Gaussian Spectrum Research Articles

Defining a Superlens Operating Regime for Imaging Fluorescent Molecules

It has been shown that thin metal-based films can at certain frequencies act as planar near-field lenses for certain polarization components. A desirable property of such “lenses” is that they can also enhance and focus some large transverse spatial frequency components which contain sub-diffraction limit details. Over the last decade there has been much work in optimizing designs to reduce effects (such as material losses and surface roughness) that are detrimental to image reconstruction. One design that can reduce some of these undesirable effects, and which has received a fair amount of attention recently, is the stacked metal-dielectric superlens. Here we theoretically explore the imaging ability of such a design for the specific purpose of imaging a fluorescent dye (the common bio-marker GFP) in the vicinity of the superlens surface. Our calculations take into consideration the interaction (damping) of an oscillating electric dipole with the metallic layers in the superlens. We also assume a Gaussian frequency distribution spectrum for the dipole. We treat the metallic-alloy and dielectric-alloy layers separately using an appropriate effective medium theory. The transmission properties are evaluated via Transfer matrix (-matrix) calculations that were performed in the MatLab and MathCad environments. Our study shows that it is in principle possible to image fluorescent molecules using a simple bilayer planar superlens. We find that optimal parameters for such a superlens occur when the peak dipole emission-frequency is slightly offset from the Surface Plasmon resonance frequency of the metal-dielectric interfaces. The best resolution is obtained when the fluorescent molecules are not too close ( nm) or too far ( nm) from the superlens surface. The realization and application of a superlens with the specified design is possible using current nanofabrication techniques. When combined with e.g. a sub-wavelength grating structure (such as in the far-field superlens design previously proposed [1]) or a fast near-field scanning probe, it could provide a means for fast fluorescent imaging with sub-diffraction limit resolution.

Effect of Chorus Latitudinal Distribution on Evolution of Outer Radiation Belt Electrons

Primary result on the impact of the latitudinal distribution of whistler-mode chorus upon temporal evolution of the phase space density (PSD) of outer radiation belt energetic electrons was presented. We evaluate diffusion rates in pitch angle and momentum due to a band of chorus frequency distributed at a standard Gaussian spectrum, and solve a 2-D bounce-averaged momentum-pitch-angle Fokker–Planck equation at L = 4.5. It is shown that chorus is effective in accelerating electrons and can increase PSD for energy of ∼ 1 MeV by a factor of 10 or more in about one day, which is consistent with observation. Moreover, the latitudinal distribution of chorus has a great impact on the acceleration of electrons. As the latitudinal distribution increases, the efficient acceleration region extends from higher pitch angles to lower pitch angles, and even covers the entire pitch angle region when chorus power reaches the maximum latitude λm = 45°.

Using theΔ3statistic to test for missed levels in mixed sequence neutron resonance data

The ${\ensuremath{\Delta}}_{3}(L)$ statistic is studied as a tool to detect missing levels in the neutron resonance data where two sequences are present. These systems are problematic because there is no level repulsion, and the resonances can be too close to resolve. ${\ensuremath{\Delta}}_{3}(L)$ is a measure of the fluctuations in the number of levels in an interval of length $L$ on the energy axis. The method used is tested on ensembles of mixed Gaussian orthogonal ensemble spectra, with a known fraction of levels $(x%)$ randomly depleted, and can accurately return $x$. The accuracy of the method as a function of spectrum size is established. The method is used on neutron resonance data for 11 isotopes with either $s$-wave neutrons on odd-$A$ isotopes, or $p$-wave neutrons on even-$A$ isotopes. The method compares favorably with a maximum likelihood method applied to the level spacing distribution. Nuclear data ensembles were made from 20 isotopes in total, and their ${\ensuremath{\Delta}}_{3}(L)$ statistics are discussed in the context of random matrix theory.

A practical cross-section for scattering from rough surfaces at very low grazing angles in both the forward and backward directions

In this paper we develop an extension of the small slope approximation (SSA) for scattering from randomly rough Dirichlet surfaces, which includes some multiple scattering. This extension is designated by SSA+. We focus on scattering at very low grazing angles where multiple scattering of both the incident and scattered fields is of importance. Numerical results for the SSA+ bistatic scattering cross-section for very low forward grazing angles are presented using the Gaussian roughness spectrum and for both very low forward and very low backward grazing angles using the Pierson–Moskowitz and modified power law spectra. The results are restricted to an angle of incidence of 80°. It is shown that when the lowest-order SSA gives reasonably accurate results, the SSA+ increases the accuracy up to at least the final 0.2° of grazing in the forward direction. In the backward direction, the SSA+ gives good results for the Pierson–Moskowitz spectrum, but the results are less dramatic.

