Order Beam Research Articles

Expansion of an Object-Oriented Framework to Consider Reddy Model for Reticulated Structures

Classical software’s to perform structural analysis using the Finite Element Method (FEM) considers the Euler-Bernoulli and Timoshenko beams theories. However, these theories may not provide stress results with sufficient accuracy. Therefore, this study presents the expansion of an open-source object-oriented framework for structural analysis of frame structural models considering the Reddy beam model. Also, is presented a 3D Reddy formulation to perform linear and nonlinear geometric analysis. The computational implementation evidence the importance of use object-oriented frameworks, and open-source codes. The developed examples clearly shows the improvements in the shear stress prediction when considering higher order beams formulations in a frame element, and clarify for graduate and undergraduate students the diferences between the most usual beams formulations.

Inversion Formulas by the Use of Bessel Beams of Integer and Fractional Orders

Inversion Formulas by the Use of Bessel Beams of Integer and Fractional Orders

Field correlations of multimode optical beams in underwater turbulence

For multimode optical beams, field correlations at the receiver plane are found in underwater turbulence. Field correlations of single high order beams in underwater turbulence are special cases of our formulation. Variations of field correlations against the underwater turbulence parameters and the diagonal length from various receiver points are examined for different multimode and single high order beams. Stronger underwater turbulence is found to reduce the field correlations of multimode and single high order optical beams. The results will be of help in heterodyne detection analysis and fiber coupling efficiency in an underwater medium experiencing turbulence.

Analysis of finite energy fresnel bessel beams scintillation level in turbulent communication links

Scintillation indices of Finite Energy Fresnel-Bessel Beams (FEFBBs) propagating for 6 Km in a turbulent atmosphere are analyzed. In this context, the effects of beam order and Gaussian beam waist on the reduction of scintillation level are evaluated. Both the point-like scintillation and the power scintillation indices are examined. The obtained results show that beam order does not have a significant impact on the scintillation levels. FEFBBs are able to reduce the power scintillation levels, then improve the system performance better than fundamental Gaussian beams. Thus, the provided results are significant for not only the performance improvement of the free-space optical (FSO) communication systems but also for the applications that require line of sight alignment namely directed infrared countermeasure (DIRCM).

High-resolution ptychographic imaging at a seeded free-electron laser source using OAM beams

Electromagnetic waves possessing orbital angular momentum (OAM) are powerful tools for applications in optical communications, quantum technologies, and optical tweezers. Recently, they have attracted growing interest since they can be harnessed to detect peculiar helical dichroic effects in chiral molecular media and in magnetic nanostructures. In this work, we perform single-shot per position ptychography on a nanostructured object at a seeded free-electron laser, using extreme ultraviolet OAM beams of different topological charge orders ℓ generated with spiral zone plates. By controlling ℓ, we demonstrate how the structural features of OAM beam profiles determine an improvement of about 30% in image resolution with respect to conventional Gaussian beam illumination. This result extends the capabilities of coherent diffraction imaging techniques, and paves the way for achieving time-resolved high-resolution (below 100 nm) microscopy on large area samples.

Collimating three-axicon zoom system for interferometric Bessel beam side lobe cancellation

Optical Bessel beams are used in numerous applications like fluorescence microscopy, material processing and optical trapping. These applications require Bessel beams having a central core with defined full width at half maximum and a defined axial length. Often, the side lobes of Bessel beams, which are associated with their non-diffracting properties, can interfere with the experimental process. We theoretically describe and practically verify the performance of a new refractive optical system to generate zoomable annular ring intensities. The ability to zoom the output ring diameter allows for flexibly choosing the Bessel beam parameters. Secondly, we introduce the use of a Michelson interferometer for destructively interfering Bessel beam side lobes in one direction. If two Bessel beams of zeroth order and first kind are coherently superposed with a small shift with respect to each other, their side lobes are enhanced in one direction and cancelled in the other direction. We suggest that applications like light-sheet microscopy can exploit the axis of destructive interference to improve their contrast.

