Pulses In Dispersive Media Research Articles

P1-5 Analysis of the propagation of ultrasonic pulses in dispersive media using group delay concept

P1-5 Analysis of the propagation of ultrasonic pulses in dispersive media using group delay concept

Control of temporal characteristics of Bessel-X pulses in dispersive media

We study Bessel-X pulses with dispersion in the cone angle that propagate without temporal spreading in a medium with group velocity dispersion (GVD). The general conditions for GVD-free propagation are given. Previously known results are encompassed as particular cases. We show that general GVD-free Bessel-X pulses, propagating at controlled phase and group velocities in the medium, can be generated in practice by means of an axicon and a circular diffraction grating.

Localized optical subcycle pulses in dispersive media

The conditions for creation of broadband localized optical fields (Bessel X pulses and focus wave modes) in dispersive media are analyzed. It is shown that transmission of focus wave modes with subcycle pulse durations through fused silica is possible.

Average energy flow of optical pulses in dispersive media

The arrival time of a light pulse at a point in space is defined using a time expectation integral over the Poynting vector. The delay between pulse arrival times at two distinct points is shown to consist of two parts: a spectral superposition of group delays (inverse of group velocity) and a delay due to spectral reshaping via absorption or amplification. The result provides a context wherein group velocity is always meaningful even for broad band pulses and when the group velocity is superluminal or negative. The result imposes luminality on sharply defined pulses.

Asymptotics and energy estimates for electromagnetic pulses in dispersive media: addendum

We review two references: one that appeared almost simultaneously with our paper [J. Opt. Soc. Am. A13, 1204 (1996)] and another that appeared later. We mention an earlier relevant paper, and we also correct two typographical errors in our paper.

Generalized eikonal approximation 1 Propagation of an electromagnetic pulse in a linear dispersive medium

The asymptotic theory of eikonal approximation permits electromagnetic fields to be described locally in terms of plane waves and the trajectory to be described as space–time rays. Properties of these space–time rays in a dispersive medium can be studied through the effective index of refraction defined by the higher-order space–time eikonal equation. From the analysis it is shown that the diffraction effects due to the finite size of the beam and the dispersion effects due to the finite pulse width can be treated in a unified manner in the generalized space–time eikonal equation. The space–time rays of a Gaussian pulse in a dispersive medium can be readily solved analytically and shown to provide results similar to those obtained by the Fourier transformation method.

Three-dimensional evolution of ultrashort pulses in dispersive media beyond the slowly varying envelope approximation

A new analytical solution for the three-dimensional evolution of femtosecond pulses in a medium with group velocity dispersion is presented. It is found that for Gaussian pulses as short as a few optical cycles, the coupling between spatial and temporal parameters becomes important, which will cause breakdown of the slowly varying envelope approximation (SVEA) equation.

Electromagnetic Pulses in Dispersive Media

We prove that an electromagnetic pulse originating at t = z = 0 and propagating in the z-direction is represented by a Bromwich integral. We discuss the asymptotic approximation of this integral for different saddle point methods. Then, it is shown that pulses have a steady component that propagates with the phase velocity and transient components that propagate with the signal velocity (according to Brillouin's definition). In many cases the signal velocity is the group velocity.We discuss different types of pulses, in particular digital pulses. For practical applications the transients are of the utmost importance since they are the main cause of pulse distortion.

Electromagnetic Pulses in Dispersive Media

We prove that an electromagnetic pulse originating at t = z = 0 and propagating in the z-direction is represented by a Bromwich integral. We discuss the asymptotic approximation of this integral for different saddle point methods. Then, it is shown that pulses have a steady component that propagates with the phase velocity and transient components that propagate with the signal velocity (according to Brillouin's definition). In many cases the signal velocity is the group velocity.We discuss different types of pulses, in particular digital pulses. For practical applications the transients are of the utmost importance since they are the main cause of pulse distortion.

Near-field and far-field propagation of beams and pulses in dispersive media

We formulate an efficient exact method of propagating optical wave packets (and cw beams) in isotropic and nonisotropic dispersive media. The method does not make the slowly varying envelope approximation in time or space and treats dispersion and diffraction exactly to all orders, even in the near field. It can also be used to determine the partial differential wave equation for pulses (and beams) to any order as a power series in the partial derivatives with respect to time and space. The method can treat extremely focused pulses and beams, e.g., from near-field scanning optical microscopy sources whose transverse spatial extent in smaller than a wavelength.

