Femtosecond snapshot imaging of propagating light itself

An ultrafast imaging technique has been developed to visualize directly a light pulse that is propagating in a medium. The method, called femtosecond time-resolved optical polarigraphy (FTOP), senses instantaneous changes in the birefringence within the medium that are induced by the propagation of an intense light. A snapshot sequence composed of each femtosecond probing the pulse delay enables ultrafast propagation dynamics of the intense femtosecond laser pulse in the medium, such as gases and liquids, to be visualized directly. Other examples include the filamentation dynamics in CS2 liquid and the propagation dynamics in air related to the interaction with laser breakdown plasma. FTOP can also be used to extract information on the optical Kerr constant and its decay time in media. This method is useful in the monitoring of the intensity distribution in the nonlinear propagation of intense light pulses, which is a frequently studied subject in the field of physics regarding nonlinear optics and laser processing.     

The effect of the absolute phase on the spectrum of a femtosecond pulse propagating in a nonlinear medium

It is shown that the spectrum of a femtosecond light pulse propagating in a nonlinear medium depends on the absolute phase. As the propagation distance increases, the effect of the absolute phase of the light pulse on its spectrum may either decrease or increase.     

Two-frequency mutual coherence function of a Gaussian beam pulse in weak optical turbulence: an analytic solution

Pulse propagation in a random medium is studied through the calculation of the two-frequency mutual coherence function. An exact integral representation is formulated for the two-frequency mutual coherence function of a Gaussian beam pulse propagating in a weakly fluctuating random medium. Based on the modified von Karman spectrum for refractive-index fluctuations, an analytic approximation to the integral representation is presented and compared with exact numerical results.     

Causality in propagation of a pulse in a nonlinear dispersive medium

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell–Bloch equations without any approximations about the strength of the input field. We study full nonlinear behaviour of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, i.e. front of the pulse, moves inside the media with velocity c even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. Our numerical demonstration is subject to the condition that the background refractive index of the medium is unity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity c even in a nonlinear medium.     

基于TI介质模型的凸起地形对平面SH波的放大作用

在模拟地震波在介质中传播过程的研究中,正演模拟是一个重要的方面。该文采用间接边界元法（IBEM）对横观各向同性（TI）不同参数介质的凸起场地中入射SH波的散射问题进行了正演模拟,研究了TI凸起场地对SH波的放大效应。放大效应是通过地表位移与基岩露头位移幅值的比值来体现的。该间接边界元法结合了层状TI半空间精确动力刚度矩阵和均布斜线荷载动力格林函数,具有较高的精度。该文分别给出了TI介质凸起中SH波散射问题在频域和时域内的解答。频域内研究分析表明,土体TI介质参数的变化会对场地位移幅值的放大谱和空间分布产生显著的影响,即改变了凸起部分和土层的动力特性,使得两者动力相互作用发生改变。时域内研究表明,SH波在凸起周围的传播同时依赖于TI介质参数的具体取值和传播方向。时域位移幅值云图清晰地展示入射波、透射波、反射波和散射波的传播过程,凸起角点产生的散射波在TI介质中传播呈现\     

传播介质特性对爆破震动信号分析中小波包时频特征的影响

传播介质是指爆破震动赖以向外传播的地层介质 ,其基本特征是影响爆破震动时频分布的主要因素之一。当传播介质中有爆破震动通过时 ,其动态响应将会因其原地结构的不同而在响应持续时间、频谱、响应的衰减等特征方面均有较大差异。本文利用岩体 (岩土混合体 )基本质量指标BQ值以及完整性系数Kv 来量化传播介质特性。通过对不同岩层地质条件下产生的爆破震动进行小波包分析 ,探讨了传播介质特性量化参数与爆破震动时频分布之间的关系。研究中发现 ,传播介质特性对单段波形小波包细节信号的主振频带分布、峰值质点振速及衰减阻尼比等时频特征参数均有较大影响 ,其中主振频带分布范围随着传播介质的完整性系数Kv 值减小而增大 ,优势频率值随完整性系数Kv 值减小而增加 ,而峰值质点振速及衰减阻尼比与完整性系数Kv 值之间的规律性不强     

