Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Spectral-line profile of turbulent gas

phases should be specified when the particle Reynolds number is higher than

Numerical study on heavy rigid particle motion in a plane wake flow by spectral element method

Experimental particle dispersion patterns in a plane wake flow at a high Reynolds number have been predicted numerically by discrete vortex method (Phys. Fluids A 1992; 4:2244-2251; Int. J. Multiphase Flow 2000; 26:1583-1607). To address the particle motion at a moderate Reynolds number, spectral element method is employed to provide an instantaneous wake flow field for particle dynamics equations, which are solved to make a detail classification of the patterns in relation to the Stokes and Froude numbers. It is found that particle motion features only depend on the Stokes number at a high Froude number and depend on both numbers at a low Froude number. A ratio of the Stokes number to squared Froude number is introduced and threshold values of this parameter are evaluated that delineate the different regions of particle behavior. The parameter describes approximately the gravitational settling velocity divided by the characteristic velocity of wake flow. In order to present effects of particle density but preserve rigid sphere, hollow sphere particle dynamics in the plane wake flow is investigated. The evolution of hollow particle motion patterns for the increase of equivalent particle density corresponds to that of solid particle motion patterns for the decrease of particle size. Although the thresholds change a little, the parameter can still make a good qualitative classification of particle motion patterns as the inner diameter changes.

Space-resolved spectral diagnosis of line-shaped laser-produced magnesium plasmas

Space-resolved spectra of line-shaped laser-produced magnesium plasmas in the normal direction of the target have been obtained using a pinhole crystal spectrograph. These spectra are treated by a spectrum analyzing code for obtaining the true spectra and fine structures of overlapped lines. The spatial distributions of electron temperature and density along the normal direction of the target surface have been obtained with different spectral diagnostic techniques. Especially, the electron density plateaus beyond the critical surface in line-shaped magnesium plasmas have been obtained with a fitting technique applied to the Stark-broadened Ly-alpha wings of hydrogenic ions. The difference of plasma parameters between those obtained by different diagnostic techniques is discussed. Other phenomena, such as plasma satellites, population inversion, etc., which are observed in magnesium plasmas, are also presented.

Spectral effects for an ultrashort pulse train propagating in a two-level atom medium

We investigate the spectra of a femtosecond pulse train propagating in a resonant two-level atom (TLA) medium. it is found that higher spectral components can be produced even for a 2 pi femtosecond pulse train. Furthermore, the spectral effects depend crucially on both the relative shift phi and the delay time tau between the successive pulses of the femtosecond pulse train.

Constrained high-order statistical blind deconvolution of spectral data

A constrained high-order statistical algorithm is proposed to blindly deconvolute the measured spectral data and estimate the response function of the instruments simultaneously. In this algorithm, no prior-knowledge is necessary except a proper length of the unit-impulse response. This length can be easily set to be the width of the narrowest spectral line by observing the measured data. The feasibility of this method has been demonstrated experimentally by the measured Raman and absorption spectral data.

Conical emission by femtosecond pulses with different spectral bandwidths

Conical emission (CE) has been investigated experimentally by laser pulses with different pulse durations and spectral bandwidths. The results show that the overall CE curve will shift as the varying of spectral bandwidth of pump laser pulse. But for pump laser pulses which have same spectral bandwidth but different pulse duration, the CE angles will be same at the spectral region close to the pump wavelength while will be different at the spectral region far away from the pump wavelength. We have also fitted the measured CE angles with X-wave model. The calculated curves and the measured CE curves match reasonably well. The best fits indicate that the group velocity of the filament pulse may be greatly controlled by controlling the spectral bandwidth of pump laser pulse. (C) 2008 Elsevier B.V. All rights reserved.

Conical Emission Patterns by Femtosecond Pulses with Different Spectral Bandwidths

Different conical emission (CE) patterns are obtained experimentally at various incident powers and beam sizes of pump laser pulses with pulse durations of 7 fs, 44 fs and 100 fs. The results show that it is the incident power but not the incident power density that determines a certain CE pattern. In addition, the critical powers for similar CE patterns are nearly the same for the laser pulses with the same spectral bandwidth. Furthermore, as far as a certain CE pattern is concerned, the wider the spectral bandwidth of pump laser pulse is, the higher the critical power is. This will hopefully provide new insights for the generation of CE pattern in optical medium.

Spectral analysis and control to obtain sub-5 fs pulses by femtosecond filamentation

A spectral-filter method is numerically demonstrated to obtain sub-5 fs pulses by using femtosecond filamentation in fused silica. Instead of employing spectral phase compensation, by properly employing a high-pass filter to select the broadened high-frequency spectra that are located almost in phase in the tailing edge of the self-compressed pulses owing to self-steepening, as short as single-cycle pulses can be obtained. For instance, for an input pulse with a duration of 50 fs and energy 2.2 mu J, the minimum pulse duration can reach to similar to 4 fs (about 1.5 cycles) by applying a proper spectral filter. (C) 2008 Optical Society of America

Spectral evolution of angularly resolved third-order harmonic generation by infrared femtosecond laser-pulse filamentation in air

We experimentally investigate the evolution of an angularly resolved spectrum of third harmonic generated by infrared femtosecond laser pulse filamentation in air. We show that at low pump intensity, phase matching between the fundamental and third-harmonic waves dominates the nonlinear optical effect and induces a ring structure of the third-harmonic beam, whereas at high pump intensity, the dispersion properties of air begin to affect the angular spectrum, leading to the formation of a nonlinear X wave at third harmonic.

Phase control of higher spectral components in the presence of a static electric field

We investigate the higher spectral component generations driven by a few-cycle laser pulse in a dense medium when a static electric field is present. Our results show that, when assisted by a static electric field, the dependence of the transmitted laser spectrum on the carrier-envelope phase (CEP) is significantly increased. Continuum and distinct peaks can be achieved by controlling the CEP of the few-cycle ultrashort laser pulse. Such a strong variation is due to the fact that the presence of the static electric field modifies the waveform of the combined electric field, which further affects the spectral distribution of the generated higher spectral components.

Spectral distributions of harmonic generation from electron oscillation driven by intense femtosecond laser pulses

The characteristics of harmonic radiation due to electron oscillation driven by an intense femtosecond laser pulse are analyzed considering a single electron model. An interesting modulated structure of the spectrum is observed and analyzed for different polarization. Higher order harmonic radiations are possible for a sufficiently intense driving laser pulse. We have shown that for a realistic pulsed photon beam, the spectrum of the radiation is red shifted as well as broadened because of changes in the longitudinal velocity of the electrons during the laser pulse. These effects are more pronounced at higher laser intensities giving rise to higher order harmonics that eventually leads to a continuous spectrum. Numerical simulations have further shown that by increasing the laser pulse width broadening of the high harmonic radiations can be limited. (C) 2005 Elsevier B.V. All rights reserved.

Cluster explosion investigated by linearly chirped spectral scattering of an expanding plasma sphere

Femtosecond explosive processes of argon clusters irradiated by linearly chirped ultraintense laser pulses have been investigated by 90 degrees side spectral scattering. The spectral redshift and blueshift, which correlate with the cluster explosion processes have been measured for negatively and positively chirped driving laser pulses, respectively. The evolution of the heated-cluster polarizability indicates that the core of the cluster is shielded from the laser field in the beginning of the explosion and enhanced scattering occurs after the fast explosion initiates. Evidence of resonant heating is found from the coincidence of enhanced scattering with enhanced absorption measured using the transmitted spectra. Anomalously large-size clusters with very low gas density have been observed in this way and can be used as clean and important cluster targets.