Pulse dynamics in an optical fiber with linear intermode coupling and Kerr nonlinearity dispersion

The effect of Kerr nonlinearity dispersion on the envelope duration and the velocity of the envelope maximum for a wave packet propagating in an optical fiber and formed by two coupled copropagating waves is studied. The critical (threshold) energy of wave packet collapse can substantially be diminished and the supraluminal mode of propagation of the pulse envelope maximum in a nonamplifying medium can be realized owing to a significantly higher nonlinearity dispersion in such systems in comparison with “single-wave” ones.     

Wave packets in smoothly inhomogeneous dispersive media

In the quasi-optical aberration-free approximation, a parabolic equation for the envelope of an electromagnetic wave packet propagating along a geometric optical ray in a smoothly inhomogeneous isotropic medium with time dispersion is obtained. The corresponding Green’s function is found whose parameters are determined by integrating a system of ordinary differential equations. The effects of the combined influence of the refraction, diffraction, and dispersion on the evolution of the packet are analyzed; in particular, the effects that cause precession of the envelope waves about the binormal to the propagation trajectory are considered.     

Self-focusing of wave packets and envelope shock formation in nonlinear dispersive media

The self-action of three-dimensional wave packets is analyzed analytically and numerically under the conditions of competing diffraction, cubic nonlinearity, and nonlinear dispersion (dependence of group velocity on wave amplitude). A qualitative analysis of pulse evolution is performed by the moment method to find a sufficient condition for self-focusing. Self-action effects in an electromagnetically induced transparency medium (without cubic nonlinearity) are analyzed numerically. It is shown that the self-focusing of a wave packet is accompanied by self-steepening of the longitudinal profile and envelope shock formation. The possibility of envelope shock formation is also demonstrated for self-focusing wave packets propagating in a normally dispersive medium.     

Wave packet dynamics in a nonlinear tunnel-coupled structure of right- and left-handed media

The dynamics of a wave packet formed by tunnel-coupled forward and backward waves in a waveguide structure consisting of media with different signs of real parts of their refractive indices is investigated. Expressions for coupled-wave amplitude and reflection and transmission coefficients that are corrected for absorption are derived in the linear approximation. The expressions governing the wave-packet duration and propagation velocity of its envelope maximum are derived, taking into account the second-order dispersion, cubic nonlinearity, and dispersion of the nonlinearity. The possibility of efficient control of the forward wave velocity by applying an external magnetic field is demonstrated.     

On the reality of supraluminal group velocity and negative delay time for a wave packet in a dispersion medium

It is shown that, in the case of the supraluminal group velocity of a wave packet in a dispersion medium, a wave packet with a smooth (analytical) envelope does propagate with a supraluminal velocity. In the case of a negative group velocity, the signal maximum does arrive at the detector earlier than at the transmitter. These facts are consistent with both the finiteness of the velocity of light in free space for information transfer (in the case of supraluminal propagation velocity) and the principle of causality (in the case of negative delay time). Basically, the effect of negative delay time may be employed for predicting an observable effect.     

Structural features of self-action of laser radiation in the electromagnetic induced transparency mode

Structural features of the laser radiation self-focusing dynamics in the electromagnetic induced transparency (EIT) band are studied for an atomic system with a Λ-type energy level diagram. Effective nonlinearity of an EIT medium is manifested primarily as nonlinear dispersion (dependence of the group velocity on the wave amplitude). Qualitative analysis of the dynamics of self-action of laser pulses, which is confirmed by numerical simulation, shows that nonlinear evolution of a 3D wave packet follows the scenario of self-focusing, which serves as the background on which the envelope profile turnover and the formation of a shock wave occur at an advanced rate.     

