Complex space-time rays and their application to pulse propagation in lossy dispersive media

Asymptotic transient field solutions of the form A(r,t) exp [iS (r, t)], where S is a rapidly and A a slowly varying function of space and time, may be analyzed in terms of wave packets with central frequency ω =-∂S/∂t and central wavenumber k = ∇S. When the (dispersive) medium is lossless, stationary, and homogeneous, wave packets with constant real ω and k move along straightline trajectories called space-time rays. In the presence of dissipation and (or) when the input signal has an exponential amplitude dependence, S is complex. The corresponding wave packets with constant complex ω and k move along complex space-time rays, i.e., along trajectories defined in a complex (r, t) coordinate space. The properties of complex space-time rays and of the fields propagating along them, and their relation to physical fields observed on real (r, t) coordinates, are illustrated for a plane pulse with Gaussian envelope and frequency swept carrier, launched into a lossy environment. Tracking of spatial and temporal maxima is performed by ray techniques, and a paraxial ray regime is defined that permits discussion of a signal velocity. Special attention is given to ray focusing and the associated phenomena of pulse compression. It is shown how a complex input frequency profile can be synthesized so as to achieve optimum compression at a real space-time observation point in a lossy medium. The general results are applied in detail to a cold dissipative plasma, and a representative set of numerical calculations is included.     

Transmission-mode y.i.g. dispersive filter for wide-band pulse compression

It has recently been reported that yttrium-iron-garnet microwave variable-delay lines can be operated in a transmission mode of operation rather than in the usual reflection mode of operation by optical-contact bonding quarterwave plates to both ends of the y.i.g. rod.1.2 This is a distinct advantage for many delay-line applications, because the undelayed direct feedthrough can be suppressed to a much higher degree when input and output lines are at opposite ends of the y.i.g. rod, which is mounted in a tightly fitting hole in a brass block. One of the most promising applications of the y.i.g. delay line is in wide-band microwave pulse-compression filters. The successful operation of a y.i.g. delay line, to obtain compressed signals in a transmission with large suppression of direct leakage of undelayed signals, is reported.     

On radar pulse scattering from ionized media

Some preliminary work relating to the pulse radar return from ionized media, such as fireballs resulting from nuclear explosions and the wakes of high-speed reentry vehicles, is reported. In all cases the objective is to retrieve the envelope of the backscattered signal correctly related in time to the transmitted pulse.     

在时域内计算色散媒质中光脉冲的传输

得到了时域内色散媒质中光脉冲传输的计算公式，并提出了时域内色散媒质中显式的光束传播法。计算了短脉冲在具有二阶色散效应的定向耦合器内的传输、计算结果同参考文献中的一致，但本文的计算方法简单、方便、实用。     

Wave packets in strongly dispersive media

An analytical study of the evolution of slowly varying wave pulses in strongly dispersive media which takes into account dispersive correction terms involving higher derivatives of the group velocity is given. A higher order differential equation for the envelope function is derived and solved recursively and by means of a procedure based on an analogy with the Schrödinger equation. The equation for the envelope function is used to obtain generalizations of the velocity of the pulse defined as the velocity of the center of inertia, and expressions are derived which determine the spreading of the pulse. Finally, we discuss how the presence of other wave modes affects the primary mode in the multimode case.     

Electromagnetic pulse transmission in homogeneous dispersive rock

The effect of the frequency dependence of the conductivity and permittivity of rock for pulse transmission is considered. These high-frequency dispersive effects appear to play a major role in determining the transient response of the medium. A quantitative understanding is achieved by adopting a dispersion model that consists of multiple Debye relaxation processes. It is shown that the results differ significantly from earlier transient calculations that assume frequency independent permittivities and conductivities.     

Statistical pulse compression

The seismic method in petroleum exploration is an echo-location technique to detect interfaces between the subsurface sedimentary layers of the earth. The received seismic reflection record (field trace), in general, may be modeled as a linear time-varying (LTV) system. However, in order to make the problem tractable, we do not deal with the entire field trace as a single unit, but instead subdivide it into time gates. For any time gate on the trace, there is a corresponding vertical section of rock layers within the earth, such that the primary (direct) reflections from these layers all arrive within the gate. Each interface between layers is characterized by a local (or Fresnel) reflection coefficient, which physically must be less than unity in magnitude. Under the hypothesis that the vertical earth section has small reflection coefficients, then within the corresponding time gate the LTV model of the seismic field trace reduces to a linear time-invariant (LTI) system. This LTI system, known as the convolutional model of the seismic trace, says that the field trace is the convolution of a seismic wavelet with the reflection coefficient series. If, in addition, the reflection coefficient series is white, then all the spectral shape of the trace within the gate can be attributed to the seismic wavelet. Thus the inverse wavelet can be computed as the prediction error operator (for unit prediction distance) by the method of least squares. The convolution of this inverse wavelet with the field trace yields the desired reflection coefficients. This statistical pulse compression method, known as predictive deconvolution with unit prediction distance, is also called spike deconvolution. Alternatively, predictive deconvolution with greater prediction distance can be used, and it is known as gapped deconvolution. Other pulse compression methods used in seismic processing are signature deconvolution, wavelet processing, and minimum entropy deconvolution.     

