Elliptical Gaussian Research Articles

Investigation of scattering of a pair chiral spheres

We study the complex scattering of a pair of chiral spheres in the elliptical Gaussian beam. A system identification model of scattered field is established for two chiral spheres when they are irradiated by electromagnetic beam. Variations of the radar cross section both of isolated chiral sphere and a pair of chiral spheres versus the chiral parameter are developed and we also studied the behavior of the coefficients of scattering waves from two chiral spheres. It is found that when the chiral parameter valued in a range, it may reduce the radar cross section, and the false targets surrounding the real target may not only confuse Radar; but also reduce the radar cross-section of the real target. The method used in this article may have the property of simplicity and can also be used to research scattered field of three or more chiral spheres.

Coupling characteristics and kurtosis parameter of partially coherent beams in turbulent atmosphere

ABSTRACTCoupling properties and kurtosis parameter (K parameter) of arbitrary beams propagating through atmospheric turbulence are investigated. A correlation factor (C4-factor) is introduced to describe the influence of turbulence on coupling characteristics. The general analytical expression for C4-factor of arbitrary beams in atmospheric turbulence is derived. It is shown that C4-factor of arbitrary beams in the turbulent atmosphere depends on the initial second-order moments and fourth-order moments and turbulence quantities. Taking the partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam as an example, we can obtain that C4-factor decreases as structure constant of the refractive index fluctuations and inner scale increase, and waist width and transverse coherence length decrease when z > 5 km. Moreover, K parameter of PCAEHG beam in turbulent atmosphere converges to 2 when propagation distance is large enough. It indicates that the profile of PCAEHG beams in turbulent atmosphere finally evolves into fundamental Gaussian distribution.

Analytical model for a single multiphoton absorption process

We present a theoretical analysis of a single [Formula: see text]-photon absorption process. We found an approximate analytical but closed-form expression of the normalized transmittance for a thin nonlinear material under an elliptic Gaussian incident beam. The obtained expression can be used to fit the experimental [Formula: see text]-scan traces, allowing the determination of material’s multiphoton absorption coefficient and Rayleigh lengths of the input elliptic Gaussian beam.

Elliptical Gaussian beam propagation in nonlinear fibres with focusing and defocusing refractive profiles

The paper shows systematic analysis of elliptical Gaussian beam (GB) propagating in self-focusing/self-defocusing media of Kerr type with focusing/defocusing linear refractive profiles. Instead of solving commonly accepted Nonlinear Schrödinger Equation (NLS) we propose equations of geometrical optics: complex eikonal equation and complex transport one. Eikonal equation let us derive immediately the ordinary differential equations for principle widths omitting this way complicated variational process and virial theory used in nonlinear optics. From the transport equation we obtain first order ordinary differential equation for complex amplitude evolution and conservation principle for energy flux in the elliptical GB cross-section. For combined effects of diffraction, nonlinear refraction and focusing/defocusing graded-index factor we observe three types of the solutions for the elliptical radius of principle beam widths: self-focusing or self-defocusing together with diffraction widening, stationary and oscillatory ones under and without collapse effect. We prove here that principle curvatures of the wave front can introduce into our description the additional ellipticity of the beam, which can effectively limit collapse effect. Moreover, we discuss the evolution of elliptical Gaussian beam in nonlinear self-defocusing fibre with focusing refractive profile presenting conditions for existence of elliptical spatial solitons. We discuss here also the influence of initial wave front curvatures on elliptical Gaussian beam evolution in nonlinear inhomogeneous fibres of Kerr-type.

Statistical properties of partially coherent radially and azimuthally polarized rotating elliptical Gaussian beams in oceanic turbulence with anisotropy.

