Superposition Of Gaussian Beams Research Articles

Intrinsic dichroism in amorphous and crystalline solids with helical light

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

Elastic common-receiver Gaussian beam migration of 4C ocean-bottom node data

Four-component ocean-bottom node (OBN) surveys allow for the imaging of subsurface elastic properties for oil and gas exploration in deepwater environments. However, sparse acquisition sampling for the high-quality imaging of OBN data is challenging. To alleviate this problem, a common-receiver domain 4C elastic Gaussian beam migration method based on elastic reciprocity transformation that considers the monopole/dipole characters of sources and receivers is developed. Common-receiver migration also is computationally efficient in an OBN survey wherein the number of shots usually exceeds the number of geophones. P/S and up-/downgoing wavefield decompositions are accomplished on the “virtual source side” during migration. A decomposition matrix and a wavefield extrapolation formula are derived from the elastic Kirchhoff-Helmholtz integral with the representation of the Green’s function as a superposition of Gaussian beams. The local slant stack is performed on the common-receiver recordings that are subjected to more optimized sampling, which is less sensitive to aliasing. The performance of the method on synthetic data is validated using the coarse sampling of OBNs in a deepwater and ultradeepwater environment.

Intrinsic spatial chirp of subcycle terahertz pulsed beams

We present an analysis of spatial chirp in subcycle pulsed beams corroborated by spatiotemporal electro-optic sampling measurements of terahertz radiation. Modeling the subcycle pulsed beam as a superposition of monochromatic Gaussian beams, free-space propagation is shown to directly lead to lateral spatial chirp with the spectrum on-axis substantially bluer than the overall energy spectrum. The two-transverse $+$ one-temporal dimensional profile of terahertz subcycle pulsed beams from organic crystals DSTMS and OH1 are measured and compared with observed spatiospectral correlations consistent with the model.

Propagation-Invariant Off-Axis Elliptic Gaussian Beams with the Orbital Angular Momentum

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane.

Spatial Optical Traps Based on Multibeam Interference

A model of the formation of spatial optical traps for capturing, moving, and orienting microparticles is proposed that is based on a superposition of Gaussian beams in various geometric configurations with controllable parameters.

Spatially controlled nano-structuring of silicon with femtosecond vortex pulses

Engineering material properties is key for development of smart materials and next generation nanodevices. This requires nanoscale spatial precision and control to fabricate structures/defects. Lithographic techniques are widely used for nanostructuring in which a geometric pattern on a mask is transferred to a resist by photons or charged particles and subsequently engraved on the substrate. However, direct mask-less fabrication has only been possible with electron and ion beams. That is because light has an inherent disadvantage; the diffraction limit makes it difficult to interact with matter on dimensions smaller than the wavelength of light. Here we demonstrate spatially controlled formation of nanocones on a silicon surface with a positional precision of 50 nm using femtosecond laser ablation comprising a superposition of optical vector vortex and Gaussian beams. Such control and precision opens new opportunities for nano-printing of materials using techniques such as laser-induced forward transfer and in general broadens the scope of laser processing of materials.

Application of Gaussian pulsed beam decomposition in modeling optical systems with diffraction grating.

A diffraction grating is one of the most commonly used components in ultrafast optical systems such as pulse stretchers and compressors. Hence, modeling the temporal dispersion and spatiotemporal distortions associated with the angular dispersion of a diffraction grating is very crucial for wave optical modeling of such systems. In this paper, the Gaussian pulsed beam decomposition (GPBD) method is extended to handle the propagation of ultrashort pulses, with arbitrary spatial and spectral profiles, through complex ultrashort pulse shaping systems containing diffraction gratings. Although the diffraction efficiencies are not rigorously computed, the GPBD method enables modeling of the large angular dispersion of idealized diffraction gratings without running into an impractically large number of spectral samples as in the case of Fourier-transform-based methods. The application of the extended method is demonstrated by performing the wave optical propagation of an ultrashort pulse through a single diffraction grating and then through a Treacy compressor system. By combining the Treacy compressor with the Martinez grating pair stretcher with internal lenses, the pulse shaping through a complete chirped pulse amplification (CPA) setup is modeled. Finally, the effects of using real dispersive lenses in the Martinez stretcher on the output pulse of the CPA setup are presented. For analysis of the output pulses, methods of computing the spatiotemporal and spatio-spectral amplitudes of the output pulse from the phase correct superposition of individual Gaussian pulsed beams are presented.

Пространственные оптические ловушки на основе многопучковой интерференции

In present work is demonstrated a model for the formation of spatial optical traps for capturing, moving and angular orientation of microparticles based on the superposition of several Gaussian beams in various geometric configurations with controlled parameters.

