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Polarization plays a crucial role in light–matter interactions; hence its overall manipulation is an essential key to unlock the versatility of light manufacturing, especially in femtosecond laser direct writing. Existing polarization-shaping techniques, however, only focus on their manipulation in the transverse plane of light beams, i.e., two-dimensional control. In this paper, we propose a novel passive strategy that exploits a class of femtosecond laser written space varying birefringent elements to shape the polarization state along the optical path. As a demonstration, we generate a three-dimensional structured Bessel beam whose linear polarization state slowly evolves along the focus (typ. 90° within 60λ). Such a "helically polarized" Bessel beam allows imprinting "twisted nanogratings" in SiO2 glass which result in an extrinsic optical chirality at a micrometric scale and own a high optical rotation. Our work provides new perspectives for three-dimensional polarization manipulation and insights into applications in structured light, light–matter interaction, and chiral device fabrication. [ABSTRACT FROM AUTHOR]

The beam with longitudinally varied polarization provides a new dimension for polarization applications, such as material processing, longitudinal depth detection, optical communications, etc. A few different methods have so far been investigated, including spatial light modulators and diffractive optical elements. However, these methods have complex optical path, large volume, which are difficult to integrate. Here, a birefringent dielectric metasurface is demonstrated, which is capable of generating Bessel beam whose polarization state continuously rotates along the propagation direction. According to the design, when a linearly polarized light illuminates on the metasurface, the outgoing light becomes linearly polarized zero‐order Bessel beam, whose polarization angle changes as the propagation distance increases. Experimental measurements are successfully carried out. Such scheme may open new doors for potential applications in depth perception, microscopic detection, and so on. [ABSTRACT FROM AUTHOR]

A method to construct the boundary shape function (BSF) and then two novel methods are developed to obtain the solutions of fourth-order singularly perturbed beam equation and nonlinear boundary value problem (BVP). In the first-type algorithm, the free function is a series of complete basis functions, while the corresponding BSFs are new bases. The trial functions with fractional powers exponential are suitable for the singularly perturbed beam equation under fixed-end and simply supported boundary conditions. With the aid of the BSF, we can improve the asymptotic and uniform approximations to exactly satisfy the prescribed boundary conditions. In the second-type algorithm, the solution of a nonlinear BVP is viewed as a boundary shape function, while the free function is regarded as a new variable. With this means, the fourth-order nonlinear BVP is exactly converted to an initial value problem with a new variable, the terminal value of which is unknown, when the initial conditions are given. The computed order of convergence and an error estimation are given. Numerical illustrations, including the singularly perturbed examples, show that the present methods, based on the new idea of the BSF, are highly effective, accurate, and fast convergent. [ABSTRACT FROM AUTHOR]

In this paper we discuss the motion of a beam in interaction with fluids. We allow the beam to move freely in all coordinate directions. We consider the case of a beam situated in between two different fluids as well as the case where the beam is attached only to one fluid. In both cases the fluid-domain is time changing. The fluid is governed by the incompressible Navier-Stokes equations. The beam is elastic and governed by a hyperbolic partial differential equation. In order to allow for large deformations the elastic potential of the beam is non-quadratic and naturally possesses a non-convex state space. We derive the existence of weak-solutions up to the point of a potential collision. [ABSTRACT FROM AUTHOR]

Long-distance, free space applications of orbital angular momentum (OAM) beams are limited by power loss and environmental turbulence. Although there have been many studies on the generation of high-power OAM beams, it is difficult to create a generated beam that is resistant to wander disturbance in low coherence conditions, let alone maintain the multiplexing of the OAM modes. In this work, we propose a partially coherent beam combining technology that enables generation of disturbance resistant and high-power OAM beams by controlling the spatial correlation of the light field with a partially coherent beam array. The OAM state of the generated beam can be transformed between single mode and multimode as designed. A multiplexed correlation vortex, which has low coherence and contains multiple spectral bands in OAM space, is produced experimentally. In a wander environment, the scintillation index and the relative power fluctuation of the multiplexed correlation vortex beam are reduced to 41% and 52% of those of completely coherent beams, respectively. These results represent a new methodology for OAM mode generation and show great potential for applications in complex environments. [ABSTRACT FROM AUTHOR]

In terms of research, the elliptical antenna arrays (EAA) synthesis is relatively novel. As it does not have to be circular in construction, this novel synthesis can maneuver the primary beam in the right direction, making it easier to realize. The amplitude and angular location of the ellipse, as well as the eccentricity of the ellipse, are all taken into account in the optimization process. The proposed hybrid algorithm is the SSWOA (Salp Swarm Whale Optimization Algorithm), which combines the Salp Swarm Optimization Algorithm (SSA) with the Whale Optimization Algorithm (WOA). The SSA algorithm serves as a guide, while the WOA algorithm serves as a helper in this method. We discover that optimization has a faster convergence time and high convergence accuracy when considering the benefits of SSA and WOA and applying them to the synthesis of antenna array layouts. If Griewank, Rosenbrock, Sphere, and Rastrigin test functions are used, it's worth noting that the hybrid method outperforms both WOA and SSA. [ABSTRACT FROM AUTHOR]