Study on the Generation of 1.9 μm Mode Superposition Conversion Laser by Double-End Off-Axis Pumping

In this paper, the Laguerre–Gaussian (LG) mode superposition is obtained by using the technology of double-end off-axis pumping Tm:YLF crystal, and the LG mode superposition is achieved by combining the extra-cavity conversion method. The impact of changing the off-axis distance on the order of Hermite–Gaussian (HG) mode and the topological charge of LG mode is studied. The results show that when the off-axis distance of the pump source at both ends is tuned, when the off-axis distance is in the range of 260 μm~845 μm, the single-ended 0~10 order HG mode can be obtained. Subsequently, the mode converter is placed to obtain the LG mode beam, and the double-end simultaneously pumps the crystal to obtain the superimposed LG mode. The tuning off-axis quantity changes the topological charge number. When P = 0, l1=l2, the superimposed LG mode is a single-ring spot, and the vortex beam center’s dark hollow area increases with the topological charge number. When P = 0, l1=−l2, the superimposed LG mode is a petal-like spot. The number of petals differs from the topological charges of two opposite numbers. Finally, in the case of changing the topological charge number of the double-ended LG mode, the output of the vortex array structured beams of the tuning mode order 1.9 μm Tm:YLF is completed in the case of conversion and superposition.

Spin-orbit interaction in quasi-monochromatic singular beams

It is shown that the magnitude of the spin-orbit coupling is the energy efficiency of energy transfer between orthogonally polarized beam components. The energy efficiency changes as the Gaussian beam propagates through the anisotropic crystal. For a fundamental Gaussian beam, the energy efficiency cannot exceed 50%, and for elegant Hermite-Gaussian and Laguerre-Gaussian beams of higher orders, the energy efficiency can reach a value close to 100%. At the same time, for ordinary higher-order Hermite-Gaussian and Laguerre-Gaussian mode beams, the energy efficiency can only slightly exceed 50%. It is shown that zero-order Bessel-Gaussian beams are capable of achieving an energy efficiency close to 100% when an axial optical vortex is generated in the orthogonally polarized beam component when passing through an anisotropic medium, in both monochromatic and polychromatic light. It is shown that for elegant polychromatic Laguerre-Gaussian or Hermite-Gaussian beams, the energy efficiency is reduced to a value not exceeding 50%. The spin moment is compensated by a change in the orbital momentum of the entire beam, which occurs as a result of the difference in topological charge (TC) in the orthogonally polarized components by 2 units.

Propagation of hollow higher-order cosh-Gaussian beam in human upper dermis

Optical detection, measurement, and treatment methods are widely used in the medical industry nowadays. The evolution of radiated beams, received power and beam size play vital roles while developing devices. The propagation properties of hollow higher-order cosh-Gaussian beam (HHOCGB) while propagating in human upper dermis tissue are derived analytically and analyzed numerically. The impact of the hollowness parameter, beam order, operating wavelength, and Gaussian beam waists on the beam’s intensity profile is examined. Received power and beam size variations are analyzed considering operating wavelength and Gaussian waist width. According to the results, as the beam propagates, its profile rapidly evolves into a shape with a circular Gaussian peak in the center and petals at the corner. Dark hollow regions are observed among the petals. Furthermore, the received power by HHOCGBs with a higher Gaussian waist width is more than those received by beams with a lower Gaussian waist width. However, at far field, operating at a lower wavelength prevents the increase of the beam spread. Thus, the obtained results will be significant in the bio-optical disease detection and treatment technology development.

Inverse‐Design Methodology for Generating Twisted Ultrasonic Motor in Free Space

A new level of freedom is made possible by orbital angular momentum (OAM), which can be used to create twisted ultrasonic motors for particle manipulation and control. For steady and free‐flowing particle management, it is essential to produce acoustic OAM beams of high order and high quality. However, this task is difficult due to the phased array's fundamental restriction of insufficient resolution or aperture. Herein, a generic approach is presented to inverse design that may be used to improve the OAM beam quality and produce twisted ultrasonic motors in free space. In comparison to the previous direct‐design method, up to a 14% improvement in amplitude uniformity and a 12 dB improvement in signal‐to‐noise ratio (SNR) of OAM modes are achieved. These notable benefits enable the ultrasonic motor to operate with a straightforward and compact system while enabling steady particle rotation in free space with an undersampled phased array, which is not possible with the conventional technique. This study paves the way for effective particle control, high‐fidelity communication, and other OAM‐based technologies by providing an inverse‐design framework for optimizing OAM.