Modeling of laser ponderomotive self-focusing in plasma within the paraxial complex geometrical optics approach

Laser ponderomotive self-focusing in an underdense homogeneous plasma is studied within the paraxial complex geometrical optics (PCGO) approach implemented in a hydrodynamic code in two-dimensional planar geometry. The self-focusing of a PCGO Gaussian beam is compared to simulations performed with a paraxial electromagnetic code. Good agreement has been found for beam powers less than three times the critical power and for plasma densities 5%–10% of the critical density. Besides Gaussian beams, PCGO allows to reproduce spatially modulated beams by superposition of Gaussian beams, mimicking a speckle pattern. Although the statistics of speckle patterns generated with PCGO reproduces well the speckle statistics of optically smoothed beams, a PCGO speckle is larger than optical speckles, carrying thus higher power such that they overestimate self-focusing effects. To overcome this issue, an algorithm is proposed within PCGO framework: it consists of superposing several Gaussian beams forming a speckle such that self-focusing effects are eventually well controlled. It is found that the superposition of three Gaussian beams with appropriate initial conditions leads to a reduction of the PCGO speckle intensity enhancement.

General superpositions of Gaussian beams and propagation errors

Gaussian beams are asymptotically valid high frequency solutions concentrated on a single curve through the physical domain, and superposition of Gaussian beams provides a powerful tool to generate more general high frequency solutions to PDEs. We present a superposition of Gaussian beams over an arbitrary bounded set of dimension $m$ in phase space, and show that the tools recently developed in [ H. Liu, O. Runborg, and N. M. Tanushev, Math. Comp., 82: 919--952, 2013] can be applied to obtain the propagation error of order $k^{1- \frac{N}{2}- \frac{d-m}{4}}$, where $N$ is the order of beams and $d$ is the spatial dimension. Moreover, we study the sharpness of this estimate in examples.

Acoustic Field of a Linear Phased Array: A Simulation Study of Ultrasonic Circular Tube Material.

As ultrasonic wave field radiated by an ultrasonic transducer influences the results of ultrasonic nondestructive testing, simulation and emulation are widely used in nondestructive testing. In this paper, a simulation study is proposed to detect defects in a circular tube material. Firstly, the ultrasonic propagation behavior was analyzed, and a formulation of the Multi-Gaussian beam model (MGB) based on a superposition of Gaussian beams is described. The expression of the acoustic field from a linear phased-array ultrasonic transducer in the condition of a convex interface on the circular tube material is proposed. Secondly, in order to make the tapered probe wedge better fit the curved circular tube material and carry out the ultrasonic inspection of the curved surface, it was necessary to pare the angle probe wedge. Finally, acoustic field simulations in a circular tube were carried out and analyzed. The simulation results indicated that the method of ultrasonic phased-array inspection is feasible in circular tube testing. Tube materials with different curvatures need different array element lengths and widths to get the desired focused beam.

Pulse smearing and profile generation in CO2 laser micromachining on PMMA via raster scanning

CO2 laser micromachining is an efficient and cost effective way for fabricating many polymeric microfluidic devices. Apart from direct laser writing also called vector cutting, raster scanning of CO2 laser beam is an indispensable part of fabrication process. Raster scanning is commonly used to create different types of microstructures on the surface. Polymethyl methacrylate (PMMA) is an important polymeric substrate for various microfluidic devices. In this research work, CO2 laser based raster scanning process has been explored for generation of microstructures of different widths and depths. The influence of high raster speeds on individual laser pulse shape has been discussed. Pulse smearing phenomenon was found to be detrimental to intensity of the laser beam. Reduction in energy intensity due to pulse smearing has been determined experimentally. Effects of process parameters on micromachined structure's output parameters have been detailed. An unique theoretical model has been developed for prediction of micromachined depth and profile on the basis of conservation of energy principal and superposition of Gaussian beams. The model takes into account the vertical pulse overlapping as well as pulse smearing effect. Evolution of surface in raster scanning has been discussed theoretically and experimentally. Developed model was found to be predicting the depth and evolved micro-structure profile close to actual depths and profile. The maximum prediction error for different power and scanning speed settings were less than 7.23%.

Regularities of femtosecond filamentation in the case of superposition of Gaussian and annular laser beams

The self-action of high-power femtosecond laser beams with a radiation wavelength of 800 nm (formed by superposition of Gaussian and annular beams) in air is theoretically modelled. A detailed analysis of self-focusing and filamentation of this radiation is performed based on the numerical solution of the spectral equation of the unidirectional propagation of a wave packet with allowance for the nonlinearity of the medium, and by tracing averaged diffraction-optical rays. It is shown that, in terms of the diffraction-beam optics, the outer annulus forms a waveguide, which facilitates self-trapping of the central part of the combined beam, supplying the light energy to the filament. The spatial stability of this waveguide depends on the energy stored in the annulus and on the distance from the latter to the beam axis.

Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

Elementary Green function as an integral superposition of Gaussian beams in inhomogeneous anisotropic layered structures in Cartesian coordinates

The Gaussian Beam Summation and the Gaussian Launching Methods in Scattering Problem

This paper is mainly devoted to application of the Gaussian beam summation technique in electromagnetic simulations problem. Gaussian beams are asymptotic solutions of the Helmholtz equation within the paraxial approximation. Since they are insensitive to ray transition region, several techniques based on Gaussian beam are used to evaluate high frequency EM wave equation, which overcome partially or fully the difficulties of singular regions (caustics, zero field in shadow zones). This paper concentrates on the explicit formulation of the electromagnetic field scattered from radar target. In this approach, when the incident field illuminates the target, the scattering is accounted in a complex weighing function. The wave field at a receiver is evaluated as superposition of Gaussian beams concentrated close to rays emerging from the target, passing through the neighbor of the receiver.

Propagation of optical vortex beams and nucleation of vortex-antivortex pairs in disordered nonlinear photonic lattices

The propagation of optical vortex beams through disordered nonlinear photonic lattices is numerically studied. The vortex beams are generated by using a superposition of several Gaussian laser beams arranged in a radially-symmetric manner. The paraxial nonlinear Schrodinger equation describing the longitudinal propagation of the beam array through nonlinear triangular photonic lattices with two-dimensional disorder is solved numerically by using the split-step Fourier method. We find that due to the spatial disorder, the vortex beam is destabilized after propagating a finite distance and new vortex-antivortex pairs are nucleated at the positions of perfect destructive interference. We also find that in the presence of a self-focusing nonlinearity, the vortex-antivortex pair nucleation is suppressed and the vortex beam becomes more stable, while a self-defocusing nonlinearity enhances the vortex-antivortex pair nucleation.

Optimal Error Estimates for First-Order Gaussian Beam Approximations to the Schrödinger Equation

Gaussian beams are generally local asymptotic solutions to the linear wave equations in the high-frequency regime. Each Gaussian beam is concentrated around a specific ray path determined by the underlying Hamiltonian system. Expressed as some superposition of Gaussian beams, Gaussian beam approximation is expected to be a high-frequency asymptotic solution which remains globally valid even around caustics. We derive optimal first-order error estimates for first-order Gaussian beam approximations, in both continuous and discrete levels, to the Schrodinger equation equipped with a WKB initial data. Our error estimates are valid for any spatial dimension and unaffected by the presence of caustics. Some numerical tests are presented to validate the theoretical results.

Propagation of a General Gaussian Beam by Paraxial Ray Tracing in an Arbitrary Optical System

The propagation of a partially coherent Gaussian beam in a homogeneous medium can be explained with various methods. One of them is Gaussian shell model beams [1–8]. It uses the Gaussian Schell-model source whose irradiance distribution and degree of coherence are both Gaussian. We will describe Gaussian beams as the ray distribution L as functions of linear and angular coordinates. Of course, since the Gaussian Shell model beam can be produced by a superposition of independent coherent Gaussian beams, our concept is similar to the Gaussian Shell model concept. However, the goal of the present paper is to describe the propagation of general Gaussian beams through an arbitrary optical system by using the geometrical paraxial ray tracing method. In other words, many rays propagate through a reference plane, these rays distribute with the Gaussian profile in linear and angular direction cosine coordinates, and every ray propagates according to the laws of geometrical optics. At first, we introduce the ray distribution density of a circular symmetric Gaussian beam and investigate how that Gaussian beam propagates through an arbitrary axially symmetric optical system or in a homogeneous medium under the paraxial approximation, and we determine the physical meanings of the parameters. Also, we introduce the complex parameter q and the Lagrange invariant L for this general Gaussian beam and discover that this Gaussian beam also follows the Kogelnik ABCD law, just as a classical coherent Gaussian beam does.

Fresnel filtering of Gaussian beams in microcavities

We study the output from the modes described by the superposition of Gaussian beams confined in the quasi-stadium microcavities. We experimentally observe the deviation from Snell's law in the output when the incident angle of the Gaussian beam at the cavity interface is near the critical angle for total internal reflection, providing direct experimental evidence on the Fresnel filtering. The theory of the Fresnel filtering for a planar interface qualitatively reproduces experimental data, and a discussion is given on small deviation between the measured data and the theory.

A Gaussian beam approach for computing Wigner measures in convex domains

A Gaussian beam method is presented for the analysis of the energy of the high frequency solution to the mixed problem of the scalar wave equation in an open and convex subset $\Omega$ of $IR^n$, with initial conditions compactly supported in $\Omega$, and Dirichlet or Neumann type boundary condition. The transport of the microlocal energy density along the broken bicharacteristic flow at the high frequency limit is proved through the use of Wigner measures. Our approach consists first in computing explicitly the Wigner measures under an additional control of the initial data allowing to approach the solution by a superposition of first order Gaussian beams. The results are then generalized to standard initial conditions.