Elliptical Beam Research Articles

Self-focusing, self-trapping and self-phase modulation of elliptical q-Gaussian laser beams in collisionless plasma

Self-focusing, self-trapping and self-phase modulation of elliptical q-Gaussian laser beams in collisionless plasma

Propagation of Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beam in anisotropic turbulence

The beam spreading, spectral degree of coherence and evolution behavior of the intensity profile of partially coherent Lorentz-Gaussian elliptical multi-Gaussian correlation Schell-Model beam propagating in anisotropic atmospheric turbulence are studied. The analytical expressions of cross-spectral density function, as well as root mean square (rms) beam width, are derived based on the extended Huygens-Fresnel principle and the relationship of Lorentz distribution and Hermitian Gaussian function. With the increases of propagation distance, the elliptical beam will first evolve into Gaussian beam and then change back to elliptical beam. In anisotropic atmospheric turbulence, the influence of the inner scale of turbulence on the spectral degree of coherence and rms beam width are obviously greater than that of the outer scale. For Lorentz-Gaussian elliptical multi-Gaussian correlated Schell-Model beams, better propagation performance was found in anisotropic atmospheric turbulence with larger anisotropic factor and smaller inner scale.

MeerKAT Holography Measurements in the UHF, L, and S Bands

Radio holographic measurements using the MeerKAT telescope are presented for each of its supported observing bands, namely UHF (544–1087 MHz), L (856–1711 MHz), and S (1750–3499 MHz). Because the UHF-band receiver design is a scaled version of that of the L band, the electromagnetic performance in these two bands are expectedly similar to one another. Despite also being linearly polarized, S-band receivers have an entirely different design and distinct performance characteristics from the lower two bands. As introduced in previous work for the L band, evidence of higher order waveguide mode activation also appears in S-band measurements but there are differences in its manifestation. Frequency-dependent pointing (beam squint), beamwidth, beam ellipticity, error beam, instrumental polarization, and cross-polarization power measurements are illustrated for each of MeerKAT’s observational bands in a side-by-side style to facilitate the comparison of features. The derivation of collimation errors and main reflector surface errors from measurements made at these relatively low observation frequencies is also discussed. Results include elevation and ambient temperature effects on collimation, as well as the signatures of collimation degrading over time. The accompanying data release includes a snapshot of full Jones matrix primary beam patterns for all bands and antennas with corresponding derived metrics.

Stimulated Brillouin Scattering of Elliptical q-Gaussian Laser Beams in Plasmas with Axial Density Ramp: Effect of Self-Focusing

Stimulated Brillouin Scattering of Elliptical q-Gaussian Laser Beams in Plasmas with Axial Density Ramp: Effect of Self-Focusing

Transverse energy propagation and interference of elliptical Gaussian beams

Elliptical Gaussian beam (EGB) has many different physical properties from circular Gaussian beam. In this paper, the transverse energy flux and intensity of one and two coherent EGBs are studied. In our simulation, the transverse energy flux and intensity varying with waist ratio are discussed in detail. It has been found that through increasing the waist ratio, the transverse energy flux after interference would be strengthened significantly. Although the transverse energy flux is much weaker than the longitudinal energy flux, its signal to noise ratio has been verified to be strong enough for detection. Our derivations are still reasonable for another simulation with general experimental parameters. The simulation results are considered to be helpful for some physical experiments using the transverse energy flux of Gaussian beam, such as an important application in electromagnetic response produced by interaction of high-frequency gravitational waves.

Propagation-Invariant Off-Axis Elliptical Beams and their Orbital Angular Momentum

Propagation-Invariant Off-Axis Elliptical Beams and their Orbital Angular Momentum

Lines-based rotating beam profiling algorithm using pixel ionization chamber with dead pixels

