Action of nonstationary linear systems on the time-dependent spectrum of ultrashort light pulses

The spectral and temporal properties of laser light pulses are adequately characterized by the time-dependent spectrum. Response functions are investigated in the frequency as well as in the temporal domain which are suitable for describing the interaction of these pulses with nonstationary (and stationary) systems. The results are applied to physically important systems: the Fabry-Perot étalon, transmission through glass, absorption of molecules, reflection by semiconductors and the optical gate. The conditions are investigated under which the response functions can be measured by applying a square-law detector. An uncertainty relation is formulated for the time-dependent spectrum.     

Energy spectrum of the ensemble of weakly nonlinear gravity-capillary waves on a fluid surface

We consider nonlinear gravity-capillary waves with the nonlinearity parameter ? ～ 0.1–0.25. For this nonlinearity, time scale separation does not occur and the kinetic wave equation does not hold. An energy cascade in this case is built at the dynamic time scale (D-cascade) and is computed by the increment chain equation method first introduced in [15]. We for the first time compute an analytic expression for the energy spectrum of nonlinear gravity-capillary waves as an explicit function of the ratio of surface tension to the gravity acceleration. We show that its two limits—pure capillary and pure gravity waves on a fluid surface—coincide with the previously obtained results. We also discuss relations of the D-cascade model with a few known models used in the theory of nonlinear waves such as Zakharov’s equation, resonance of modes with nonlinear Stokes-corrected frequencies, and the Benjamin-Feir index. These connections are crucial in understanding and forecasting specifics of the energy transport in a variety of multicomponent wave dynamics, from oceanography to optics, from plasma physics to acoustics.     

Energy of a solid sphere under nonstationary oscillations

Analytical solution for spherically symmetric nonstationary oscillations of acoustic and elastic solid sphere is given. Time dependence of potential, kinetic and internal energy of a solid sphere is analyzed. The received results are of practical importance for a wide range of problems connected to testing of material dynamic strength parameters and to the problems of optimizing (minimizing) energy needed for fracture of solids.     

Time vs. ensemble averages for nonstationary time series

We analyze whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)−x(t), e.g. x(t,T)=ln(p(t+T)/p(t)) in finance and economics, where p(t) is a price, and the assumption is that the increment is distributed independently of t. We apply Tchebychev’s Theorem to the construction of statistical ensembles, and then show that the convergence in probability condition is not satisfied when applied to time averages of functions of stationary increments. We further show that Tchebychev’s Theorem provides the basis for constructing approximate ensemble averages and densities from a single, historic time series where, as in FX markets, the series shows a definite ‘statistical periodicity’. The convergence condition is not satisfied strongly enough for densities and certain averages, but is well-satisfied by specific averages of direct interest. Rates of convergence cannot be established independently of specific models, however. Our analysis shows how to decide which empirical averages to avoid, and which ones to construct.     

线谱非平稳性与Dopplerlet测距测速

水中航行物的辐射噪声中的线谱特征通常被用来提高声呐的检测性能,本文用线谱特征来估计水中航行物的距离和速度。文中给出了四条水中航行物的时变谱图像和线谱图的例子,从这些例子中可以看到线谱非平稳性的一些时频形态,线谱非平稳反映的航行状态变化和由于辐射噪声与水声信道相互作用产生密集的干涉条纹等现象。文章指出了其中有二组特征蕴藏的目标距离和速度信息,线谱和干涉条纹。利用Dopplerlet变换和匹配投影算法提取到线谱中蕴藏的目标距离和速度信息。用计算机模拟验证了本方法的可行性,编写了较好的算法,并调查了算法的性能。在此基础上,从海上实验数据中估计出水中航行物的距离和速度,其估计值与海上实验实际的距离和速度相符。     

Description of diffraction and focusing of ultrashort pulses on the basis of a nonstationary Kirchhoff-Sommerfeld method

The scalar problem of the propagation of a plane-wave pulse behind a diaphragm is solved. The calculation is performed on the basis of the nonstationary Kirchhoff-Sommerfeld integral and decomposition of the pulse in terms of wavelets. Two types of diaphragms, circular and square, are studied. The propagation of a pulse under focusing conditions is calculated. The Green’s function of the diffraction problem for a circular opening with and without aberration-free focusing is constructed.     