Interactions between collective multi-layered cells and an off-axis high-order Bessel beam (HOBB) are investigated. The generalized Lorenz-Mie theory is applied to derive the expansion of HOBB. Based on the additional theorem, multiple scattering of collective multi-layered nanoparticles is obtained by considering the tangential continuous boundary conditions. The present theory and codes are proven to be effective by comparing with the simulations obtained from the computer simulation technology (CST) software. Numerical results concerning the effects of beam order, beam conical angle, spherical layer number, core radius and outer layer radius, outer layer refractive index and the spherical number on the scattering of various types of aggregated multi-layered particles are displayed in detail, which may provide critical support for analytically understanding the optical scattering characteristics of aggregated multi-layered biological cells of complex shapes and may find important applications in manipulating multi-layered biological structures. [ABSTRACT FROM AUTHOR]

The deflection of Euler–Bernoulli beams under stochastic dynamic loading, exhibiting purely viscous behavior, is characterized by partial differential equations of the fourth order. This paper proposes a computational method to determine the approximate solution to such equations. The functions are approximated using two‐dimensional shifted Legendre polynomials. An operational matrix of integration and an operational matrix of stochastic integration are derived. The operational matrices assist in breaking down the problem under consideration into a set of algebraic equations that may be solved using any known numerical technique that leads to the solution of the stochastic beam equation. The well‐posedness of the problem is studied. The proposed methodology is demonstrated to be practical for addressing the novel stochastic dynamic loading problem by confirming the outcome using a few numerical examples. Thus the effectiveness and applicability of the technique are ensured. The solution quality is explored through diagrams. The accuracy of the method is substantiated by comparing it with the Runge–Kutta method of order 1.5 (R–K 1.5). The absolute error caused by the proposed technique is comparably much less than R–K 1.5. A simulation analysis is carried out with MATLAB, and an algorithm is developed. [ABSTRACT FROM AUTHOR]

Structured light fields, especially high-order Poincaré sphere (HOPS) beams, are attracting increasing attention for their intriguing properties and extensive applications. Here, we demonstrate a cascaded mode converter for generating HOPS beams of different orders. The cascaded mode converter is composed of q-plates and half waveplates, which realize switchable generation of HOPS beams of multiple different orders with reliable performance. Exponential growth of the available number of HOPS beams of different orders is achieved. The local polarization state and the order of the HOPS beams can be used as two degrees of freedom to encode 2 bits of information. The proposed method makes it possible to generate multiple and ultrahigh order Poincaré sphere beams and may have potential application in communication systems. [ABSTRACT FROM AUTHOR]

An analysis of electromagnetic scattering by perfect electromagnetic conductor (PEMC) sphere using Bessel beam incidence is presented which is based on the generalized Lorenz–Mie theory (GLMT). The PEMC is famous for the generalization of the renowned concept of perfect electric and perfect magnetic conductor (PEC and PMC). The scattering problem is solved by representing the Bessel beam fields i.e., incident and scattered in the context of vector spherical wave functions (VSWFs). The unknown expansion field coefficients can be found out by solving linear equations which are attained from the implementation of boundary conditions (BCs) of PEMC sphere. Computations of the scattering cross-section C sca and the extinction cross-section C ext are performed. The impact on scattering and extinction cross-section for admittance parameter, conical angle, and sphere size parameter are analyzed. Considering a special case for conical angle i.e., α = 0 ∘ , the numerical results of scattering cross-section for Bessel beam and plane wave are same. [ABSTRACT FROM AUTHOR]

Electron vortex beams (EVBs, also known as twisted electron beams) possess an intrinsic orbital angular momentum (OAM) with respect to their propagation direction. This intrinsic OAM represents a new degree of freedom that provides new insights into investigating the dynamics of electron impact ionization. In this communication, we present, in the first Born approximation (FBA), the angular profiles of the triple differential cross section (TDCS) for the (e, 2e) process on CH 4 and NH 3 molecular targets in the coplanar asymmetric geometry. We compare the TDCS of the EVB for different values of OAM number m with that of the plane wave. For a more realistic scenario, we investigate the average TDCS for macroscopic targets to explore the influence of the opening angle θ p of the twisted electron beam on the TDCS. In addition, we also present the TDCS for the coherent superposition of two EVBs. The results demonstrate that the twisted (e, 2e) process retrieves the p-type character of the molecular orbitals, which is absent in the plane wave TDCS for the given kinematics. The results for the coherent superposition of two Bessel beams show the sensitivity of TDCS toward the OAM number m. [ABSTRACT FROM AUTHOR]

We obtain a transform that relates the standard Bessel–Gaussian (BG) beams with BG beams described by the Bessel function of a half-integer order and quadratic radial dependence in the argument. We also study square vortex BG beams, described by the square of the Bessel function, and the products of two vortex BG beams (double-BG beams), described by a product of two different integer-order Bessel functions. To describe the propagation of these beams in free space, we derive expressions as series of products of three Bessel functions. In addition, a vortex-free power-function BG beam of the mth order is obtained, which upon propagation in free space becomes a finite superposition of similar vortex-free power-function BG beams of the orders from 0 to m. Extending the set of finite-energy vortex beams with an orbital angular momentum is useful in searching for stable light beams for probing the turbulent atmosphere and for wireless optical communications. Such beams can be used in micromachines for controlling the movements of particles simultaneously along several light rings. [ABSTRACT FROM AUTHOR]