A new class of partially coherent radially and azimuthally polarized rotating elliptical Gaussian (PCRPREG and PCAPREG) beams is introduced. The analytical expressions of the PCRPREG and PCAPREG beams propagating through anisotropy oceanic turbulence are derived based on the extended Huygens-Fresnel principle and the spatial power spectrum of oceanic turbulence. The effects of beam waist size w0, coherence width σ0, propagation distance z and oceanic turbulence parameters on the evolution statistics properties of PCRPREG and PCAPREG beams are studied in detail by numerical simulation. Our results indicate that with the increase of the propagation distance in the far field region, the normalized initial profile with a doughnut-like distribution of PCRPREG and PCAPREG beams gradually converts into a flat-topped one, and finally evolves into a Gaussian-like beam profile. We also find that the salinity-induced turbulence fluctuation makes a greater contribution to the decrease of beam quality compared with the temperature-induced turbulence fluctuation. Furthermore, the full width at half maximum becomes wider for the larger propagation distance z and wavelength λ or the smaller dissipation rate ε. Our work will pave the way for the development of underwater optical communication and underwater laser radar in oceanic environment.

Vortex astigmatic Fourier-invariant Gaussian beams.

We find a two-parameter family of astigmatic elliptical Gaussian (AEG) optical vortices, which are free space modes up to scale and rotation. We calculate total normalized orbital angular momentum of AEG vortices, which can be an integer, fractional and zero, and which is equal to the algebraic sum of two terms reflecting the contribution of the vortex and astigmatic components of the light field. In any transverse plane, such a beam has an isolated n-fold degenerate intensity null on the optical axis (an optical vortex) embedded into an elliptical Gaussian beam. In addition to the quadratic elliptical phase, a beam has the phase of a cylindrical lens rotated by an angle of 45 degrees with respect to the principal axes of the ellipse of the Gaussian beam intensity distribution. The degenerated central intensity null in these beams does not split it into n spatially separated intensity nulls, as is usually assumed for elliptical astigmatic beams.

Homogenization with coherent light illuminated beam shaping diffusers for vision applications: spatial resolution limited by speckle pattern

BackgroundHomogenizing properties of beam shaping diffusers illuminated with coherent laser light was studied with special regard on their use in vision applications.ExperimentalTwo diffusers projecting circular pattern at different scattering angles (Thorlabs Engineered Diffuser™) were illuminated with different spatial intensity distribution (elliptical Gaussian, nearly flat-top and granular multimode fiber output, respectively) collimated beams.ResultsThe intensity distribution measured at high angular resolution with a CMOS sensor revealed the granular (speckle) pattern of the projected light having contrast of nearly 1. The smallest speckle size (highest speckle density) could be obtained at the largest aperture size using nearly flat-top and multimode fiber illumination.ConclusionAs an important measure of the homogeneity for vision applications the apparent local contrast was calculated as the function of the spatial averaging. Although, the homogeneity requirements depend on the actual application, the usability of such diffusers in combination with coherent light sources is in general strongly limited in megapixel resolution imaging applications, unless time-varying speckle averaging methods can be applied.

Влияние скорости сканирования на формирование ТЛИПСС радиально-симметричным и эллиптическим гауссовым фемтосекундным лазерным пучком

Влияние скорости сканирования на формирование ТЛИПСС радиально-симметричным и эллиптическим гауссовым фемтосекундным лазерным пучком

Propagation of partially coherent four-petal elliptic Gaussian vortex beams in atmospheric turbulence.

The beam spreading and evolution behavior of the intensity profile and coherent vortices of partially coherent, four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence are studied. The analytical expressions for cross-spectral density function, as well as root mean square (rms) beam width, are derived based on the extended Huygens-Fresnel principle. Results showed that, unlike the partially coherent four-petal Gaussian vortex beams, the partially coherent four-petal elliptic Gaussian vortex beam could change its petal number into six. The dependencies of occurrence, appearance, and transition speed from four- to six-petal profile on the topological charge, the beam order, and the ellipticity factor are illustrated. The far field behaviors of partially coherent four-petal elliptic Gaussian vortex beams propagating in atmospheric turbulence and are compared in free space. Beams with larger topological charge, smaller beam order, and larger ellipticity factor were found to be less influenced by atmospheric turbulence. Further, the ellipticity factor can be used as an additional degree of freedom in controlling the conservation distance of coherence vortices' topological charge.