Time evolution of few-cycle pulse in a dense V-type three-level medium

Propagation of a few-cycle laser pulse in a dense V-type three-level atomic medium is investigated by the numerical solution of the full Maxwell–Bloch equations without the rotating wave and slowly varying envelope approximations, and the numerical solution is obtained by using the predictor–corrector method and the finite-difference time-domain method. It is shown that, due to the strength of the electric field induced by the macroscopic polarization in a dense medium being stronger than that in a dilute medium and the influence of the near dipole–dipole (NDD) interaction, the time evolution of a few-cycle pulse in the dense medium is remarkably different from that in the corresponding dilute medium. In the dilute medium, oscillation arises at the trailing edge of the pulse; while in the dense medium, it appears at both the leading and trailing edges of the pulse; moreover, the oscillation at the leading edge is more obvious with the pulse area decreasing. The carrier-envelope phase has an obvious difference in the two cases with and without NDD interaction. The ratio, γ, of the transition dipole moments has strong influence on the time evolution and split of the pulse. In the dense medium, when?γ?= 1, NDD interaction delays propagation and split of the pulse; while when?γ?> 1, NDD interaction accelerates propagation and split of the pulse, moreover, the phenomenon is more obvious with the input pulse area decreasing. In the dilute medium, the larger area pulse doesn't split when?γ?= 1 while it splits when?γ?> 1.     

Efficient analysis of temporal broadening of a pulsed focused Gaussian beam in scattering media

We show that the temporal broadening of a pulsed, tightly focused TEM(00) beam propagating in a scattering medium can be accurately modeled as a convolution between the initial pulse profile and an effective impulse response that is given by the propagation behavior of an infinitely thin pulse in the said medium. The impulse response is obtained with a Monte Carlo (MC) analysis of the propagating photons in the impulse. Our algorithm is 2 orders of magnitude less complex than the full MC solution of the pulse propagation problem. The accuracies, however, are comparable even for scattering path lengths that are 20 times the mean free path.     

Coherence theory of electromagnetic wave propagation through stratified N-layer media

The theory of second-order coherence in connection with wave propagation through a stratified N-layer (SNL) medium is developed. Especially, the influence of the SNL medium on the propagation of the coherence generated by a given state of coherence at the entrance plane of the medium is considered. The generalization of the van Cittert-Zernike theorem is obtained, and the propagation of the second-order coherence from a quasi-homogeneous surface distribution or a rough surface is calculated. Furthermore, the influence of SNL media on the coherence properties of a pulse is calculated.     

Physical significance of the group velocity in dispersive,ultrashort gaussian pulse dynamics

The properties of ultrashort gaussian pulse propagation in a dispersive, attenuative medium are reviewed with emphasis on the pulse velocity. Of particular interest is the group velocity whose physical interpretation loses meaning in causally dispersive materials as the temporal pulse width decreases into the ultrashort pulse regime. A generalized definition of the group velocity that applies to ultrashort pulses in causally dispersive materials is provided by the centroid velocity of the pulse Poynting vector whose properties are described here. In particular, it is shown that this physical velocity measure approaches the group velocity for any value of the initial pulse carrier frequency and at any fixed value of the propagation distance in the limit as the initial pulse width increases indefinitely. This then provides a convenient measure for determining when the group velocity approximation is valid.     

Effect of intensity dependent higher-order dispersion on femtosecond pulse propagation in quantum well waveguides

We have studied theoretically the dispersion of ultrafast coherent pulses in GaAs/AlGaAs quantum well waveguide structures as a function of optical intensity. Semiconductor Bloch equations are used to obtain the polarization induced in the medium due to an incident Gaussian electromagnetic beam. The partial differential equation describing the pulse propagation in the presence of group velocity dispersion is used to analyze the role of higher-order dispersion on femtosecond pulse propagation in the waveguide. Due consideration has been given to the intensity dependent optical susceptibility of the medium. The results of the numerical analysis manifest significant influence of higher-order dispersion on femtosecond pulse propagation over short waveguide distance.     

Quantum coherence effects in a Raman amplifier

We have studied optical pulse propagation in a Raman fiber amplifier doped with a three-level medium and driven by a control laser pulse. We analyze the spatial-temporal dynamics of pulse propagation for different atomic initial conditions. The propagation of an optical pulse through the amplifier can be sustained by a control laser that induces transparency via quantum coherence, which is useful for extending the distance between optical repeaters. Under certain conditions, amplification is achieved without population inversion. The results could be useful for laser control of optical pulses in amplifiers and waveguides.     

Pulse centroid velocity of the Poynting vector

The evolution of the pulse centroid velocity of the Poynting vector for both ultrawideband rectangular and ultrashort Gaussian envelope pulses is presented as a function of the propagation distance in a dispersive, absorptive dielectric material. The index of refraction of the material is described by the Lorentz-Lorenz formula in which a single-resonance Lorentz model is used to describe the mean molecular polarizability. The results show that, as the propagation distance increases above a value that is on the order of an absorption depth at the pulse carrier frequency, the centroid velocity of an ultrawideband/ultrashort pulse tends toward the rate at which the Brillouin precursor travels through the medium. For small propagation distances when the carrier frequency of the optical pulse lies in the absorption band of the material, the centroid velocity can take on superluminal and negative values.     