中频脉中压缩信号数字化直接产生技术研究

该文提出了一种脉冲压缩中频信号数字化产生方法及硬件实现方案,对其中的一些关键问题做出了定量分析;在此基础上完成了一套波形产生器,可产生6种中频15MHz、带宽1MHz、时宽等于或小于300s的线性调频、非线性调频信号。测试表明其谐波与杂散均优于-68dB,完全达到工程应用要求。     

Picosecond optical pulse compression from gain-switched 1.3 ?m distributed-feedback laser diode through highly dispersive single-mode fibre

The first demonstration to compress the linearly chirped optical pulses from a gain-switched distributed-feedback laser diode (DFB-LD) is described at 1.3 ?m wavelength. By travelling through a highly dispersive single-mode fibre with 48 ps/nm normal dispersion, a 26 ps (FWHM) pulse having red-shift frequency chirping of 85 GHz (FWHM) is compressed to 8.3 ps with the time-bandwidth product of 0.71.     

Propagation of transients in dispersive dielectric media

The propagation of transient electromagnetic fields in dispersive dielectric media is studied. The dielectric medium is assumed to be linear, isotropic, and homogeneous, and is described by the Debye model. Incident fields are assumed to be transverse electromagnetic plane wave pulses. The dielectric body can assume the form of infinite half space or an infinite circular cylinder, either of which may be homogeneous or stratified. The electric fields induced in the dielectric are calculated from time-domain Maxwell's equations using the finite-difference time-domain method.<>     

Acoustic emission source location in dispersive media

In this paper, the acoustic emission source (AE) is located by a non-iterative method using the time-of-arrival (TOA) of several events, received in an array of sensors arbitrary positioning in the 3D space. If at least two event velocities are different, a common property in dispersive propagation, and the array of sensors is not lying in a plane, a close-form estimation of the source–sensors distances, AE time and material constant is derived. Moreover, a direct estimation of the source position is achieved using the multidimensional scaling approach. In simulation experiments, the proposed method detects accurately the location of AE sources, reducing also the ambiguity introduced by noisy arrival times.     

High-order compact schemes for dispersive media

Staggered high-order compact (HOC) finite difference schemes are developed for modelling electromagnetic wave propagation in dispersive media. The main advantage of HOC schemes is their very low dispersion error, which is dominant in low-order methods. The high accuracy of HOC schemes is demonstrated by examples of wave propagation through first-order Debye and Lorentz media in one dimension.     

Time-domain finite-element modeling of dispersive media

A general formulation is described for time-domain finite-element modeling of electromagnetic fields in a general dispersive medium. The formulation is based on the second-order vector wave equation and incorporates the dispersion effect of a medium via a recursively evaluated convolution integral. This evaluation is kept to second order in accuracy using linear interpolation within each time step. Numerical examples are given to validate the proposed formulation     

High-energy SBS pulse compression

An efficient two-cell stimulated Brillouin scattering (SBS) pulse-compressor design that can be scaled to large laser-pulse energies is described and a numerical model has been developed that accurately predicts the performance of this pulse-compressor system over a wide range of operating parameters. The compression of a 2.5 J input pulse from a width of 15.8 to 1.7 ns is experimentally demonstrated with 80 percent energy efficiency. A design of an SBS pulse compressor to compress a 25 J pulse to a pulse width less than 1 ns with 80 percent energy efficiency is presented     

Energy relations for waves in strongly dispersive media

Expressions for the averaged stored energy, energy flow, and energy velocity of quasi-monochromatic waves in temporally and spatially dispersive media have been extended to take into account broad-band signals in strongly dispersive media.     

High-order FDTD and auxiliary differential equation formulation of optical pulse propagation in 2-D Kerr and Raman nonlinear dispersive media

We reformulate the existing auxiliary differential equation (ADE) technique in the context of the finite-difference time-domain analysis of Maxwell's equations for the modeling of optical pulse propagation in linear Lorentz and nonlinear Kerr and Raman media. Our formulation is based on the polarization terms and allows simple and consistent implementation of such media together with the anisotropic perfectly matched layer (APML) absorbing boundary condition. The disadvantages of the ADE technique, i.e., requiring additional storage for auxiliary variables, has been overcome by adopting the high-order finite-difference schemes derived from the previously reported wavelet-based formulation. With those techniques, we demonstrate in two-dimensional setting an effective and accurate numerical analysis of the spatio-temporal soliton propagation as a consequence of the physically originated balanced phenomena between the self-focusing effect of nonlinearity and the pulse broadening effects of the temporal dispersion and of the spatial diffraction.