Nonlinear transformation of a spectrum of femtosecond laser pulses in a gas-filled microcapillary

Features of light pulse propagation and nonlinear optical transformation of the spectrum generated by titanium-sapphire laser pulses (τ_0.5 = 27 fs, λ₀ = 790 nm) have been studied experimentally in a 50-cm cylindrical hollow waveguide (microcapillary with 280-μm diameter core) filled with gaseous molecular nitrogen and helium. Stable guided propagation of light pulses with an intensity of ~1.5⋅10¹⁴ W/cm² in the fundamental EH₁₁ mode of the gas-filled capillary has been demonstrated. Exact focusing of the laser light made it possible to obtain rather high relative (≥95%) and absolute (~60%) energy transmission efficiencies for the pulses at gas pressures equal to or lower than 760 Torr. A method to determine the nonlinear phase shift of the pulses has been proposed. Values of the nonlinear refractive index n₂ ≈ 4.5⋅10^–23 cm²/(W⋅Torr) (N₂) and n₂ ≈ 2.8⋅10^–23 cm²/(W⋅Torr) (He) have been found. A short-wavelength shift in addition to the Kerr nonlinearity has been shown to be contributed by the generated electron plasma at high pulse intensities (≥10¹⁴ W/cm²).     

Energy and momentum of sound pulses

The energy and momentum of three-dimensionally localized sound pulses are shown to be constant in time for propagation in fluids of negligible viscosity. Further, the energy always exceeds the product of the momentum and the speed of sound. This property follows from the fact that three-dimensionally localized pulses are necessarily converging or spreading (they have a focal region). A consequence of this convergence/divergence is that the associated pressure gradient, density gradient and particle velocity are not purely longitudinal, as they are for pulses localized in only one dimension. The velocity remains curl-free up to second order, however. Analytic values of energy and momentum are obtained from a particular localized solution of the wave equation.     

Passive compression of microwave pulses with a bounded spectrum by a nonreflective cavity

The effect of the bandwidth of a microwave pulse on the efficiency of its compression by a nonreflective cavity is considered as applied to linear accelerators. In the case of a Gaussian pulse, it is shown that the optimal time dependence of the phase approaches the quadratic dependence upon a decrease in the bandwidth.     

On the spectrum dynamics of extremely short pulses in a uniaxial crystal

The spectral dynamics of a two-component pulse propagating in a uniaxial crystal is analytically researched. Frequencies corresponding to the maximums of spectral density of components are found. The criterion of frequency modulation of the pulse which propagates along an optical axis of crystal is received.     

Shape of spectrum with ensemble of 2-body random hamiltonians

Monte-Carlo calculations ind-s shell space have been done using two-body random interactions, to obtain ensemble-averagem-particle scalar moments up to fourth order. A shift of the spectrum shape from semi-circle to Gaussian with respect to the increase in number of particles can be clearly seen in terms of the ensemble-averaged fourth moment.     

Noiselike pulses with a broadband spectrum generated from an erbium-doped fiber laser

An erbium-doped fiber laser that produces a train of intense noiselike pulses with a broadband spectrum and a short coherence length is reported. The noiselike behavior was observed in the amplitude as well as in the phase of the pulses. The maximum spectral width obtained was 44 nm. The high intensity and the short coherence length of the light were maintained even after propagation through a long dispersive fiber. A theoretical model indicates that this mode of operation can be explained by the internal birefringence of the laser cavity combined with a nonlinear transmission element and the gain response of the fiber amplifier.     

On the dynamics of a spectrum of extremely short pulses in biaxial crystals

The spectral dynamics of the pulses propagating in biaxial crystals is analyzed. It is shown that the spectral densities of pulse components will have maxima at the frequencies satisfying the phase and group synchronism conditions.     

Coherent control of chirality in ensemble of randomly oriented molecules using a sequence of short laser pulses

The universal algorithm of choosing the train of short laser pulses, which could selectively excite the specific enantiomers in a racemic mixture of rotationally cold molecules, is proposed. Its application is illustrated on example of laser control of content of different chiral conformations in the mixture of hydrogen peroxide molecules. Methods of detection of racemity breaking in case of dynamical chirality are also discussed.