To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. The proposed approach has two advantages. The first is the rapid (for the first few iterations) achievements of an acceptable error in the calculation of an optical element that forms a primitive distribution compared to a complex one. The second advantage is the convenience of reconfiguration. Since a complex distribution is assembled from primitive parts, it can be reconfigured quickly or dynamically by using a spatial light modulator (SLM) by moving and rotating these components. Numerical results were confirmed experimentally. [ABSTRACT FROM AUTHOR]

Increasing the depth of field (DOF) is a crucial issue for imaging through scattering media. In this paper, an improved genetic algorithm is used to modulate the wavefront of light through scattering media, by which high-quality refocusing and imaging through scattering media are achieved. Then, the DOF of the imaging system is effectively extended by further modulating the refocused beam into a non-diffraction beam. Two kinds of non-diffraction beams, i.e., a Bessel beam and Airy beam, were produced as a demonstration. The experimental results show that compared to the Gaussian beam, the DOF of the imaging system by combining the wavefront shaping and non-diffraction Bessel beam or Airy beam can be improved by a factor of 1.1 or 1.5, respectively. The proposed method is helpful for the technical development of high-quality imaging through scattering media with a large DOF. [ABSTRACT FROM AUTHOR]

We propose a compact method to experimentally synthesize a class of vector beam arrays with periodic higher-order Poincaré sphere (HOPS) polarization states by engineering the spatial coherence structure of a partially coherent light source. We demonstrate that the spatial coherence structure and polarization state of the partially coherent source can be simultaneously controlled using a phase-only spatial light modulator and a common-path interferometric arrangement with the aid of a complex-random-mode representation method. We show experimentally that the polarization state of a single HOPS beam in the source plane can be mapped into a beam array generated in the far field, and the degree of polarization of the beam array can be conveniently controlled with spatial coherence engineering. Our method provides an alternative way to synthesize beam arrays with structured coherence and polarization properties. [ABSTRACT FROM AUTHOR]

Terahertz technology and vortex beams have demonstrated powerful capabilities in enhancing the channel capacity of communication systems. This work proposes a design strategy of dual-band and dual-function 3-bit coding metasurface based on beam polarization characteristics. The unit cell of the metasurface is composed of two pattern structures, which has the ability to flexibly and independently control the reflection phases of incident plane wave at two frequency bands. The metasurface designed in this work is a combination of two patterns according to the addition operation and the convolution operation. The 3-bit coding metasurface generates two orbital angular momentum (OAM) beams with a deflection of 12.1° with modes l 1 = + 1 and l 2 = − 1 under the y-polarized incidence at 0.6 THz. Similarly, the designed metasurface produces two OAM beams with a deflection of 16.5° under the incidence of x-polarized wave at 0.9 THz, and the modes are l 3 = + 1 and l 4 = − 2 . The full-wave simulation results agree well with the theoretical predictions, which could prove the correctness and effectiveness of the proposed method. The metasurface designed according to this method has potential applications in multiple-input multiple-output (MIMO) communication systems. [ABSTRACT FROM AUTHOR]

Cone-beam computed tomography (CBCT) produces high-resolution of hard tissue even in small voxel size, but the process is associated with radiation exposure and poor soft tissue imaging. Thus, we synthesized a CBCT image from the magnetic resonance imaging (MRI), using deep learning and to assess its clinical accuracy. We collected patients who underwent both CBCT and MRI simultaneously in our institution (Seoul). MRI data were registered with CBCT data, and both data were prepared into 512 slices of axial, sagittal, and coronal sections. A deep learning-based synthesis model was trained and the output data were evaluated by comparing the original and synthetic CBCT (syCBCT). According to expert evaluation, syCBCT images showed better performance in terms of artifacts and noise criteria but had poor resolution compared to the original CBCT images. In syCBCT, hard tissue showed better clarity with significantly different MAE and SSIM. This study result would be a basis for replacing CBCT with non-radiation imaging that would be helpful for patients planning to undergo both MRI and CBCT. [ABSTRACT FROM AUTHOR]

In this paper, the flexural vibration of uniform and non-uniform rotating shafts based on the Timoshenko beam theory is investigated. Considering shear deformation and gyroscopic effects to build an exact framework of a solution, the fourthorder differential equation of vibration is solved by an analytical method. The overall transfer matrix of the system formed by a series of flexible distributed in addition to lumped elements is achieved. The results obtained by the distributed lumped modeling technique (DLMT) are verified with other techniques. The damped frequencies obtained by the hybrid modeling method for a multistep gas turbine rotor system using the Euler-Bernoulli and Timoshenko beam theories are compared with the results of the transfer matrix method (TMM). It is shown that the presented method provides highly accurate results, while with no compromise, it can be simply and effectively employed for complex systems. It is also shown how the Hooke and Jeeves and the ant colony optimization (ACO) besides the direct enumeration method can be applied to obtain the damped natural frequencies of complicated vibrational systems such as the gas turbine rotors. The comparison between the frequency and damping ratio values obtained by the optimization and direct enumeration methods shows less than 1% error for different cases. [ABSTRACT FROM AUTHOR]

We describe the construction of an optical-space, cylindrical black hole induced by high pressure in a dense fluid. Using an approximate analogy between curved spacetime and optics in moving dielectric media, we derive the mass of the black hole thus created. We describe the resulting optical-space using a Bessel beam profile and Snell's law to understand how total internal reflection produces a cylindrical, optic black hole. [ABSTRACT FROM AUTHOR]