Spectral switches of a double slit with a movable central part in the far-field

The far-field spectral properties for a broad-band Gaussian spectrum incident on a double slit with a movable central part are investigated. The analytic expression is first derived and some numerical examples based on it are given to illustrate the anomalous behavior of the diffracted spectrum. It is found that the important effect called spectral switches can be controlled by simply moving the central part of the double slit. This control mechanism has the merit of easier implementation than previous schemes which modulate some properties of the light source (e.g. spatial coherence or spectral bandwidth) to achieve it.

Investigation of Non-Gaussian Doppler Spectra Observed by Weather Radar in a Tornadic Supercell

Abstract Radar Doppler spectra that deviate from a Gaussian shape were observed from a tornadic supercell on 10 May 2003, exhibiting features such as a dual peak, flat top, and wide skirt in the nontornadic region. Motivated by these observations, a spectral model of a mixture of two Gaussian components, each defined by its three spectral moments, is introduced to characterize different degrees of deviation from Gaussian shape. In the standard autocovariance method, a Gaussian spectrum is assumed and biases in velocity and spectrum width estimates may result if this assumption is violated. The impact of non-Gaussian weather spectra on these biases is formulated and quantified in theory and, consequently, verified using four experiments of numerical simulations. Those non-Gaussian spectra from the south region of the supercell are further examined and a nonlinear fitting algorithm is proposed to estimate the six spectral moments and compare to those obtained from the autocovariance method. It is shown that the dual-Gaussian model can better represent observed spectra for those cases. The authors’ analysis suggests that vertical shear may be responsible for the flat-top or the dual-peak spectra in the lower elevation of 0.5° and their transition to the single-peak and wide-skirt spectra in the next elevation scan of 1.5°.

Superconducting fluctuations near the FFLO state

The Fulde, Ferrell, Larkin & Ovchinnikov (FFLO) state consists in a modulation of the superconducting order parameter due to Zeeman effect. In a Ginzburg-Landau approach, higher order terms than usual in the gradient expansion, i.e. quartic terms, are needed to take into account the FFLO modulation. The role of this quartic term in addition to the quadratic usual term in a Gaussian fluctuation spectrum have been investigated for heat capacity C and paraconductivity s near a FFLO state for both isotropic and anisotropic cases. In the isotropic (resp. anisotropic) case, the power laws are drastically different (resp. similar) in comparison with the homogeneous superconductivity case. Nevertheless, for the anisotropic case the anisotropic ratio δxx/δyy is quite different for a FFLO phase than for a BCS one. In addition, we predict anomalous power laws near the tricritical point where the normal phase and the two superconducting (uniform and FFLO) phases are merging. The multiple crossovers associated with the phase transitions between homogeneous, tricritical and inhomogenous fluctuation regimes thus may serve as a powerful tool to identify the FFLO phases.

Dynamic Evolution of Outer Radiation Belt Electrons due to Whistler-Mode Chorus

Following our preceding work, we perform a further study on dynamic evolution of energetic electrons in the outer radiation belt L = 4.5 due to a band of whistler-mode chorus frequency distributed over a standard Gaussian spectrum. We solve the 2D bounce-averaged Fokker–Planck equation by allowing incorporation of cross diffusion rates. Numerical results show that whistler-mode chorus can be effective in acceleration of electrons at large pitch angles, and enhance the phase space density for energies of about 1 MeV by a factor of 102 or above in about one day, consistent with observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm. Moreover, neglecting cross diffusion often leads to overestimates of the phase space density evolution at large pitch angle by a factor of 5–10 after one day, with larger errors at smaller pitch angle, suggesting that cross diffusion also plays an important role in wave—particle interaction.

Image quality simulations in X-ray mammography

The application of tunable monochromatic X-rays to mammography can improve the image quality and reduce the radiation dose to the patient. A new generation of quasi-monochromatic, high-flux X-ray sources is currently under development, based on Thomson scattering of photons produced by a laser on a highly focused electron beam. In this paper we investigate the effect of different spectral distributions on the image contrast on 2 cm, 4 cm, 6 cm, 8 cm breast mammographic phantoms containing details of different composition (tumor mass and calcification details) and thickness. In the simulations we assume a homogeneous breast composition and three compositions (25%; 50% and 75% glandular) are investigated. We simulate monochromatic, quasi-monochromatic and polychromatic X-ray sources in order to define the optimal energies that maximize the image quality parameter. In particular we compare the simulations of the Gaussian quasi-monochromatic spectra. having different energy standard deviations (1, 2, 3, 4, 5 keV) with traditional X-ray tubes spectra. Results show that Gaussian spectra having an energy spread of about 1 keV standard deviation call improve the image quality of about 30% with respect to traditional X-ray tube ones.

