On the nonlinear propagation of few-cycle pulses in a uniaxial crystal

The soliton-like dynamics of few-cycle optical pulses propagating in a uniaxial crystal at an arbitrary angle to the optic axis is analytically studied. Solutions describing the one-dimensional dynamics of pulses representing coupled states of the ordinary and extraordinary field components are analyzed. The ordinary component can contain an arbitrary number (down to one period) of optical oscillations, whereas the extraordinary component is a unipolar video pulse. The effect of small-scale transverse perturbations on the propagation of such pulses is considered. Regions of values of parameters of the medium and the pulse in which the propagation is stable are found. The spectrum of the ordinary component is shown to substantially depend on the sign of the birefringence of the crystal as well as on the angle at which the pulse propagates with respect to the optic axis.     

On the effect of transverse perturbations on the propagation of soliton-like two-component pulses in a uniaxial crystal

The combined approach including the method of analytic continuation of dispersion parameters to the complex plane and an averaged variational principle of the Ritz-Whitham type is used for studying the propagation of a soliton-like two-component pulse in a uniaxial crystal in the direction perpendicular to its optic axis. The ordinary component of the soliton is a pulse with an arbitrary number of light oscillations (down to one period), and the extraordinary component is a video pulse. Such a pulse is shown to be stable against small transverse perturbations, including small-scale ones.     

Propagation of an ultimately short electromagnetic pulse in a nonlinear medium described by the fifth-order Duffing model

We discuss propagation of an ultimately short (single-cycle) pulse of an electromagnetic field in a medium whose dispersion and nonlinear properties can be described by the cubic-quintic Duffing model, i.e., by an oscillator with third-and fifth-order anharmonicity. A system of equations governing the evolution of a unidirectional electromagnetic wave is analyzed without using the approximation of slowly varying envelopes. Three types of solutions of this system describing stationary propagation of a pulse in such a medium are found. When the signs of the anharmonicity constants are different, then the amplitude of a steady-state pulse is limited, but its energy may grow on account of an increase in its duration. The characteristics of such a pulse, referred to as an electromagnetic domain, are discussed.     

On the passage of an extremely short electromagnetic pulse through a ferroelectric layer embedded in a paraelectric

The refraction and reflection of an extremely short pulse of electromagnetic radiation on a layer of a ferroelectric are considered. For an incident pulse, a stationary pulse propagating without distortions in a paraelectric was used. It is shown that low-amplitude pulses undergo a strong reflection at the entrance to a ferroelectric medium and are not recovered after passage through the layer. High-amplitude pulses are reflected to a considerably lesser extent and can turn into a new stationary pulse after passage through the layer of a ferroelectric. The refraction is accompanied by excitation of polarization oscillations localized at the boundaries of the layer. The intensity of these oscillations and the fraction of the reflected wave are significantly different in cases of similar or opposite polarities of the ferroelectric and incident pulse.     

Extremely short electromagnetic pulses in a resonant medium with a permanent dipole moment

The propagation of an extremely short (one cycle long) pulse of an electromagnetic field in a medium whose resonant transition is characterized by both diagonal and off-diagonal matrix elements of the dipole-moment operator is considered theoretically. The set of Maxwell-Bloch equations without the approximation of the slowly varying envelopes is used. Two types of solutions of this set, which are found describing the steady-state propagation of an electromagnetic pulse in such a medium.     

Compression of single-cycle mid-infrared pulses by Raman-active molecular modulators

We show theoretically how high-order stimulated Raman scattering in the impulsive pump-probe regime can be used for generation of single mid-infrared (MIR) single-cycle pulses. The propagation of MIR probe pulses in a hollow waveguide filled with a Raman-excited gaseous medium, with a probe delay in the maximum of the molecular oscillations, results in spectral broadening covering almost 2 octaves. The spectral phases of this broadening can be compensated for by use of an output glass window with anomalous dispersion in the MIR. The spectral and temporal characteristics of the output pulses and the mechanism of pulse compression are studied by use of numerical and analytical solutions, and compression of a 70-fs input pulse at 4 microm to a single-cycle 6.5-fs output pulse is shown.     

Propagation of a short pulse in a medium with a resonance relaxation: The exact solution

A new analytical representation is obtained for the fundamental solution (Green’s function) to the problem of the propagation of a short pulse in an arbitrary medium with a single resonance relaxation process. The analytical representation is based on the generalized function of the local response of a linear medium [1] and includes the well-known Debye and Lorentz relaxation models as particular cases. The representation is used to determine the complete set of possible types of behavior for a short pulse propagating in the medium.     