Fabrication of a through hole in a polyimide film (PI) was demonstrated by holographic ultraviolet (UV) nanosecond laser processing with a computer-generated hologram displayed on a phase-only spatial light modulator (SLM). The UV laser was directly modulated into a Bessel beam by a diffractive axicon displayed on the SLM. The direct modulation contributed to improved light-utilization efficiency of the UV laser and a simplified optical setup compared to the conventional method based on a combination of an SLM and harmonic generation using a nonlinear optical crystal. The Bessel beam reduced the number of pulse shots required for through-hole fabrication to 1/5 compared to the Gaussian beam near the ablation threshold energy of the PI film. Furthermore, adaptive optics was implemented in holographic laser processing to compensate for aberrations in the optical setup. The aberration was reduced to 1/5 compared with before the compensation. The proposed method is suitable for improving the throughput and accuracy of drilling, cutting, and additive manufacturing using UV lasers with industrial requirements. [ABSTRACT FROM AUTHOR]

The expressions of the axial and transverse acoustic radiation forces of a rigid sphere arbitrarily positioned in a zero-order Mathieu beam are derived in this paper. The expansion coefficients of the off-axis zero-order Mathieu beam are obtained using the addition theorem of the Bessel functions, and numerical experiments are conducted to verify the theory. The three-dimensional acoustic radiation forces on a rigid sphere are studied when the beam is set at different ellipticity parameters, half-cone angles, and offsets of the incident wave relative to the particle center. Simulation results show that the axial acoustic radiation forces of the rigid sphere are always positive, but the transverse forces vary with the positions of the particle and the beam parameters. Also, by changing the frequency, half-cone angle, and offset of the zero-order Mathieu beam, the value and direction of the transverse forces can be adjusted, which has applications in controlling the rigid sphere to be close to or away from the beam axis. Furthermore, the finite element model is set up to verify the theoretical model, and the results obtained by the two methods are in good agreement. This work may contribute to a better understanding of the underlying mechanisms of the particle manipulation with different acoustic beams. [ABSTRACT FROM AUTHOR]

Enhancing the infrared window transmittance of zinc sulfide (ZnS) is important to improve the performance of infrared detector systems. In this work, a new hybrid micro/nanostructure was fabricated by an optimal Bessel femtosecond laser on ZnS substrate. The surface morphologies and profiles of ASS ablated by a 20× microscope objective Bessel beam are described, indicating that the nanoripples on the micropore were formed by the SPP interference and the SPP scattering in a particular direction. Further, the maximum average transmittance of ASS increased by 9.7% and 12.3% in the wavelength ranges of 5~12 μm and 8~12 μm, respectively. Finally, the antireflective mechanism of the hybrid micro/nanostructure is explored using the novel electromagnetic field model based on the FDTD method, and we attribute the stable antireflective performance of ASS in broadband to the interface effective dielectric effect and LLFE. [ABSTRACT FROM AUTHOR]

This work presents a 12-element 360° azimuth plane scanning planar circular antenna array for compact THz wireless devices. Proposed array comprises of 12 bow-tie Yagi-Uda directional antennas, operating within 0.235–0.322 THz band where each antenna achieves a maximum radiation beam for an angle of around 30°, arranged in a circular fashion to cover 360°. Individual antennas are stamped on a silicon dioxide (SiO2) dielectric substrate having compact dimensions of 1.35 mm × 1 mm × 0.06 mm and employ gold material of thickness 5 µm as a conducting material in the top and bottom planes. Maximum peak gain of each antenna is found to be 10.4 dBi at 0.322 THz within the operating band. Three parasitic elements are employed as directors to enhance the directional properties. Initially, a single element bow-tie Yagi-Uda antenna design is presented and then followed by a 6-element and 12-element circular antenna array design. Exhibiting compact dimensions, higher directivity, better performance and simple design lead to a suitable module for smart THz wireless scanning devices in the range of IEEE 802.15.3d (0.252–0.325 THz) standard and H-band (0.22–0.32 THz). [ABSTRACT FROM AUTHOR]

This paper considers the analysis of slender single‐sided transversely cracked beams with a linear variation of width where transverse displacements can occur exclusively due to axial tensile forces. The simplified model where the crack is represented through an internal hinge endowed with a rotational spring that takes into account the cracked cross section's residual stiffness has already established itself as a decent alternative to the detailed 2D or 3D finite element, offering a good ratio between the accuracy of its results against the computational efforts required. The first stage of the presented research proved that the solutions of the bending governing differential equations with directly included axial tensile force are not required. However, the need for enhancement of the model's governing parameters clearly emerged. Thus, the definitions of the moment lever arm and rotational spring stiffness were studied and fittingly updated. In the last stage, the modelling of the considered phenomenon by a newly derived one‐dimensional beam finite element with closed‐forms of the element's stiffness matrix and load vector was executed. At the end of the study, the performance and the quality of the newly obtained solutions were verified through several comparative case studies that complement the derivations. [ABSTRACT FROM AUTHOR]