In a pencil beam scanning proton therapy system, critical beam parameters, including the spot size, spot center position, and tilt angle, are monitored for security by beam profile detectors such as two-dimensional (2D) pixel-segmented ionization chambers. A method, named lines-based beam profiling (LBBP), is proposed to identify the five geometric parameters μx,μy,σx,σy,θ of rotating elliptical beam profiles using several lines (rows and columns) in the 2D detector data. The method provides solid results even in the presence of dead pixels, which can be located using a wavelet analysis. Simulation experiments were used to define the number of lines used by the LBBP method and to characterize its performance as a function of the signal-to-noise (SNR). For SNR greater than 30, the root mean square errors (RMSEs) of the beam spot size, spot center position, and rotation angle obtained with the LBBP method are less than 0.16 mm, 0.05 mm, and 0.78 degrees, respectively. The LBBP method was applied to the data collected by a pixel chamber illuminated by an X-ray source, demonstrating the capability of identifying dead pixels and providing more accurate measurements of the beam spot size and center position than the standard Gaussian fitting.

Expanding non-axisymmetric beams in spherical coordinates with cylindrical wave spectrum decomposition

Description of structured beams in spherical coordinates is critical in studying the interaction between beams and spherical particles. The work extends the cylindrical wave spectrum decomposition (CWSD) method to non-axisymmetric beams, applied herein to the elliptical Gaussian beam, cosine Gauss beam and Hermite-Gauss beam as examples. It is shown that for these beams the beam shape coefficients (BSCs) can be expressed in one dimensional integrations and hence numerical calculations can be performed very efficiently. The beam fields reproduced by using these BSCs show satisfactory faithfulness to the rigorous expression of the given fields. Typically, the difference between them is less than 10−8.

Optically driven liquid crystal droplet rotator

In this study, the rotation of liquid crystal droplets induced by elliptically polarized laser light was investigated using optical tweezers. The rotation mechanism was analyzed based on the arrangement of liquid crystal molecules within the droplets. The change in the rotation behavior of nematic liquid crystal (NLC) droplets was evaluated by varying the droplet size. The experimental results were analyzed based on the waveplate effect and light-scattering process. The rotation behavior of cholesteric liquid crystal droplets was examined by varying the droplet size and helical pitch, which was controlled by the chiral dopant concentration. The results are discussed in terms of the selective reflection of the incident beam by the helical structure. The dependence of the rotation frequency on the ellipticity of the incident beam was also studied. The main contribution to the rotation gradually changes from light transmission to reflection with increasing chirality of the droplet. An NLC rotator system was constructed using holographic optical tweezers. Such an optically controllable rotator is a typical micro-optomechanical device. Complex flow fields, including multiple vortex and localized shear fields, were realized at the micron scale.

Reduced Plasma Frequency Calculation Based on Particle-in-Cell Simulations

We propose a scheme to calculate the reduced plasma frequency of a cylindrical-shaped electron beam flowing inside of a cylindrical tunnel, based on results obtained from Particle-in-cell (PIC) simulations. In PIC simulations, we modulate the electron beam using two parallel, non-intercepting, closely-spaced grids which are electrically connected together by a single-tone sinusoidal voltage source. The electron energy and the beam current distributions along the length of the tunnel are monitored after the system is operating at steady-state. We build a system matrix describing the beam's dynamics, estimated by fitting a 2x2 matrix that best agrees with the first order differential equations that govern the physics-based system. Results are compared with the theoretical Branch and Mihran model, which is typically used to compute the plasma frequency reduction factor in such systems. Our method shows excellent agreement with the theoretical model, however, it is also general. Our method can be potentially utilized to determine the reduced plasma frequencies of electron beams propagating in differently-shaped beam tunnels, where no theoretical model yet exists, such as the case of a cylindrical or elliptical electron beam propagating inside of a metallic beam tunnel of cylindrical, square, or elliptical cross-section. It can be applied also to electron beams composed of multiple streams.

Independent and intensity-adjustable dual-focused vortex beams via a helicity-multiplexing metalens

Independently tailoring two or more focused vortex beams and controlling their intensity distributions in one device is indispensable in optical trapping and manipulation fields. We propose the phase equation for a helicity-multiplexing metalens generating dual-focused vortex beams based on the propagation phase and geometry phase. The metalens can independently manipulate dual-focused vortex beams, i.e., their focal lengths, lateral displacements, and topological charges could be independently tailored. Moreover, we can adjust their relative focal intensity by modulating the ellipticity of the incident beam. Such metalenses allow for advanced research and applications in trapping and rotating microparticles.