Suppression of temporal spread of ultrashort pulses in dispersive media by Bessel beam generators

Linear-optical solutions to the problem of temporal broadening of ultrashort light pulses propagating in air or in solid optical samples are proposed and tested by computer simulations. A special holographic-element setup is analyzed in detail.

Group-velocity-dispersion-compensated propagation of short pulses in dispersive media

An optical scheme based on a single angularly dispersive element is proposed for canceling group-velocity dispersion for pulse propagation in dispersive media. It is demonstrated experimentally that a pulse duration of 100 fs is preserved throughout the travel of a 248-nm-pulse through a 75-mm-long fused-silica slab.

Numerical simulation of time-domain EM scattering by shallow subsurface objects

The time-domain ElectroMagnetic(EM) scattering by buried objects in dispersive media is calculated with FD-TD method. The FD-TD formula in Debye dispersive media (both the complex permeability and the complex permittivity are described by Debye equations) are deduced, and the absorbing boundary condition is given. The validity of FD-TD method in lossy media is verified through comparing the FD-TD’s results and the other ones. The propagation of transient pulses in dispersive media is studied in detail. The scattering pulses and the wiggle traces for typical buried objects are given.

Asymptotics and energy estimates for electromagnetic pulses in dispersive media

We examine electromagnetic pulse propagation in anomalously dispersive media, using the Debye model as an example. Short-pulse, long-pulse, short-time, and long-time approximations and amplitude rate-of-decay estimates are derived with asymptotic methods. We also study the following problem: If we know only the peak amplitude and the energy density of an incident pulse, what can be said about the amplitude of the propagated pulse? We provide tight upper and lower bounds for the propagated amplitude, which may be useful in controlling the electromagnetic interference or the damage produced in dispersive media. We explain a factor-of-nine effect in the speed of pulses in a Debye model for water, which seems to have been previously unnoticed, and we also explain some observations from experimental studies of pulse propagation in biological materials. Finally, we propose some guidelines for sample size in transmission time-domain spectroscopy studies of dielectrics. Most of our results are easily extended to multiple space dimensions.

Self-tuning of dissipative solitons to the zero-dispersion point

It is shown that optical pulses in dispersive media with dissipation and saturable broadband gain experience frequency self-shifting toward the point of zero group-velocity dispersion. The decreasing dispersion leads to a strong compression of the pulses at constant pulse energy. The ultrashort pulses that result from this evolution have a duration limited only by the third-order group-velocity dispersion of the medium. A set of solitonlike pulses is found that has a continuous spectrum of velocities, and a selection rule is presented to determine the unique solution established from an arbitrary initial pulse form.

Generation and propagation of high intensity short acoustic pulses in dispersive media

Experiments on laser generation of acoustical pulses, amplitude 10 MPa and duration 1 μs, and their propagation in different liquids have been carried out. Propagation was measured in both pure liquids and structured media. Nonlinearity and dispersion caused evolution of the propagating signals. Some theoretical treatment of the results indicate the possibility of obtaining data on spectral features of the nonlinear response of the medium.

Self-steepening of optical pulses in dispersive media

We describe an analytical solution of the modified nonlinear Schrödinger equation with the inclusion of the self-steepening term. The results are applied, in particular, to the case of pulse propagation in optical fibers; the role of anomalous dispersion is analyzed, and asymmetric temporal behavior is seen.

Self-focusing of short light pulses in dispersive media

Group velocity dispersion is incorporated in a numerical model for self-focusing of short light pulses. It makes possible the propagation of pulses at powers exceeding the critical one and in this limit temporal and spatial splitting occurs. The phase variation of the pulse is analyzed with respect to subsequent compression.

Reply to "Comment on 'Test of local causality with very short light pulses' "

A clarification concerning the solution of the initial-value problem for the propagation of light pulses in dispersive media is given. In a proper interpretation, this solution corresponds to two single pulses traveling in opposite directions. Furthermore, a critical review of important research related to Rubin's arguments but not mentioned by him in the preceding Comment [Phys. Rev. A 41, 1727 (1990)] is presented.

Propagation of short optical pulses in dispersive medium

A theoretical analysis of the propagation of transform-limited short pulses in the medium of oscillators (Lorentz model) is presented. In particular, a temporal-modes expansion of the propagating field is introduced for the nonresonance and the resonance cases. It is shown that the medium dispersion causes severe distortions in the pulse shape. The proper choice of medium parameters and/or spectral filtering of the different temporal modes may allow the formation of arbitrary pulse shapes. >