In this study, the post-buckling behavior of a transverse functionally graded beam is investigated. Euler–Bernoulli beam theory (EBT) and shear deformable beam theories are taken into account in deriving the mathematical models of the beam using the vector approach. Timoshenko theory (TBT) and six different higher order beam theories (HOBT), namely Reddy, Touratier, Soldatos, Karma, Akavcı and Violet, are considered as shear deformable beam theories. It has been shown that mathematical models of shear deformable beam theories can be obtained using the vector approach. There are two different models developed for shear deformable beam theories depending on normal and shear forces and moment. It is found that the model which is named as Model 2 in this study yield inappropriate results. The functionally graded materials are characterized by using power law functions. The non-dimensional integro-non-linear differential equations system is solved analytically. The critical load values calculated for EBT, TBT and HOBT theories depending on different material conditions and slenderness ratio values are presented in tables. In addition, pitchfork bifurcation diagrams are drawn showing the post-buckling behavior of the beam. In addition, the regions where the examined beam theories are valid depending on the slenderness coefficient are shown. [ABSTRACT FROM AUTHOR]

In this paper, a novel design of superlens based on photonic bandgap structure for high resolution point spread function (PSF) is reported at a wavelength of 3 μm. The lens is able to generate a non-diffraction Bessel beam with a number of focusing points with variant resolution limits. The optimized structure provides high resolution in both lateral and axial directions. The maximum achieved lateral resolution of PSF is down to ~ 0.27λ with corresponding axial resolution down to ~ 0.57λ attaining a FOM, the inverse of the product of both resolution limits, of ~ 6.49. Meanwhile, the maximum axial resolution is down to ~ 0.4λ with corresponding lateral resolution down to ~ 0.33λ with a FOM of ~ 7.34. In addition, the proposed design is able to generate a focusing point extended in space up to ~ 0.98 µm with a sub-diffraction lateral resolution down to ~ 0.47λ. Furthermore, the reported superlens demonstrates a sub-diffraction focusing in lateral direction along the range the bandgap wavelengths (from 2.4 to 3.6 µm) showing a significant increase of focal depth when decreasing the operating wavelength. Remarkably, a high focal depth up to ~ 1.77 µm is achieved at the operating wavelength of 2.6 µm. The suggested design has a tremendous potential in 3D biological imaging and biosensing applications. [ABSTRACT FROM AUTHOR]

Dicing is a critical step in the manufacturing process for the application of sapphire. In this work, the dependence of sapphire dicing on crystal orientation using picosecond Bessel laser beam drilling combined with mechanical cleavage was studied. By using the above method, linear cleaving with on debris and zero tapers was realized for the A1, A2, C1, C2, and M1 orientations, except for the M2 orientation. The experimental results indicated that characteristics of Bessel beam-drilled microholes, fracture loads, and fracture sections of sapphire sheets were strongly dependent on crystal orientation. No cracks were generated around the micro holes when laser scanned along the A2 and M2 orientations, and the corresponding average fracture loads were large, 12.18 N and 13.57 N, respectively. While along the A1, C1, C2, and M1 orientations, laser-induced cracks extended along the laser scanning direction, resulting in a significant reduction in fracture load. Furthermore, the fracture surfaces were relatively uniform for A1, C1, and C2 orientations but uneven for A2 and M1 orientations, with a surface roughness of about 1120 nm. In addition, curvilinear dicing without debris or taper was achieved to demonstrate the feasibility of Bessel beams. [ABSTRACT FROM AUTHOR]

In this work, we fabricated the antireflection microstructures (ARMs) on ZnSe surfaces using a femtosecond Bessel direct laser writing in burst mode. The morphology and transmittance performance of ARMs with different single-pulse energies (from 200 nJ to 500 nJ), different burst modes (burst 1, 3, and 5 modes), different periods (from 3 μm to 6 μm), and different arrangements were investigated. The results revealed that tetragonally arranged ARMs fabricated by 500 nJ of single-pulse energy, the burst 3 mode, and a period of 3 μm show the best transmittance performance. The average transmittance of the ARMs was about 17.13% higher than that of bulk ZnSe in the range of 8–12 μm, and the highest transmittance of 81.75% (an improvement of 18.63% on one side of the ZnSe) was achieved at 12.36 μm. This process makes it possible to enhance ARMs' transmittance in the infrared wavelength range by using direct laser writing in burst mode. [ABSTRACT FROM AUTHOR]

We report on an optical setup to generate multi-Bessel beam profiles combining a refractive axicon and a spatial light modulator. Based on their particular beam profile, Bessel beams offer advantageous properties for micro drilling processes and internal volume processing, especially for transparent materials. In addition, the laser power of industrial, ultrashort pulsed lasers has increased significantly over the last few years, offering the possibility for highly efficient processes using multi-spot profiles. Our optical concept combines the dynamic possibilities of beam splitting using a spatial light modulator with the benefits of Bessel beams, which facilitates multi-Bessel beam processing. Beside the simulation and experimental evaluation of the generated multi-Bessel beams, we exemplify the applicability of the developed module for the perforation of thin metal foils by micro drilling. [ABSTRACT FROM AUTHOR]

A flexible beam is recognized as a lightweight structure that is prone to excessive vibration, resulting in poor performance. Thus, controlling unwanted vibration is necessary to maintain the system's performance. Therefore, this study presents a technique to suppress undesired vibration in a flexible beam structure by introducing active vibration control (AVC). However, to develop an effective controller, an appropriate flexible beam model must first be obtained. In recent times, one of the best methods employed to model a flexible beam structure is system identification via a swarm intelligence algorithm. In this study, an intelligent algorithm acknowledged as cuckoo search (CS) was acquainted. The capability of the proposed algorithm was verified using three robustness techniques which were correlation test, pole-zero diagrams and mean square error (MSE). The simulation result showed that the CS algorithm achieved superior performance by achieving the lowest MSE of 6.1547x10-9, a correlation test between a 95% confidence level and high stability. Next, a proportionalintegral-derivative (PID) controller tuned by the Ziegler-Nichols method was developed using the transfer function accomplished from the CS model. Two types of interference, namely single and multiple sine waves were introduced to validate the effectiveness of the controller. The controller successfully achieved a 30.2 dB of attenuation level for both disturbances. [ABSTRACT FROM AUTHOR]