Stress resultants governing equations of any beam theory by direct manipulation of 3D equilibrium

In this article, the author shows that the equilibrium equations of any one-dimensional theory can be obtained by direct manipulation of the indefinite 3D elasticity equations: σ i j , i + p j = 0 . It is found that there is no need to refer to Newton-type or Lagrange-type equations to write the equilibrium in terms of stress resultants. Such ‘direct manipulation’ is illustrated by considering various problems, from the simplest to the most complex. First, the bar case is analyzed and the well-known equilibrium normal stress resultant equation is obtained: N z z , z + q z = 0 ; second, the Timoshenko beam theory is tackled; finally, the case of arbitrary higher order beam theories based on the Carrera Unified Formulation is treated. The equations of a new, unprecedented higher-order beam theory are derived directly from the indefinite equilibrium equations as an example of the capabilities of the proposed method. The manipulation introduced consists of the following points: (i) the 3D elasticity is first written for each degree of freedom (dof) of the beam theories; (ii) the respective stress resultants are used to replace stress components in the latter equations; (iii) the derivatives on the beam axis z do not affect the nature of the indefinite equilibrium equations and these derivatives are applied directly to the respective stress resultants; (iv) the derivatives on the section coordinate x – y should 1 – change the sign of the respective stress resultants, 2 – be applied to the functions of x, y used to define the stress resultants. These points have been proved by referring to the principle of virtual work and splitting the differential operators of the strain-displacement relations into two parts: over the section derivatives along the beam axis derivatives. Some possible further generalizations are discussed in the appendix; in particular, the extension to is briefly discussed.

Bending Analysis of Steel-Concrete Composite Beams with Porosity

This study investigated the bending behavior of a simply supported pervious composite beam using the finite element method based on cubic order beam theory. The cubic order axial displacement was assumed and solved using shear stress-free conditions on the extreme surfaces of the composite beam. For simplicity, this study considered one-dimensional axial displacement. Three nodded finite elements were assumed, and each node had eight unknowns. Shear locking was eliminated in the present model by numerical integration of the stiffness matrix. A uniform porosity distribution was implemented in the upper layer of the composite beam. The damping ratio was also considered for the bending analysis. The accuracy of the present model makes it robust for the analysis of composite beams.

Set of mathematical models for Bessel-Gauss beams coupling into the parabolic-index fiber under the influence of atmospheric turbulence and random jitter.

The expression of efficiency for Bessel-Gauss (BG) beams coupling into the parabolic fibers (PF) after passing through the Cassegrain antenna system is first derived. The effects of atmospheric turbulence and random jitter of the coupling lens on the efficiency are also taken into account to improve the practical applicability of our model. This article use a BG beam with a wavelength of 1550 mm and fiber with a core radius RF of 50 μm and a relative refractive index difference ζ of 0.01 for simulation testing. The optimal parameters of the antenna system are determined: the radius of the primary mirror and the secondary mirror is 8.33 cm and 1.25 cm, respectively. The coupling efficiency of BG beams of different orders reaches above 94% simultaneously when the lens's focal length is 7.8 cm. After taking into account the transmission efficiency of the antenna system, the system's total efficiency for BG beams of different orders averages 76.33%, when the transmission distance is 1 km. The results show that the same degree of turbulence and random jitter have different influences on the coupling efficiency of BG beams of different orders, and lower-order BG beams have better resistance to turbulence and jitter during propagation and coupling. Moreover, the effect of the guided mode field on the coupling efficiency and the resistance to turbulence varies for different values of mode radial index in the fiber p. The guided mode with p = 0 not only enables the BG beams of different orders to achieve the highest transmission efficiency in the coupling system almost simultaneously but also the random jitter and turbulence have less influence on the coupling efficiency of this mode. It means that the BG beams can have higher efficiency when coupled to the mode with p = 0 after long-distance transmission. This property of the fiber mode at p = 0 provides conditions for the simultaneous propagation of multiple BG beams in a parabolic fiber, which provides a theoretical basis for higher transmission capacity. This research work provides a theoretical model for the theoretical study of vortex beams and optical communication, which is beneficial for the design and application of vortex beams and has instructive meaning for practical engineering design.

