exhibits diversity in topological geometry and intensity pattern. The topological rule that the zero net topological charge and helicity conservation hold for the entire PSA is also confirmed. Based on our experiment setup consisting of a computer-controlled spatial light modulator (SLM), the PSA morphology can be flexibly customized and dynamically regulated by modulating the parameters of constituent beams. Our scheme provides a convenient device for manipulating polarization singularities and can facilitate the potential applications of singular optics.

Topological charge of a superposition of identical parallel single-ringed Laguerre-Gaussian beams

We study a superposition of several identical parallel single-ringed Laguerre-Gaussian beams. Both for the initial plane and for the far field, we show analytically and confirm numerically that if the weighting coefficients of the superposition are real-valued (i.e. all the beams have the same phase, but may have different amplitudes), the net topological charge of the superposition is equal to the topological charge of each constituent beam. It is also shown that a phase delay between the beams allows changing the net topological charge of the superposition. By measuring the net topological charge it is possible to analyze the received optical signal in a data transmission system that utilizes vortex beams, combining spatial multiplexing and orbital angular momentum multiplexing.

A simulation and experimental study of dual-wavelength dye laser amplifiers

AVLIS requires a high average power laser beam of multiple wavelengths. There are two general ways to achieve such a beam. One is generating different wavelength laser beams by individual dye laser MOPA chains, then spatially combining them by a beam combiner. The other is combining different wavelength laser beams into one beam first, then co-amplifying it by a common MOPA chain. The latter one is more efficient. To further develop the method, this paper demonstrates a simulation and experimental study of dual-wavelength dye laser amplifiers. The one of the most critical parameters of a dual-wavelength laser beam is the power ratio of the two constituent beams, which can vary during the co-amplification. The simulation results show that for two laser beams with small wavelength difference, the spatial combination mismatches of two beams are the more dominant factor than the spectral differences in affecting the power ratio during the co-amplification. The result of the experiment is in good agreement with the simulation.

Radially self-accelerating Stokes vortices in nondiffracting Bessel-Poincaré beams.

We theoretically propose and experimentally generate the nondiffracting Bessel-Poincaré beams whose Stokes vortices radially accelerate during propagation. To this end, we design the Bessel beams whose intensity is specified to be uniformly distributed along the longitudinal direction. By superposing two such Bessel beams having different helical phases and mutually orthogonal polarizations, the synthesized vector beam is endowed with the polarization singularity that can rotate about the optical axis, while the total intensities maintain their profiles. Radially self-accelerating Stokes vortices in the resulting beam can be manipulated by adjusting the predefined parameters in the constituent beams.

Conservation of the half-integer topological charge on propagation of a superposition of two Bessel-Gaussian beams

We theoretically show that by continuously varying the amplitude of a constituent beam in the superposition of two Bessel-Gaussian (BG) beams with topological charges (TCs) $m$ and $n$ the TC of the entire superposition can be controlled. Between the constituent beams, there is a topological competition. For some parameters of the BG beams, TC of the superposition equals $n$, while for other parameters, it is equal to $m$. In the center of such a superposition (on the optical axis), there is an $m$-fold degenerate intensity null (optical vortex with the TC of $m<n$), whereas $n--m$ optical vortices with the unitary TC are in the beam periphery. We demonstrate that when the amplitudes of the constituent beams tend to be equal, peripheral vortices ``move'' to infinity. In this case, superposition of two BG beams has a half-integer TC, and this TC is conserved on propagation in space. The fractional part of the TC is, however, ``hidden'' in the infinity (``hidden'' phase). Conservation of the half-integer TC of an optical vortex on propagation is shown.

Architected material analogs for shape memory alloys

Architected material analogs for shape memory alloys

Knotted nodal lines in superpositions of Bessel-Gaussian light beams

A simple analytical way of creating superpositions of Bessel-Gaussian light beams with knotted nodal lines is proposed. It is based on the equivalence between the paraxial wave equation and the two-dimensional Schr\"odinger equation for a free particle. The $2D$ Schr\"odinger propagator is expressed in terms of Bessel functions, which allows to obtain directly superpositions of beams with a desired topology of nodal lines. Four types of knots are constructed in the explicit way: the unknot, the Hopf link, the Borromean rings and the trefoil. It is also shown, using the example of the figure-eight knot, that more complex structures require larger number of constituent beams as well as high precision both from the numerical and the experimental side. A tiny change of beam's intensity can lead to the knot "switching".