Temporal ghost imaging of a time object,dispersion cancelation,and nonlocal time lens with bi-photon state

We present a theory of temporal diffraction, temporal imaging of a bi-photon state, and temporal ghost imaging of a time object. By applying factional Fourier transform to the bi-photon wave packet propagating in space, we could obtain a theory that shows the physical origin of dispersion cancelation, temporal imaging, nonlocal effects of time lenses, and temporal ghost imaging. We introduce the temporal diffraction distance for bi-photon wave packet and show that the bi-photon wave packet behaves like a single wave packet whose temporal diffraction distance is determined by the coherent sum of the temporal diffraction distances for the signal and the idler beams. This property yields the well known dispersion cancelation, the recovery of original bi-photon wave packet in temporal imaging, and the nonlocal combination of two time lenses placed in different arms. We also propose a method for ghost imaging of an arbitrary time object.     

Nonlinear transformation of wave packets in weakly dispersive media

We study the propagation of nonlinear modulated waves in weakly dispersive media within the framework of the Korteveg- de Vries equation. It is shown that strong generation of overtones and mean flow by the modulated packet results in asymmetry of the wave packet envelope with respect to both horizontal and vertical axes and makes the envelope skewed. The motion of the wave packet is accompanied by the emission of low-frequency and high-frequency waves that propagate in different directions from the packet. As a result, the mean amplitude of the wave packet decreases with distance. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 354–358, April 1999.     

On the velocity of propagation of a frequency-modulated wave packet in a dispersive absorbing medium

It is shown that the velocity of propagation of a frequency-modulated wave packet through a strongly dispersive absorbing medium can be significantly different from (either higher or lower than) that of a non-frequency-modulated wave packet. This difference is attributed to the absorption dispersion of the medium. The easiest way to take the absorption dispersion into account is to use the formalism of the complex group velocity of a wave packet. This paper considers the propagation of a linear frequency-modulated wave packet, whose carrier frequency is close to the frequency of a spectral absorption line of the medium.     

Retrieving the Amplitude and Phase Parameters of an Ultrashort Wave Packet by Autocorrelation Methods

Based on an analysis of the signal of an interferometric intensity autocorrelator, we demonstrate theoretically and experimentally a simple technique for retrieving the temporal distributions of the amplitude and phase of an ultrashort light pulse. Assuming that a phase-modulated wave packet has a Gaussian envelope, we derive an analytical expression for the autocorrelator signal in the cases of linear- and quadratic-chirp optical pulses. The experimental and theoretical results are in excellent agreement. In particular, we show that a linear chirp (quadratic phase modulation) can be measured with a good experimental accuracy of no worse than 10%. This yields the possibility of measuring the parameter k₂, which describes the dispersion characteristics of a medium in the second order of the dispersion theory, with the same accuracy. Measuring a quadratic chirp by the proposed method is possible only if such a chirp is sufficiently large.     

On the propagation of a light pulse in the “transparency window” of a medium with population inversion

The propagation of a light pulse through a layer of a substance with population inversion and, correspondingly, with an anomalous dispersion in the transparency range is considered. It is shown that, when the wave packet approaches the layer of the substance with a strong anomalous dispersion, two additional wave packets arise at the rear boundary of the layer. One of these packets has a negative energy and moves in the layer from its rear to the front boundary, while the other packet moves away from the rear boundary of the layer into a vacuum. As the initial wave packet comes into contact with the front boundary of the layer of the substance, it meets the packet of the negative energy. As a result, the two packets annihilate one another, after which only one packet remains, which moves away from the layer.     

Wave packets propagation in quantum gravity

Wave packet broadening in usual quantum mechanics is a consequence of dispersion behavior of the medium which the wave propagates in it. In this paper, we consider the problem of wave packet broadening in the framework of Generalized Uncertainty Principle(GUP) of quantum gravity. New dispersion relations are derived in the context of GUP and it has been shown that there exists a gravitational induced dispersion which leads to more broadening of the wave packets. As a result of these dispersion relations, a generalized Klein-Gordon equation is obtained and its interpretation is given.     