Random vibration study of functionally graded porous curved beams with elastically restrained ends

Firstly, the random vibration characteristics of functionally graded porous (FGP) curved beams with elastically restrained ends are studied. An efficient model is presented by the Timoshenko beam theory and spectral-Chebyshev method. In this paper, three different types of porous distribution are considered, and the relationship between porosity coefficient and material parameters is determined according to the typical mechanical properties of open cell foam metal. Four types of curved beams with different curvatures are selected for the study, which are elliptical beam, parabolic beam, hyperbolic beam and circular beam. The one-dimensional admissible displacement functions of the FGP curved beam are constructed by Chebyshev polynomials of the first kind with Gauss-Lobatto sampling points discretization. Three artificial boundary springs are used to impose elastic boundary constraints at the ends of the curved beam. The pseudo excitation method is used to apply stationary and non-stationary random excitations, including point excitation and base acceleration excitation. The stationary random vibration responses of the FGP curved beam with different boundary conditions, involving the power spectral density (PSD) and root mean square (RMS) values of displacement, velocity and acceleration, are calculated and agreed well with the finite element method (FEM). At last, the RMS values of the non-stationary random vibration response of the FGP curved beam are given.

Design of off-axis double reflection freeform miniaturized antenna

The asymmetrical divergence angle distribution of elliptical laser beam produced by a laser diode (LD) severely limits the application. In this paper, an off-axis double reflection freeform miniaturized antenna design method is proposed to collimate, shape, and transmit elliptical beams from LD. Based on the law of conservation of energy, reflection vector theory, and equal optical path principle, two freeform mirrors are constructed simultaneously by using the three-dimensional point-by-point construction iterative method. The simulation results show that the maximum divergence angle of the output light is compressed to 3.42 μrad, and the ratio of beam waist (RBW) of the output beam is reduced from 3.0000 to 1.0668 at the target plane (L=1 km). The volume of the antenna is 3229.99 cm 3 and the design realizes the miniaturization of the antenna. In addition, the effects of wavelength shift, astigmatism, and the offset of the light source on the collimation effect are analyzed. These research results will provide a practical method to collimate and shape the laser beam and increase the transmission efficiency of the optical communication system. Meanwhile, the proposed optimization method to obtain optimal parameters can be applied to design the initial structure of the freeform surface, and the method of constructing a line light source model in the design process can also provide a reference for the study of astigmatism of LD.

Experimental study of transverse effects in planar dielectric wakefield accelerating structures with elliptical beams

The main obstacle to the practical implementation of the dielectric wakefield acceleration (DWA) concept is the development of the beam breakup instability due to transverse dipole wakefields generated when the beam propagates off axis in the accelerating structure. One of the methods to suppress this instability is to elliptically shape the beam and accelerate it in a planar structure. Here, we report a detailed experimental investigation of the transverse dynamics of elliptical beams in planar dielectric structure with parameters mimicking future DWA modules. Both dipole and quadrupole wakefields' effects on beam stability and projected emittance were studied. This study has highlighted the importance of counteracting quadrupole wakefields in future DWA implementations.

Application of a scattering foil to increase beam transmission for cyclotron based proton therapy facilities

In proton therapy, high dose rates can reduce treatment delivery times, allowing for efficient mitigation of tumor motion, as well as increased treatment efficiency and patient throughput. In cyclotron-based facilities, however, high dose rates are difficult to achieve at low-energies. In current facilities, the emittance after the degrader is matched in both transversal planes using circular collimators; this does not provide an optimal matching to the acceptance of the following beamline. However, transmission can be substantially improved by transporting maximum acceptable emittances in the X and Y planes, but at the cost of an elliptical beam shape at the gantry entrance, leading to gantry angle-dependent beam shapes at the isocenter. Here we demonstrate that equal emittances in both planes can be recovered at the gantry entrance using a thin scattering foil, thus ensuring gantry angle-independent beam shape at the isocenter. Using modified beam optics and thin scattering foil placed in the beamline, we demonstrate experimentally that low-energy beam transmission can be increased by a factor of three compared to the currently used beam optics, whilst preserving gantry angle-independent beam shapes, at the cost of a large beam size. We expect that this approach could also bring a similar transmission improvement in other cyclotron-based proton therapy facilities.