14-fs high temporal quality injector for ultra-high intensity laser

We present a chirped pulse amplification (CPA) Ti:Sa laser generating sub-15 fs pulses with expected high temporal quality. Gain-narrowing in the pre-amplifier is balanced by a variable spectral reflectivity mirror and by a fine adaptation of the saturation conditions. A crossed polarized wave generation (XPW) filter is introduced to enhance the contrast, reduce the pulse duration and improve the spectral quality. The pulses are generated at 10 Hz repetition rate, with pulse energy of 110 μJ and very clean Gaussian spectrum. The temporal contrast is evaluated by a measurement before the XPW filter and calculations of the enhancement by the filter. The potential temporal incoherent contrast is 10 12 and the coherent contrast 10 10. The performance of the system makes it suitable as an injector for petawatt lasers operating in the double-CPA scheme.

A NUMERICAL METHOD FOR ELECTROMAGNETIC SCATTERING FROM DIELECTRIC ROUGH SURFACES BASED ON THE STOCHASTIC SECOND DEGREE METHOD

In this paper, we propose an iterative numerical approach based on the stochastic second degree (SSD) algorithm in combination with a new splitting of the impedance matrix to analyze electromagnetic scattering from 1-D dielectric rough surfaces. The embedded matrix-vector product is computed using the banded matrix iterative approach/canonical grid (BMIA/CAG) and the spectral acceleration (SA) technique. For Gaussian surface with Gaussian spectrum, through extensive numerical simulation, it is observed that for HH polarization, the proposed method requires roughly one half number of iterations as needed by the forward-backward method with spectral acceleration (FBM-SA). When the rms height is small, the proposed method takes more run time; when the rms slope is no less than 0.33 and rms height is no less than 1:0‚, where ‚ is the wavelength, the proposed method is more e-cient. More importantly, it obviously improves the convergence properties over FBM-SA by changing cases from divergent to convergent when rms height is no less than 2:0‚ and rms slope is no less than 0.55 except for one extreme case. For VV polarization, the proposed method is less computationally e-cient in terms of run time and number of iterations than FBM-SA. However, as far as convergence properties are considered, similar to HH polarization, the proposed method improves over FBM-SA when the rms height and rms slope are large. Hence for both polarizations, the proposed method demonstrates its suitability when dealing with truly rough surfaces.

An experimental study of spatial evolution of statistical parameters in a unidirectional narrow‐banded random wavefield

Unidirectional random waves generated by a wavemaker in a 300‐m‐long wave tank are investigated experimentally. Spatial evolution of numerous statistical wavefield parameters is studied. Three series of experiments are carried out for different values of the nonlinear parameter ɛ. It is found that the frequency spectrum of the wavefield undergoes significant variation in the course of the wavefield evolution along the tank. The initially narrow Gaussian spectrum becomes wider at the early stages of the evolution and then narrower again, although it still remains wider than the initial spectrum at the most distant measuring location. It is found that the values of all the statistical wave parameters are strongly related to the local spectral width. The deviations of various statistical parameters from the Gaussian statistics increase with the width of the spectrum so that the probability of extremely large (the so‐called freak) waves is highest when the local spectral width attains maximum. The deviations from the Rayleigh distribution also become more pronounced when the nonlinearity parameter ɛ is higher. It is found that the Tayfun and Fedele 3rd order random wavefield model provides an appropriate description of the observed phenomena. An attempt is made to relate the spatial variations of the wavefield statistics reported here to the wavefield recurrence, as suggested recently.

Differences and analogies between linearly chirped and colored double pulses in the femtosecond regime

A mathematical description is reported that allows the comparison of femtosecond colored double pulses and linearly chirped pulses with Gaussian spectra. Formulas are presented for the corresponding momentary angular frequencies of the two parameterizations and a relation is derived so that they match at the two moments in time when the double pulses are most intense. In a liquid-phase intrapulse-dumping experiment, the performance of the two pulse shape types is directly juxtaposed. Their applicability in other phase-sensitive processes is also briefly discussed.

Lateral displacement of a Gaussian beam reflected from absorbing media

Lateral displacements of well-focused beams reflected from absorbing media are demonstrated in this paper. The incident beam is modeled as a tapered wave with a Gaussian spectrum. The field solutions are obtained on both sides of the interface by solving analytically from Maxwell's equations and by matching the boundary conditions at the interface. Numerical simulations are presented and the field values as well as the time-averaged power densities are computed. The influences of the polarization, the angle of incidence and the beam width on the displacement are discussed. The origin of the displacement lies in the absorption of the media, for which there is a phase shift between the incident and reflected waves. Because of this phase shift, the center of the reflected beam does not coincide with that of the incident one, similar to the Goos–Hänchen shift.