Multidirectional digital scanned light-sheet microscopy enables uniform fluorescence excitation and contrast-enhanced imaging

Light-sheet fluorescence microscopy (LSFM) has emerged as a powerful method for rapid and optically efficient 3D microscopy. Initial LSFM designs utilized a static sheet of light, termed selective plane illumination microscopy (SPIM), which exhibited shadowing artifacts and deteriorated contrast due to light scattering. These issues have been addressed, in part, by multidirectional selective plane illumination microscopy (mSPIM), in which rotation of the light sheet is used to mitigate shadowing artifacts, and digital scanned light-sheet microscopy (DSLM), in which confocal line detection is used to reject scattered light. Here we present a simple and passive multidirectional digital scanned light-sheet microscopy (mDSLM) architecture that combines the benefits of mSPIM and DSLM. By utilizing an elliptical Gaussian beam with increased angular diversity in the imaging plane, mDSLM provides mitigation of shadowing artifacts and contrast-enhanced imaging of fluorescently labeled samples.

Performance analysis of LMS filters with non-Gaussian cyclostationary signals

Abstract The least mean-square (LMS) filter is one of the most common adaptive linear estimation algorithms. In many practical scenarios, e.g., digital communications systems, the signal of interest (SOI) and the input signal are jointly wide-sense cyclostationary. Previous works analyzing the performance of LMS filters for this important case assume Gaussian probability distributions of the considered signals. In this work, we provide a transient and steady-state performance analysis that applies to non-Gaussian cyclostationary signals. In the considered analysis, the SOI is modeled as a perturbed response of a linear periodically time-varying system to the input signal. We obtain conditions for convergence and derive analytical expressions for the non-asymptotic and steady-state mean-squared error. We then show how the theoretical analysis can be effectively applied for two common non-Gaussian classes of input distributions, the class of elliptical compound Gaussian distributions, and the broad class of Gaussian mixture distributions. The accuracy of our analysis is illustrated for system identification and signal recovery scenarios that involve linear periodically time variant systems and non-Gaussian inputs.

Second-order statistics of a partially coherent electromagnetic rotating elliptical Gaussian vortex beam through non-Kolmogorov turbulence.

Based on the extended Huygens-Fresnel principle, analytical formulas for the cross-spectral density matrix elements of a partially coherent electromagnetic rotating elliptical Gaussian vortex (PCEREGV) beam through non-Kolmogorov turbulence are derived and the corresponding second-order statistics are investigated numerically. The numerical calculations of the PCEREGV beam are first developed to validate the correctness of the analytical results. Our findings show that the transverse spectrum density with an initially elliptical annular shape splits into two light spots during the beam propagation. By choosing appropriate parameters of the beam and the turbulence, we can maximize the spectrum density and control the spectral states of coherence and polarization so as to alleviate the influence of the turbulent atmosphere effectively.

Effects of the turbulent atmosphere and the oceanic turbulence on the propagation of a rotating elliptical Gaussian beam

Based on the extended Huygens–Fresnel integral, the average intensity, the gradient force and the effective beam width in the x- and y-directions of a rotating elliptical Gaussian (REG) beam in the turbulent atmosphere and the oceanic turbulence are explored analytically and numerically. It is shown that the intensity patterns of the REG beam in the atmospheric and the oceanic turbulences spin anticlockwise within a certain propagation range and always keep unimodal distributions during the propagation. Meanwhile, the numerical experiments of the REG beam are carried out to verify the theoretical analytical results. By comparative analysis, the effective beam widths can be adjusted by varying the turbulent characteristic parameters and the initial beam waist of the REG beam. The intensity modulation of the REG beam through the turbulent atmosphere and the oceanic turbulence can be realized.