Integrating multiple independent functions into a single optical component is one of the most important topics in research on photoelectric systems. In this paper, we propose a multifunctional all-dielectric metasurface that can achieve a variety of non-diffractive beams depending on the polarization state of the incident light. Using the anisotropic TiO2 rectangular column as the unit structure, the three functions of generating polygonal Bessel vortex beams under left-handed circularly polarized incidence, Airy vortex beams under right-handed circularly polarized incidence and polygonal Airy vortex-like beams under linearly polarized incidence are realized. In addition, the number of polygonal beam sides and the position of focal plane can be adjusted. The device could facilitate further developments in scaling complex integrated optical systems and fabricating efficient multifunctional components. [ABSTRACT FROM AUTHOR]

Periodic nanohole arrangements constitute an important building block of advanced photonic devices. Aside from standard nanofabrication tools, a direct laser‐based approach is introduced here, that enables single‐step and point‐by‐point machining of arrays of holes with subwavelength diameters and depths reaching several micrometers at the surface of fused silica. The method relies on a simple optical arrangement including an axicon combined with an amplitude mask to shape the laser intensity in appropriately truncated micro‐Bessel beams of adjustable length. The suitability and limitations of the technique are investigated to fabricate arrays of cylindrical nanoholes with tunable depths. In particular, the challenge of avoiding crosstalk effects during the laser‐writing process of high‐density arrays is explored. The achievability of square arrays of nanoholes at the surface of fused silica, with diameters down to 200 nm and variable depths from 3 to 20 µm at a spatial density defined by a pitch of 1.5 µm is demonstrated. The performance level shows the potential of the direct‐laser‐processing method towards the realization of integrated devices, offering a highly flexible and cost‐effective alternative technique to current nanofabrication methods. [ABSTRACT FROM AUTHOR]

This article outlines the use of Fredholm integral equations (also known as Fredholm transformation approach) for free vibration analysis of non-uniform and stepped axially functionally graded (AFG) beams. The method is shown to be capable of dealing with beams of arbitrary variations of both cross section dimensions and material properties. Tabulated results of free vibration analysis for beams with various classical boundary conditions are presented. The governing equation with varying coefficients is transformed to Fredholm integral equations. Natural frequencies can be determined by requiring that the resulting Fredholm integral equation has a non-trivial solution. Our method has fast convergence, and obtained numerical results have high accuracy. Effects of axial force and shear deformation are investigated on the natural frequencies of AFG beams. The accuracy of obtained results is verified with those obtained in other available references. The present results are of benefit to optimum design of non-homogeneous tapered beam structures and graded beams of special polynomial non-homogeneity. [ABSTRACT FROM AUTHOR]

The number of mirror segments, mirror geometry and orientation are essential parameters when assessing the beam-shaping capabilities of deformable mirrors. Here, we use a Liquid Crystal on Silicon Spatial Light Modulator (LCoS-SLM) to mimic the mechanical design of a deformable mirror and quantitatively analyse the effect of the number of mirror segments and their geometrical structure on resulting structured modes. Our approach can be used as a test bed prior to designing a deformable mirror for high power beam shaping. [ABSTRACT FROM AUTHOR]

Coherent anti-Stokes Raman scattering (CARS) spectroscopy plays an important role in chemical analysis for transient flow dynamics. Due to the turbulent ambient conditions, the CARS spectrum often suffers from a poor signal-to-noise ratio (SNR) and cannot provide a convincing measurement. Here, we report on a CARS spectroscopic method using a Bessel beam to enhance the spectral fidelity and SNR in a quasi-turbulent environment. Compared with traditional CARS, the measurement accuracy is significantly improved by taking advantage of the anti-scattering and self-healing characteristics of the Bessel beam. Our preliminary results indicate that Bessel beam CARS could be a promising method for high precision turbulent flow measurement fields. Graphical Abstract [ABSTRACT FROM AUTHOR]

Determination of polarization states of electromagnetic waves plays a crucial role in photonic applications. However, it is very challenging to determine the polarization state of continuous terahertz (THz) waves. Here, a metasurface‐like metallic waveguide array (MWA) is proposed to address this by measuring both the phase difference and amplitude ratio of its two orthogonal components based on generation and interference of polarization‐multiplexing vortex beams. When a full‐polarized THz wave passes through the MWA, its two orthogonal components will be converted into +1st‐ and −1st‐order Bessel vortex beams, respectively. Their projection components in a proper polarized direction can interfere with each other, and their initial phase difference can be measured in real‐time owing to its linear relationship with the azimuth of the dark fringe in interference patterns. The two Bessel beams can be further collected separately using a linear polarizer to obtain their amplitude ratio. Therefore, the polarization state of incident waves can be determined with both the phase difference and amplitude ratio. The proposed method enables a convenient polarization determination of continuous THz waves and has great potential for developing polarization‐dependent investigations and applications in THz detection, communication, and sensing. [ABSTRACT FROM AUTHOR]