Electromagnetic beam scattering of the anisotropic medium cylinder

Based on the conservation of electromagnetic energy, a theoretical model, which can equate the electromagnetic anisotropic medium to be the electromagnetic isotropic medium, is established. The correctness of this proposed model is verified, and method of using the model is presented. In case of the condition that the wavelength of electromagnetic wave being similar to the geometrical parameters of the cylinder, the equivalent permittivity of the cylinder of gypsum crystal in the elliptical Gaussian beam varies with its geometrical parameters, beam parameters and beam propagation direction are studied. The results show that the equivalent permittivity fluctuated changes with the increase of the radius of the cylinder, and the change of the equivalent permittivity is very small with the increase of the length of the cylinder, and the electromagnetic mechanisms of the phenomena are presented. The analytical expression of the scattered field of an anisotropic cylinder being irradiated by an electromagnetic wave beam with a general direction is studied, the correctness of the results obtained from this analytical expression are tested by the results from the references. It is found that the radius of the cylinder and the angle between the electromagnetic wave propagation direction and the symmetry axis of the cylinder have a great effect on the scattering, and the length of the cylinder, the distance between the beam and cylinder and the beam waist width and so forth have little effects on scattering.

Complex source point theory of paraxial and nonparaxial elliptical Gaussian beams.

Using the operator transformation technology, we extend the circular Gaussian beam based virtual (complex) sources method to investigate the paraxial and nonparaxial propagation properties of the elliptical Gaussian beams (EGBs) with planar or cylindrical wavefronts travelling in free space. The paraxial approximation analysis reveals the self-reappearance and self-focusing propagation features for the EGBs with cylindrical wavefront under proper parameter conditions. We further introduce the nonparaxial theory to derive the analytical expressions for the field distribution of an EGB in free space, and confirm that these intriguing propagation features can still be observed with added nonparaxial correction. Comparing with the paraxial approximation results, it is worth noting that there is a clear deviation of the on-axial intensity and phase distributions near the self-focusing position on the basis of nonparaxial correction solution. Our results reveal that the anisotropic diffraction of light propagating through homogeneous medium or free space is possible. The approach in this work can easily be generalized to other beam models with elliptical geometry, which allows us to correctly predict some important information about their near field propagation characteristics for various applications.

Generation of elliptical airy vortex beams based on all-dielectric metasurface

Elliptical airy vortex beams (EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m|+1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.

Non-linear Hygrothermal Structural Analysis of the Elliptical Dome of the Church in the Universidad Laboral, Gijon, Spain

ABSTRACT The Church of the Laboral University of Gijón has the world’s largest elliptical masonry roof with a 40.8 m major axis. This large structure is vertically self-supported with 20 pairs of masonry ribs crossing each other and horizontally supported by means of two elliptical ring beams at the top of the dome. In order to study this historic building, this paper presents the overall three-dimensional structural numerical analysis of the roof. It includes nonlinearities due to materials, geometry, and contacts between structural elements of the building. Temperature, moisture content, and dead loads are included in the hygrothermal structural analysis of the dome. In this nonlinear numerical analysis displacements, stress, cracking, and crushing are evaluated. The influence of moisture content on the structure performance and other relevant conclusions are presented.

The multi-consecutive optical bottles generated from the chirped elliptical Pearcey Gaussian vortex beams

The evolution of the chirped elliptical Pearcey Gaussian vortex (CEPGV) beams in free space is numerically investigated. The optical bottle and multi-consecutive optical bottles can be directly generated from an elliptical Pearcey Gaussian beam with central vortices and the second-order chirp. In particular, the focusing intensity of CEPGV beams will increase when the elliptical structure deflects larger or the ratio of the long axis to the short axis of the ellipse is larger. Furthermore, we can obtain multi-consecutive optical bottles by manipulating elliptical structure parameters and second-order chirp factors. In the meantime, the transverse intensity distributions at foci of CEPGV beams appear like a slit in a fixed direction. Our results show that the focusing intensity, the focal length and the transverse intensity distribution of CEPGV beams during the propagation can be controlled.