Generation of mode-switchable nanosecond pulsed cylindrical vector beams and vortex beams from a Q-switched solid-state laser

We reported and demonstrated a Q-switched solid-state laser for the generation of mode-switchable nanosecond pulsed cylindrical vector beams and vortex beams between different orders. In the cavity, an order-switchable Q-plate, consisted of two Q-plates and two quarter wave plates, was applied to achieve the mode-switch between two different orders by adjusting the angles of quarter wave plates. Besides, two extra quarter wave plates and a Faraday rotator were utilized to realize the intracavitary self-reproducibility of cylindrical vector beams and vortex beams, respectively. The experimental results show that by using two Q-plates of 1st and 3rd orders, the cylindrical vector beams and vortex beams of 2nd and 4th orders can be directly generated from the solid-state laser. For the 2nd order cylindrical vector beam and vortex beam, the slope efficiency, pulse width, and repetition rate are 7.2%, 415 ns, and 227 kHz, respectively. To the best of our knowledge, it is the first time to realize the controlled generation of mode-switchable cylindrical vector beams and vortex beams between two different orders from a solid-state laser.

Free Vibration Analysis of Steel-Concrete Pervious Beams

This study investigated the free vibration analysis of steel-concrete porous beams with partial or complete shear interface using a finite-element model based on the cubic order beam theory. The present model assumes uniform porosity distribution along the beam thickness. It is assumed that the axial displacement will vary cubically along the thickness of the layer. The cubic order beam theory is implemented using a continuous C0 finite element containing three nodes and each node has eight degrees of freedom. Shear locking is eliminated in the present model by the numerical integration of the stiffness matrix. Comparing the present model with the published literature, it is found that the present model is robust in predicting the free vibration of the steel-concrete porous beam.

Complete transport of intensity equation for phase retrieval of optical vortex beams

We derive the complete form of the transport of intensity equation (TIE) for an arbitrary wave field, in which additional terms describing the effect of optical vortices are included. The Poynting vector of optical vortices goes in a spiral around the vortex core through space. Consequently, the intensity variation is not observable in the manner of wave propagation, thereby precluding the possibility of phase retrieval via near-field intensity measurements. This difficulty is elegantly overcome by introducing a hard-edged aperture, as a common procedure to produce the required Neumann boundary signal, to break the azimuthal symmetry of the propagation, and visualize the rotation of the beam’s local Poynting vector around the aperture boundary. The basic principle, numerical solution, and practical implementation of how to use this new version of TIE for phase retrieval of arbitrary wave fields including optical vortices are developed. Based on the new approach, we present the first experimental demonstration of non-interferometric phase retrieval of Laguerre–Gaussian vortex beams of different orders using only two near-field intensity measurements. Our results consummate the basic theoretical framework of TIE and represent an important step towards phase retrieval of arbitrary wave fields carrying phase singularities.