This paper proposes a synthesis and optimization procedure to generate user-specific shaped and multiple beams in any arbitrary 3D space. The synthesis method generates independently controllable multiple beams over different azimuth and elevation angles with variable peak powers. These multiple beams can form any user-defined shaped pattern with an optimum number of beams, their power, and placement in the θ , ϕ angles using the proposed direct synthesis method. Different evolutionary algorithms are employed to optimize the beam peak parameters to mitigate the ripple, side lobe level, and beam spread. The synthesis method is validated on a fully functional integrated 5G mmWave phased array for various shaped beam patterns. Measured sector, isoflex beams between θ = ± 40 ∘ , c s c 2 , and dual beams with unequal powers are presented and compared with the shaped beam synthesis method. [ABSTRACT FROM AUTHOR]

In this paper, using positive symmetric functions, we offer two new important identities of fractional integral form for convex and harmonically convex functions. We then prove new variants of the Hermite-Hadamard-Fej'er type inequalities for convex as well as harmonically convex functions via fractional integrals involving an exponential kernel. Moreover, we also present improved versions of midpoint type Hermite-Hadamard inequality. Graphical representations are given to validate the accuracy of the main results. Finally, applications associated with matrices, q-digamma functions and modifed Bessel functions are also discussed. [ABSTRACT FROM AUTHOR]

The current 5G-NR standard includes the transmission of multiple synchronization signal blocks (SSBs) in different directions to be exploited in beamforming techniques. However, choosing a pair of these beams leads to performance degradation, mainly for the cases where the transmit and receive beams are not aligned, because it considers that only few fixed directions among wide beams are established. Therefore, in this article, we design a new 3GPP-standard- compliant beam pair selection algorithm based on secondary synchronization signal (SSS) angle estimation (BSAE) that makes use of multiple synchronization signal blocks (SSBs) to maximize the reference signal received power (RSRP) value at the receiver. This optimization is performed using the SSSs present in each SSB to perform channel estimation in the digital domain. Afterwards, the combination of those estimations is used to perform equivalent channel propagation matrix estimation without the analog processing effects. Finally, through the estimated channel propagation matrix, the angle that maximizes the RSRP is determined to compute the most suitable beam. The proposed algorithm was evaluated and compared with a conventional beam pair selection algorithm. Ours has better performance results. Furthermore, the proposed algorithm achieved performance close to the optimal performance, where all channel state information (CSI) is available, emphasizing the interest of the proposed approach for practical 5G mmWave mMIMO implementations. [ABSTRACT FROM AUTHOR]

We present an approach for engineering the intensity trajectory and phase gradient of light beams with arbitrary shapes by estimating their parametric equations using Freeman chain code and by applying the fast Fourier transform. The analysis of the electric field distribution expected for a given curve allows the phase extraction over each local coordinate, generating a phase pattern to be displayed over a spatial light modulator. The intensity and phase gradient of eight different shapes is encoded during our experiments. The far field intensity profiles are captured and compared in shape to those designed, while the encoded phase is demonstrated by implementing a common path interference setup with a pair of beams from the spatial light modulator. The designed beams, initially drawn either by hand or generated with software, exhibit both the intensity and phase profiles encoded onto them. [ABSTRACT FROM AUTHOR]

The article extends the formulation of a 2D geometrically exact beam element proposed by Jirásek et al. (2021) to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic relations and sectional equations that link the internal forces to sectional deformation variables. The resulting first‐order differential equations are approximated by the finite difference scheme and the boundary value problem is converted to an initial value problem using the shooting method. The article develops the theoretical framework based on the Navier–Bernoulli hypothesis, with a possible extension to shear‐flexible beams. Numerical procedures for the evaluation of equivalent nodal forces and of the element tangent stiffness are presented in detail. Unlike standard finite element formulations, the present approach can increase accuracy by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant. The efficiency and accuracy of the developed scheme are documented by seven examples that cover circular and parabolic arches, a spiral‐shaped beam, and a spring‐like beam with a zig‐zag centerline. The proposed formulation does not exhibit any locking. No excessive stiffness is observed for coarse computational grids and the distribution of internal forces is not polluted by any oscillations. It is also shown that a cross effect in the relations between internal forces and deformation variables arises, that is, the bending moment affects axial stretching and the normal force affects the curvature. This coupling is theoretically explained in the Appendix. [ABSTRACT FROM AUTHOR]

In this study, the modified Fourier method is developed to analyze thermal vibration of functionally graded porous beams based on the third-order shear deformation theory. It can provide accurate results due to satisfying both force and geometrical boundary conditions. Three different forms including uniform, linear and nonlinear temperature distribution are considered. Some important effects including patterns of porous distribution, porous coefficient, temperature rises, spring constants, and classical and non-classical boundary conditions are investigated. Based on this extensive investigation, it is worth revealing that the frequencies of the beams carrying pores with uniform distribution decrease to the same point at the critical buckling temperature, while the beams with symmetrical and un-symmetrical forms illustrate different manners in which the details are explained in this study. [ABSTRACT FROM AUTHOR]