Photon echo under excitation of a medium by pulses consisting of an arbitrary number of oscillations

Echo responses of a three-level medium formed by the λ-scheme of quantum transitions under exposure to optical pulses consisting of an arbitrary number of oscillations have been studied theoretically. The cases of pulses consisting of few optical oscillations (for which the concept of an envelope cannot be used) and combinations of such pulses and quasi-monochromatic resonance signals have been considered. The approach used can be reduced to the renormalization of dipole moments of allowed quantum transitions through their multiplication by coefficients depending on the shape and duration of pump pulses and having absolute values in the range from zero (for nonresonance pulses) to unity (for resonance quasi-monochromatic pulses and broadband pulses consisting of few oscillations, whose spectrum covers the quantum transitions). A general equation has been proposed for the pulse area. In the limit of a large number of oscillations, it transforms into the well-known definition of the area of a quasi-monochromatic signal. The characteristics of primary and longlived photon echoes have been analyzed in detail. It has been shown that, when a medium is exposed to only pulses consisting of a few oscillations, three echo responses of both types can be principally generated at each frequency of the λ-scheme. Introduction of quasi-monochromatic pulses in pump pulse series decreases the number of echoes, and their qualitative character has a non-commutative property with respect to pulse permutation in a series. The extension of the proposed approach to more complex schemes of quantum transitions with the large number of quantum levels faces no principal difficulties.     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach, the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated. The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included. The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF). The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength. The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

Effects of Higher-Order Relativistic Nonlinearity and Wakefield During a Moderately Intense Laser Pulse Propagation in a Plasma Channel

Using a variational approach,the propagation of a moderately intense laser pulse in a parabolic preformed plasma channel is investigated.The effects of higher-order relativistic nonlinearity (HRN) and wakefield are included.The effect of HRN serves as an additional defocusing mechanism and has the same order of magnitude in the spot size as that of the transverse wakefield (TWF).The effect of longitudinal wakefield is much larger than those of HRN and TWF for an intense laser pulse with the pulse length equaling the plasma wavelength.The catastrophic focusing of the laser spot size would be prevented in the present of HRN and then it varies with periodic focusing oscillations.     

Simulation of the propagation of a light pulse in a randomly inhomogeneous medium

The propagation of a Gaussian pulse in an inhomogeneous medium is considered. The detected pulse is represented as a series in the scattering multiplicities. The developed approach enables one to describe the passage of a pulse through a randomly inhomogeneous medium in the general case, beyond the framework of the diffusion approximation. The known results of the diffusion approximation are shown to represent limiting cases of the expansion constructed in the scattering multiplicities. The calculations are performed by the Monte Carlo method for cases of singly and multiply scattering media. The agreement between the results of the theoretical analysis and the numerical simulation allows one to use the approach developed in both optical problems and investigation of propagation of waves of other nature, in particular, seismic waves.     

周期量级飞秒脉冲电场在非线性克尔介质中的传输

采用时间转换法研究了周期量级飞秒脉冲电场在非线性克尔介质中的传输.由于周期量级飞秒脉冲电场的脉宽小于介质拉曼响应的特征时间,在传输过程中脉冲电场会发生剧烈的变形和分裂,并在频谱上观察到了强烈的拉曼感应频移和色散波.由于周期量级脉冲电场依赖于载波包络相位,发现在脉冲电场传输过程中,主脉冲电场和色散波电场的相位线性地依赖于初始脉冲的载波包络相位.     

Oscillatory dispersion and coexisting stable pulse trains in an excitable medium

For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses. Crucial for the bistability is that the pulses in the trains are locked into one oscillation maximum in the tail of the preceding pulse in the train.     

Rabi-oscillation-enhanced frequency conversion in quantum-dot semiconductor optical amplifiers

We investigate the nonlinear light propagation in InAs/InGaAs quantum-dot-in-a-well semiconductor optical amplifiers in the limit of strong optical excitation where Rabi oscillations are excited in the active medium. The amplifier is analyzed in a degenerate four-wave-mixing setup and characterized by its frequency conversion and creation performance. Our simulations show that the interplay between the nonlinear four-wave-mixing process and the coherent Rabi oscillations greatly influences the frequency conversion process. Rabi oscillations can be resonantly excited by the correct choice of the frequency detuning between pump and probe signals, which greatly enhances the nonlinear frequency conversion efficiency at frequencies up to several THz. We furthermore show that the coherent pulse shaping of ultrashort optical pulses in the quantum-dot medium can greatly enhance their spectral bandwidth, potentially allowing for ultra-broad-band frequency comb generation.     

Carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium

We theoretically investigate carrier-envelope phase dependence of few-cycle ultrashort laser pulse propagation in a polar molecule medium. Our results show that a soliton pulse can be generated during the two-photon resonant propagation of few-cycle pulse in the polar molecule medium. Moreover, the main features of the soliton pulse, such as pulse duration and intensity, depend crucially on the carrier-envelope phase of the incident pulse, which could be utilized to determine the carrier-envelope phase of a few-cycle ultrashort laser pulse from a mode-locked oscillator.     

Optical zoomeron as a result of beatings of the internal modes of a Bragg soliton

A new solution of two-wave Maxwell-Bloch equations has been obtained analytically and numerically. It describes the propagation of an oscillating nonlinear optical solitary wave, or optical zoomeron, in a one-dimensional periodic resonant Bragg structure. It has been shown that the appearance of large oscillations in the velocity and total amplitude of Bloch modes of the pulse is caused by beating of internal modes of the perturbed Bragg soliton.     

Dynamics of optical switching phenomena in dense media

The ultrafast optical switching phenomena in a dense medium of two-level atoms induced by arbitrary varying pulses are explained in terms of the adiabatic cancellation of the pulse by the induced polarization. The final population inversion of the medium after the passage of the pulse is found to depend on the number of oscillations the inversion exhibits during the time interval when the normalized pulse amplitude exceeds the maximum allowed value of the atomic polarization. If the inversion undergoes an integer number of oscillations in this region, then the final state of the system returns to the ground state. On the other hand, if the inversion undergoes a half integer number of oscillations in this region, the final state of the system is fully inverted. This behavior is explored analytically and illustrated numerically for the constant, sine and secant pulse shapes.     

传播效应对宽带极紫外连续谱的影响

宽带极紫外连续谱是获得阿秒脉冲的重要途径,在此过程中传播效应是影响宽带极紫外连续谱产生的重要因素,本文针对传播效应对宽带极紫外连续谱的影响,采用慢变波近似的一阶传播方程,研究了传播过程对双色场周期量级激光脉冲产生宽带连续谱及其对应的单个阿秒脉冲的影响.通过分析不同聚焦位置和介质长度的传播过程,发现介质位于焦点之后有利于产生连续谱,同时随着介质长度的变长,虽然单个阿秒脉冲峰值强度有所提高,但是产生的阿秒脉冲宽度也会增加.进一步的分析表明,在特定的双色场延迟优化下,传播效应不仅使得阿秒脉冲强度增强,还可以获得与单原子模型下具有同样脉宽的单个阿秒脉冲,而不会因为传播效应导致阿秒脉冲宽度变宽.     

On the conservation of momentum for a sound pulse reflecting from a pressure-release boundary

When a "massless" one-dimensional sound pulse (mass of a sound pulse is defined as an integral of the perturbation of density over the pulse length) reflects from a pressure-release boundary, its momentum changes sign. This obviously violates momentum conservation. However, in contrast to the case of an unbounded medium, calculation of the momentum in a bounded region includes a second-order term as well. Apparently, the second-order correction to the linear solution ensures momentum conservation in this case. The purpose of this Letter is to find a concrete form of this second-order correction. It appears that, as a result of the nonlinear interaction of the pulse with a pressure-release boundary, the latter experiences second-order net shift. This leads to the generation of a massive second-order rarefaction pulse whose momentum is directed opposite to the direction of propagation of the pulse itself. Appearance of this pulse ensures total momentum conservation.     

Effect of pulse entrapping on diffuse reflection from a resonant random medium: exact solution to the scalar albedo problem

A recently derived radiative transfer equation with three Lorentzian delay kernels is applied to an albedo problem of the scalar wave field produced by the diffuse reflection of a quasi-monochromatic pulse from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function H(μλ), extended analytically into the complex single-scattering albedo λ plane. The resulting analytic solution for the time evolution of a diffusely reflected short pulse is used to study on the whole time axis the effect of the redistribution of the energy of the propagated pulse from the front to the rear of the pulse in cases where the pulse may for most of the propagation time through the medium be 'entrapped' inside resonant scatterers. By considering the power flux through unit area of the boundary of the medium and unit solid angle, it is shown that the relative shift of an 'energy centroid' ('centre of mass') of the pulse diffusely reflected from the resonant random medium (compared with the pulse energy centriod in the non-resonant case) is equal to the parameter describing the energy accumulation inside the scatterers. This result may be used for experimental study of resonant random media with the aid of a short-pulse technique.