Control of superluminal transit through a heterogeneous medium

Abstract

We consider pulse propagation through a two component composite medium (metal inclusions in a dielectric host) with or without cavity mirrors. We show that a very thin slab of such a medium, under conditions of localized plasmon resonance, can lead to significant superluminality with detectable levels of the transmitted pulse. A cavity containing the heterogeneous medium is shown to lead to subluminal-to-superluminal transmission depending on the volume fraction of the metal inclusions. The predictions of the phase time calculations are verified by explicit calculations of the transmitted pulse shapes. We also demonstrate the independence of phase time on system width and the volume fraction under specific conditions.     

Effect of dispersion on the spectrum of partially coherent beams

Taking the Gaussian Schell-model (GSM) beam as a typical example of partially coherent beams, the analytical expressions of the spectrum of GSM beams propagating in dispersive media are derived, and the spectral properties are studied in detail. It is shown that, in comparison with propagation in free space and in turbulence, whether or not GSM beams satisfy the scaling law, the normalized spectrum of GSM beams in dispersive media changes on propagation in general, because the dispersive medium affects different spectral components differently. As compared with the free-space propagation, for the scaling-law GSM beams the dispersion results in spectrum change, and for the nonscaling-law GSM beams the dispersion gives rise to a further increase in spectral changes. The structure constant of the dispersive property of the media, the transverse coordinate of the observation point, the spatial correlation length of the source, and the propagation distance affect the spectral behavior of GSM beams; this effect is illustrated numerically.     

The imaginary components of dispersion parameters and the Stokes mode dynamics in stimulated Raman scattering

The Stokes pulse dynamics during stimulated Raman scattering has been studied in the constant pumping approximation. The nonlinear problem of interaction between a pumping wave and the Stokes component is reduced to a linear equation describing propagation of an optical pulse in the amplifying medium with imaginary components of the first-and second-order dispersion parameters, the presence of which leads to the possibility of the pulse envelope propagation at a supraluminal velocity.     

A method to measure the thermal neutron scattering properties of a sample by neutron wave propagation

For the determination of the thermal neutron diffusion coefficient for samples of limited size, it is proposed to use the neutron wave or pulse propagation method. A thin slab of the material under investigation is then placed between two blocks of a medium with known properties. Numerical calculations have been performed on such a system. It is found that, for a certain frequency and some specified conditions, the phase shift in the outer medium will be the same as if the sample had the same properties as the outer medium. This fact may be used for a measurement of the diffusion coefficient of the sample.     

Practical spread spectrum pulse compression for ultrasonic tissue imaging

Spread spectrum pulse compression is a signal processing algorithm that enhances critical system performance parameters such as signal-to-noise ratio, peak power requirements, minimum detectable signal, and total dynamic range. For this research, a digital, real-time, Barker coded, bi-phase modulator was designed and constructed, as well as a simple ultrasonic test tank containing both synthetic targets and excised goat's liver. Upon reception and demodulation of the spread spectrum ultrasonic echo, cross-correlation with a sidelobe suppression filter was performed. Due to limitations such as narrow bandwidth, and very short minimum ranges, a practical ultrasonic pulse compression system must be restricted to short code lengths. For 13 bit Barker code compression, the expected increase in signal-to-noise ratio of 11 dB was realized; at the same time greater than 30 dB of instantaneous dynamic range was maintained.     

Spatial and temporal properties of ultrashort pulses propagating in free space

Abstract

By means of the Rayleigh diffraction integral and analytic signal complex representation, the propagation equation of ultrashort pulses in free space is derived, which permits us to study spatial and temporal properties of ultrashort pulses during propagation in free space. It is shown that the pulse deformation and broadening, spectrum redshifting, narrowing and distortion can take place with increasing diffraction angle, and the pulse form changes with propagation distance in the near field, but is preserved in the far field. A comparison with previous work is also made.     

Application of the generalized rays to transient waves in an elastic half-space due to a buried line source

Summary The aim of this investigation is to study by means of the generalized rays the effects of a free surface on the propagation of elastic transient waves emanating from a line source of explosion, which varies with time as the Heaviside step function with rounded shoulders. This is accomplished by the numerical evaluation and analysis of the exact solutions provided by this theory. Graphs are obtained which show displacements and stresses as functions of time at three different receivers in the interior of an infinite medium and at the free surface of a homogeneous half-space. The character of surface responses, for short observation times, is the same as in the infinite medium, with the difference that they are all amplified (surface receiver effect). The late time surface responses are characterized by the presence of a smooth pulse representing the Rayleigh surface wave. The Rayleigh pulse in the non-vanishing surface stress takes its ultimate shape already close to the epicentre, while the Rayleigh pulse in the surface displacements developes fully at the remote distance from the epicentre.With 6 Figures