Dynamics of optical pulses in periodic nonlinear fibers

Dynamics of a two-mode wave packet with strong linear and nonlinear (cross-modulation) coupling is investigated. The effect of the initial conditions of the pulse excitation on its further transformation is considered. The possibility to control the dispersion parameters of the wave packet by varying the initial conditions of its input is pointed out. The effective parameters of the dispersion and nonlinearity that govern the dynamics of an optical pulse in a periodic nonlinear fiber light guide are obtained.     

On the theory of wave packets

In this paper we discuss some aspects of the theory of wave packets. We consider a popular noncovariant Gaussian model used in various applications and show that it predicts too slow a longitudinal dispersion rate for relativistic particles. We revise this approach by considering a covariant model of Gaussian wave packets, and examine our results by inspecting a wave packet of arbitrary form. A general formula for the time dependence of the dispersion of a wave packet of arbitrary form is found. Finally, we give a transparent interpretation of the disappearance of the wave function over time due to the dispersion—a feature often considered undesirable, but which is unavoidable for wave packets. We find, starting from simple examples, proceeding with their generalizations and finally by considering the continuity equation, that the integral over time of both the flux and probability densities are asymptotically proportional to the factor 1/|x|² in the rest frame of the wave packet, just as in the case of an ensemble of classical particles.     

Wave analysis of ray chaos in underwater acoustics

The dispersion of a wave packet in an acoustic medium is considered in the paraxial wave approximation, where the effective potential, due to variation of the speed of propagation, varies both with depth and propagation distance. The analysis of the resulting parabolic equation, similar to the Schrodinger equation, clearly demonstrates the role of ray chaos in enhancing the dispersion of the initial packet. However, wave coherence effects are also seen that suppress the effects of the ray chaos in a manner analogous to the effects of quantum chaos. (c) 1999 American Institute of Physics.     

原子链与弦中波包演化的比较分析

分析了一维单原子链中与连续弦中的波包的演化过程.弦中的波包以恒定速度移动,且保持形状不变;而原子链中的波包在演化过程中形状不断地发生变化.通过比较分析一维单原子链与弦振动的色散关系,讨论了波包演化的不同以及离散的原子链到连续弦的过渡.     

空间诱导产生艾里-贝塞尔光弹研究

利用波动方程,研究了脉冲贝塞尔光束在自由空间传输时的空间诱导群速度色散(SIGVD)效应. 结果表明,三阶SIGVD能使脉冲贝塞尔光束的时域逐渐演化为艾里分布. 由于艾里-贝塞尔光弹是一种新奇的时、空都不扩展的局域波包, 能在光与物质相互作用的很多应用领域发挥作用.因此,本文提出了 通过色散管理技术补偿二阶SIGVD,利用三阶SIGVD在自由空间产生艾里-贝塞尔光弹的方案. 为分析这种光弹的时空传输特性,数值模拟了它在色散介质中的传输情况. 结果表明,这种光弹能在色散介质中保持空域不衍射、时域不色散的稳定传输.     

Neutrino wave function and oscillation suppression

We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the electron is relativistic and the spatial size of its wave packet is much larger than the size of the crystal cell, then the wave packet of the produced neutrino has essentially the same size as the wave packet of the electron. We investigate the suppression of neutrino oscillations at large distances caused by two mechanisms: (1) spatial separation of wave packets corresponding to different neutrino masses; (2) neutrino energy dispersion for given neutrino mass eigenstates. We resolve the contributions of these two mechanisms. Received: 26 July 2005, Published online: 6 October 2005     

On the mass of a wave packet in plasma

The relativistic mass density which is transported by a quasi-monochromatic transverse wave packet is derived. The wave packet is assumed to propagate in isotropic cold collisionless plasma. The co-ordinate frame moving with the group velocity appears as the rest frame for both the mass density and the total mass of the wave packet. The equivalence of the energy-mass relation and the dispersion equation is demonstrated.     

Observation of nonspreading wave packets in an imaginary potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.