Higher moment estimation for reverberation simulation.

In recent work the second, third, and fourth spatial moments for exponentially distributed roughness with either Gaussian or von Karman spatial spectra have been presented by the author. In this talk results for the second, third, and fourth moments of reverberation pressure for perturbation theory scattering from surfaces with von Karman spectra are obtained using numerical quadrature. Results are compared to closed form expressions for the second and fourth moments obtained for Gaussian correlation functions. Methods to extend these results to the class of chi‐square distributed roughness heights of arbitrary order, which encompasses both exponential and Gaussian height distributions, are also presented.

Numerical modelling of ground‐penetrating radar response from rough subsurface interfaces

ABSTRACTGround‐penetrating radar (GPR) modelling is employed to study the electromagnetic wave scattering that emanates from a rough subsurface interface. The numerical analysis is achieved by using a finite‐difference time‐domain numerical modelling algorithm. For the 2D GPR models, the rough interfaces are generated using both Gaussian and fractal statistics. For a given root mean square interface roughness height, we study the effect that the change in correlation length has on the incident wavefield for a randomly generated surface with a Gaussian roughness spectrum. Similarly, for an interface generated using fractal statistics, we examine the effect of fractal dimension for two different values of maximum wavenumber. For the Gaussian case, the correlation length is the most important parameter in defining the target signature. But, when fractals are used, an increase in clutter is observed as the fractal dimension increases. In addition, the clutter is more pronounced when the highest value of maximum wavenumber is used. Detection performance is evaluated by utilising 3D ground‐penetrating radar models. Comparing the 3D models with and without the presence of a rough subsurface interface, increased wavefield attenuation and strong depolarization effects were observed from a fractal subsurface terrain.

Pitch Angle Distribution Evolution of Energetic Electrons by Whistler-Mode Chorus

We develop a two-dimensional momentum and pitch angle code to solve the typical Fokker-Planck equation which governs wave—particle interaction in space plasmas. We carry out detailed calculations of momentum and pitch angle diffusion coefficients, and temporal evolution of pitch angle distribution for a band of chorus frequency distributed over a standard Gaussian spectrum particularly in the heart of the Earth's radiation belt L = 4.5, where peaks of the electron phase space density are observed. We find that the Whistler-mode chorus can produce significant acceleration of electrons at large pitch angles, and can enhance the phase space density for energies of 0.5 ∞ 1 MeV by a factor of 10 or above after about 24h. This result can account for observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm.

Photoluminescence from localized states in disordered indium nitride

Photoluminescence spectra from disordered InN were studied in very high magnetic fields. The samples had Gaussian spectra with low temperature emission peaks at 0.82 and 0.98eV, respectively. The average spatial extent of the excitonic wave functions, inferred from the diamagnetic shift, is only 2–3nm. This shows that the recombination is from an ensemble of highly localized states within a landscape of a smooth (classical) disorder potential of strength of the order of 10meV. The anomalies in the temperature dependence of the photoluminescence peak and linewidth give further support to the picture of trapped photoexcited carriers.

Approach to an Effective Biological Spectrum of a Light Source

Optimal three band Gaussian spectra were determined with an additional condition on the nonvisual biological action of the spectra. With this new condition the best possible trade off between the general color rendering index (CRI) and the luminous efficiency was found. The results show that in order to keep a biological effect of a light source equal to that of Planckian light source an additional restriction on the luminous efficiency for the given CRI arises.

Storm-Time Evolution of Energetic Electron Pitch Angle Distributions by Wave-Particle Interaction

The quasi-pure pitch-angle scattering of energetic electrons driven by field-aligned propagating whistler mode waves during the 9∼15 October 1990 magnetic storm at L ≈ 3 ∼ 4 is studied, and numerical calculations for energetic electrons in gyroresonance with a band of frequency of whistler mode waves distributed over a standard Gaussian spectrum is performed. It is found that the whistler mode waves can efficiently drive energetic electrons from the larger pitch-angles into the loss cone, and lead to a flat-top distribution during the main phase of geomagnetic storms. This result perhaps presents a feasible interpretation for observation of time evolution of the quasi-isotropic pitch-angle distribution by Combined Release and Radiation Effects Satellite (CRRES) spacecraft at L ≈ 3 ∼ 4.