Bessel beams are attaining keen interest in the current era considering their unique non-diffractive, self-healing nature and their diverse applications spanning over a broad spectral range of microwave to optical frequencies. However, conventional generators are not only bulky and complex but are also limited in terms of numerical aperture (NA) and efficiency. In this study, we experimentally develop a wavelength-independent Bessel beam generator through custom-designed metasurfaces to accomplish high resolution and large depth-of-focus imaging. These meta-axicons exhibit a high NA of up to 0.7 with an ability to generate Bessel beams with a full width at half maximum (FWHM) of 300 nm (~λ/2) and a depth of focus (DOF) of 153 μm (~261λ) in a broad spectral range of 500–700 nm. This excitation approach can provide a promising avenue for cutting-edge technology and applications related to Bessel beams for imaging along with a high axial resolution and an ultra-large depth of focus. [ABSTRACT FROM AUTHOR]

Glass cleaving by Bessel-like beams is one of the leading techniques providing high processing throughput and high edge quality. With the possibility to apply it to different transparent materials, this method has great potential in the high-volume production of flat panel displays, camera windows, medical devices, and others. The principle of glass cleaving is the controlled weakening of a hard transparent material by the induction of microcracks along a tight, elongated focus. These microcracks are oriented in a predefined, constant direction, limiting the flexibility of round shape fabrication. In contrast to dynamic beam manipulation techniques, the regime of direction-independent cutting was achieved through proper temporal pulse shaping. The setup does not consist of any active components in the beam path. The obtained quality and process speed are comparable with other, more complex laser cleaving techniques. Additionally, the successful cutting of polymers is presented, which are difficult to separate by the Bessel beam due to the limited possibility of microcrack generation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the stabilization of the generalized Rao‐Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler–Bernoulli beam equation for the transversal displacement. Dissipative mechanism are provided through viscous damping for two displacements. The location of the viscous damping are divided into two groups, characterized by whether both of the top and bottom layers are directly damped or otherwise. Each group consists of three cases. We obtain the necessary and sufficient conditions for the cases in group 2 to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group 1 are left for future study. [ABSTRACT FROM AUTHOR]

Self-oscillation absorbs energy from a steady environment to maintain its own continuous motion, eliminating the need to carry a power supply and controller, which will make the system more lightweight and promising for applications in energy harvesting, soft robotics, and microdevices. In this paper, we present a self-oscillating curling liquid crystal elastomer (LCE) beam-mass system, which is placed on a table and can self-oscillate under steady light. Unlike other self-sustaining systems, the contact surface of the LCE beam with the tabletop exhibits a continuous change in size during self-sustaining curling, resulting in a dynamic boundary problem. Based on the dynamic LCE model, we establish a nonlinear dynamic model of the self-oscillating curling LCE beam considering the dynamic boundary conditions, and numerically calculate its dynamic behavior using the Runge-Kutta method. The existence of two motion patterns in the LCE beam-mass system under steady light are proven by numerical calculation, namely self-curling pattern and stationary pattern. When the energy input to the system exceeds the energy dissipated by air damping, the LCE beam undergoes self-oscillating curling. Furthermore, we investigate the effects of different dimensionless parameters on the critical conditions, the amplitude and the period of the self-curling of LCE beam. Results demonstrate that the light source height, curvature coefficient, light intensity, elastic modulus, damping factor, and gravitational acceleration can modulate the self-curling amplitude and period. The self-curling LCE beam system proposed in this study can be applied to autonomous robots, energy harvesters, and micro-instruments. [ABSTRACT FROM AUTHOR]

The free and forced vibration of a graded geometrically nonlinear Timoshenko nanobeam supported by on a nonlinear foundation is considered in this paper. The main contribution of this study is to propose a new formulation for the dynamic response of this beam by combining nonlocal and surface elasticity in addition to employing the physical neutral axis method which eliminates the quadratic nonlinearity from the equation of motion. Using the principle of virtual work, a fourth-order nonlinear partial differential equation is formulated and Galerkin technique is employed to yield a fourth-order ordinary differential equation with cubic nonlinearity in the temporal domain. The method of multiple scales is employed to obtain the analytical expression of the nonlinear frequency of the beam and its frequency response curve from a primary resonance analysis. To assess the accuracy of this analytical solution, it is compared with a numerical solution obtained using the differential quadrature method. The obtained analytical results are successfully validated for particular cases of the considered problem with results published by other authors. The effects of surface elasticity, nonlocality, the physical neutral axis, the beam aspect ratio, the power-law index and the elastic foundation coefficients on the free and forced vibration response of the graded Timoshenko nanobeam are thoroughly investigated for different types of boundary conditions. [ABSTRACT FROM AUTHOR]

Elliptic Helical Mathieu Optical Vortices (EHMOVs) are a family of elliptical vortex beams that are different from the classical circular vortex or high-order Bessel beams. We introduced the stationary phase method to efficiently generate EHMOVs by using the combined amplitude-phase modulation. Experimental results showed that EHMOV modes take the form of an ellipse folded through Cartesian axes unlike the vortices with radial circular symmetries. The optical morphology of the EHMOV beams can be flexibly adjusted by controlling two of their parameters, namely, order number and ellipticity. In addition, the derived expression for the orbital angular momentum (OAM) of the EHMOV beams indicates that the OAM of EHMOVs is in fractions, whereas that of Bessel beams is in integers. The EHMOVs with tunable or fractional-order OAM and elliptical optical vortex structures are expected to play a new and unique role in optical manipulation. [ABSTRACT FROM AUTHOR]