Calculation of light scattering of an elliptical Gaussian beam by a spherical particle.

The use of an elliptical Gaussian beam (EGB) for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively and accurately. Based on the angular spectrum decomposition (ASD) of the radial components of the beam field, we present the formulations of the BSCs for the EGB. Numerical calculations of the BSCs, the beam reconstruction, and light scattering are performed. The fidelity of the reconstructed field to the given one is discussed so as to examine the BSC calculation. A comparison of the ASD method with the quadrature and localized approximation methods leads to the conclusion that the ASD method is much faster than the quadrature method, and it is very powerful for acquiring reliable and accurate results of BSCs, even for far off-axis locations and high ellipticities of the EGB.

Horizontal spatial correlation of the ionospheric TEC derived from GPS global ionospheric maps

The spatial correlations of ionospheric day-to-day variability are investigated by statistical analysis on TEC production that provided by the Jet Propulsion Laboratory (JPL). First, we use the monthly-averaged TEC over the world to calculate the deviation of the TEC and then the spatial correlation coefficient matrix of the deviation is also derived. According to the definition of correlation distance in statistics, the spatial characteristic scale is retrieved in the Zonal and meridian directions, and their variation of solar activity levels, geomagnetic field configuration conditions and seasonal conditions are investigated in details. Our study indicates strong correlations between geomagnetic conjugate points, which are large at low-latitudes than at mid-latitudes. Furthermore, in the equatorial anomaly region, due to the process of forming double crest structure, the electron distribution at low-latitudes will be affected by the upwelling of the plasma, thus the anomaly of correlation scale is notable. The correlation scale, which usually increases in LT 6:00, peaks at LT 12:00 and LT 14:00 and then decreases. It is overall larger in the daytime and smaller in the nighttime. These spatial correlations are important for understanding the physical mechanisms that cause ionospheric weather variability. For the potential application in development of ionospheric data assimilation model, the spatial correlations are fitted by elliptic Gaussian formula scale. In general, the correlation scale is regressed better in the Zonal direction than in the Meridional direction, better in low-latitude than in middle-latitude, and better in spring and autumn than in winter and summer. These results can help us to accurately construct the background field error covariance matrix in ionospheric data assimilation.

Portfolio optimization based on GARCH-EVT-Copula forecasting models

This study uses GARCH-EVT-copula and ARMA-GARCH-EVT-copula models to perform out-of-sample forecasts and simulate one-day-ahead returns for ten stock indexes. We construct optimal portfolios based on the global minimum variance (GMV), minimum conditional value-at-risk (Min-CVaR) and certainty equivalence tangency (CET) criteria, and model the dependence structure between stock market returns by employing elliptical (Student-t and Gaussian) and Archimedean (Clayton, Frank and Gumbel) copulas. We analyze the performances of 288 risk modeling portfolio strategies using out-of-sample back-testing. Our main finding is that the CET portfolio, based on ARMA-GARCH-EVT-copula forecasts, outperforms the benchmark portfolio based on historical returns. The regression analyses show that GARCH-EVT forecasting models, which use Gaussian or Student-t copulas, are best at reducing the portfolio risk.

Beam shape coefficients calculation for an elliptical Gaussian beam with 1-dimensional quadrature and localized approximation methods

The use of a shaped beam for applications relying on light scattering depends much on the ability to evaluate the beam shape coefficients (BSC) effectively. Numerical techniques for evaluating the BSCs of a shaped beam, such as the quadrature, the localized approximation (LA), the integral localized approximation (ILA) methods, have been developed within the framework of generalized Lorenz-Mie theory (GLMT). The quadrature methods usually employ the 2-/3-dimensional integrations. In this work, the expressions of the BSCs for an elliptical Gaussian beam (EGB) are simplified into the 1-dimensional integral so as to speed up the numerical computation. Numerical results of BSCs are used to reconstruct the beam field and the fidelity of the reconstructed field to the given beam field is estimated. It is demonstrated that the proposed method is much faster than the 2-dimensional integrations and it can acquire more accurate results than the LA method. Limitations of the quadrature method and also the LA method in the numerical calculation are analyzed in detail.