Time-of-flight anemometry using a displacement plate-beamsplitter

We propose the use of a second surface mirror as a displacement plate-beamsplitter to provide significant simplification and cost reduction of time-of-flight anemometry (ToFA), without sacrificing precision and accuracy. These benefits are most pronounced for long-range applications. Our method’s principle benefits are due to the few and simple components it requires as well as low sensitivity to both temperature effects and light source incoherence. We found that precise and accurate results are possible using a common consumer mirror as the main optical element and an inexpensive diode laser as the light source, which could broaden access to laser anemometry and make many industry applications economically feasible. The nature of the design also permits an increase in range for a given laser power since the method can utilize the entire optical area of the focusing lens/mirror independent of other design considerations and the cost of a flat second-surface mirror is usually negligible. To characterize the performance of this method, we develop a Cramer–Rao bound (CRB) for a general class of ToFA’s with multiple Gaussian beams under signal-independent Gaussian white noise. For a given measurement volume, the lowest velocity uncertainty is achieved by creating a standard two-sheet geometry: power-matching the first two beams by adjusting the beamsplitter and blocking the rest of the beams is optimal. However, keeping the higher order beams permits determination of flow direction. Conditions to achieve beam power-matching are given. An anemometer is built using a diode laser with 12 mw 405 nm beam using a total of just three transmitting optical components. Our setup has an accuracy of 99.1%. The worst-case precision of 96.7% nearly achieves the CRB, although optimizing the setup more can lower the bound, and therefore allow increase in the performance by an order of magnitude or more.

Derivation of a superelement with deformable interfaces – applied to model flexure joint

Design and optimization, as well as real time control, of flexure mechanisms require efficient but accurate models. The flexures can be modelled using beam elements and the frame parts can be modelled using superelements. Such a superelement efficiently models arbitrarily shaped bodies by few coordinates, using models obtained by model order reduction. The interfaces between the frame parts and the flexures often experience considerable deformation which affects the stiffness. To define the interface deformation in a reduced order model, this paper derives a multipoint constraint formulation, which relates the nodes on the deformable interface surface of a finite element model to a few coordinates. The multipoint constraints are imposed using a combination of the Lagrange multiplier method and master–slave elimination for efficient model order reduction. The resulting reduced order models are used in the generalized-strain multi-node superelement (GMS) that was defined in (Dwarshuis et al. in Multibody Syst. Dyn. 56(4):367–399, 2022). The interface deformations can be coupled to the cross-sectional deformation of higher order beam elements (i.e. beam elements of which the deformation of the cross-sections is explicitly taken into account).This paper applies this technique to model flexure joints, where the flexures are modelled with beam elements, and the frame components and critical connections using the GMS. This approach gives generally over 94% accurate stiffness, compared to nonlinear finite element models. The errors were often more than 50% lower than errors of models which only contain beam elements.

Adiabatic evolution of optical beams of arbitrary shapes in nonlocal nonlinear media

We discuss evolution of Hermite–Gaussian beams of different orders in nonlocal nonlinear media whose characteristic length is set as different functions of propagation distance, using the variational approach. It is proved that as long as the characteristic length varies slowly enough, all the Hermite–Gaussian beams can propagate adiabatically. When the characteristic length gradually comes back to its initial value after changes, all the Hermite–Gaussian beams can adiabatically restore to their own original states. The variational results agree well with the numerical simulations. Arbitrary shaped beams synthesized by Hermite–Gaussian modes can realize adiabatic evolution in nonlocal nonlinear media with gradual characteristic length.

Multi-focusing surface-emitting lasers.

Complete control of a beam pattern requires not only projecting a two-dimensional (2D) pattern but also focusing on a three-dimensional (3D) point cloud, which is typically achieved utilizing holography under the framework of diffraction. We previously reported direct focusing from on-chip size surface-emitting lasers that utilize a holographically modulated photonic crystal cavity based on 3D holography. However, this demonstration was of the simplest 3D hologram with a single point and single focal length, and the more typical 3D hologram with multiple points and multiple focal lengths has not yet been examined. Toward direct generation of a 3D hologram from the on-chip size surface-emitting laser, we here examined a simple 3D hologram featuring two different focal lengths with a single off-axis point in each to reveal the fundamental physics. Two types of holography, one based on superimposition and the other on random tiling, successfully demonstrated the desired focusing profiles. However, both types caused a spot noise beam in the far field plane due to interference between focusing beams with different focal lengths, especially in the case of the superimposing method. We also found that the 3D hologram based on the superimposing method consisted of higher order beams including the original hologram due to the manner of the holography. Secondly, we demonstrated a typical 3D hologram with multiple points and focal lengths and successfully showed the desired focusing profiles by both methods. We believe our findings will bring innovation to mobile optical systems and pave the way to developing compact optical systems in areas such as material processing, micro fluidics, optical tweezers, and endoscopy.