Development of a new flux density function for a focusing heliostat

It is important to calculate solar flux distribution with a precise and simple method for the design and optimization of solar tower systems. In this paper, the Gaussian flux density function at the image plane is deduced after simulating the image function of the heliostat with Gaussian distribution function. The flux density distribution of various round or rectangular focusing heliostats at the receiver plane can be calculated through projection. The simulation results are compared with SolTrace analysis and experimental data. Comparison of the flux density distributions between this method and SolTrace show excellent agreement especially when the optical error is equivalent to or larger than the Gaussian function parameter of heliostat image which fits to most of heliostats in a solar tower system. Although it increases error to simulate the image of the heliostat with elliptical Gaussian distribution, compared with the experimental data, the average prediction error of the elliptical Gaussian function is 2.24%, which is less than that of SolTrace because SolTrace applies the circular Gaussian distribution for optical error which bring more errors. Therefore, the Gaussian flux density function proposed is validated and can be used to simulate and optimize the design of solar heliostats field.

Analysis of lateral binding force exerted on a bi-sphere induced by an elliptic Gaussian beam.

Based on the generalized Lorentz-Mie theory (GLMT) and the localized approximation of the beam shape coefficients, we derived the expansions of incident elliptic Gaussian (EG) beams in terms of spherical vector wave functions (SVWFs). Utilizing multiple scattering (MS) equations and electromagnetic momentum (EM) theory, the lateral binding force (BF) exerted on a bi-sphere induced by an EG beam is calculated. Numerical effects of various parameters such as beam waist widths, beam polarization states, incident wavelengths, particle sizes, and material losses are analyzed and compared with the results of a circular Gaussian (CG) beam in detail. The observed dependence of the separation of optically bound particles on the incidence of an EG beam is in agreement with earlier theoretical predictions. Accurate investigation of BF induced by an EG beam could provide an effective test for further research on BF between more complex particles, which plays an important role in using optical manipulation on particle self-assembly.

The Herschel-ATLAS: magnifications and physical sizes of 500-μm-selected strongly lensed galaxies

We perform lens modelling and source reconstruction of Submillimeter Array (SMA) data for a sample of 12 strongly lensed galaxies selected at 500$\mu$m in the Herschel Astrophysical Terahertz Large Area Survey H-ATLAS. A previous analysis of the same dataset used a single S\`ersic profile to model the light distribution of each background galaxy. Here we model the source brightness distribution with an adaptive pixel scale scheme, extended to work in the Fourier visibility space of interferometry. We also present new SMA observations for seven other candidate lensed galaxies from the H-ATLAS sample. Our derived lens model parameters are in general consistent with previous findings. However, our estimated magnification factors, ranging from 3 to 10, are lower. The discrepancies are observed in particular where the reconstructed source hints at the presence of multiple knots of emission. We define an effective radius of the reconstructed sources based on the area in the source plane where emission is detected above 5$\sigma$. We also fit the reconstructed source surface brightness with an elliptical Gaussian model. We derive a median value $r_{eff}\,\sim 1.77\,$kpc and a median Gaussian full width at half maximum $\sim1.47\,$kpc. After correction for magnification, our sources have intrinsic star formation rates SFR$\,\sim900-3500\,M_{\odot}yr^{-1}$, resulting in a median star formation rate surface density $\Sigma_{SFR}\sim132\,M_{\odot}$ yr$^{-1}$ kpc$^{-2}$ (or $\sim 218\,M_{\odot}$ yr$^{-1}$ kpc$^{-2}$ for the Gaussian fit). This is consistent with what observed for other star forming galaxies at similar redshifts, and is significantly below the Eddington limit for a radiation pressure regulated starburst.