Complete integrability and singularity confinement of nonautonomous modified Korteweg–de Vries and sine Gordon mappings

A systematic investigation on the complete integrability of the nonautonomous discrete–discrete modified Korteweg–de Vries (ΔΔmKdV) and sine Gordon (ΔΔsG) mappings is presented using Lax pair technique and singularity confinement criteria. We derive conditions on the coefficients of Lax matrices such that the ΔΔmKdV and ΔΔsG admit a Lax representation separately. We then demonstrate that the obtained conditions for each of the nonautonomous equations are indeed precisely the necessary conditions to satisfy an ultra-local version of singularity confinement criteria. A similarity reduction of both the ΔΔmKdV and ΔΔsG is obtained and shown to lead a new discrete Painleve type of equations of higher order possessing Lax representation.     

Spatio-temporal pulse propagation in nonlinear dispersive optical media

We discuss state-of-art approaches to modeling of propagation of ultrashort optical pulses in one and three spatial dimensions. We operate with the analytic signal formulation for the electric field rather than using the slowly varying envelope approximation, because the latter becomes questionable for few-cycle pulses. Suitable propagation models are naturally derived in terms of unidirectional approximation.     

Shaping of few-cycle laser pulses via a subwavelength structure

We theoretically investigate the propagation of few-cycle laser pulses in resonant two-level dense media with a sub- wavelength structure, which is described by the full Maxwell-Bloch equations without the frame of slowly varying envelope and rotating wave approximations. The input pulses can be shaped into shorter ones with a single or less than one optical cycle. The effect of the parameters of the subwavelength structure and laser pulses is studied. Our study shows that the media with a subwavelength structure can significantly shape the few-cycle pulses into a subcycle pulse, even for the case of chirp pulses as input fields. This suggests that such subwavelength structures have potential application in the shaping of few-cycle laser pulses.     

Few-optical-cycle solitons and pulse self-compression in a Kerr medium

In a transparent medium with instantaneous Kerr nonlinearity we find a new class of few-optical-cycle solitons and prove them to be the fundamental structures in pulse propagation dynamics. We demonstrate numerically that in the asymptotic stage of pulse propagation the input pulse splits into isolated few-cycle solitons where the quantity and their parameters are determined by the initial pulse. We generalize the concept of the high-order Schr?dinger solitons to the few-cycle regime and show how it can be used for efficient pulse compression down to the single cycle duration.     

On the nonlinear optics of few-cycle pulses

A brief review of the development of the nonlinear optics of few-cycle optical laser pulses is presented. Emphasis is placed on analyzing the soliton propagation modes of such pulses in the context of possible applications in optical data transmission systems.     

Three-dimensional few-cycle optical pulses in an array of carbon nanotubes inside a magnetic field

The behavior of three-dimensional few-cycle optical pulses, propagating in a system of carbon nanotubes inside an external magnetic field applied parallel to the nanotube axes and perpendicular to the direction of pulse propagation, is studied. The evolution of the electromagnetic field is classically derived using Maxwell’s equations.     

Polarization dynamics of unidirectional optical pulse evolution in a laser amplifier

Polarization dynamics of optical pulses in an isotropic two-level medium is analyzed by solving an integrable system of evolution equations without using the slowly varying envelope approximation. The analysis is focused on the regime of unidirectional pulse generation in an initially inverted medium. Qualitative difference in polarization dynamics is revealed between few-cycle and quasi-monochromatic pulse propagation     

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.     

Application of higher-order KdV——mKdV model with higher-degree nonlinear terms to gravity waves in atmosphere

Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV--mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.     

等束腰宽度超短脉冲光束传输的脉冲修正方法

利用角谱分析和傅里叶变换的方法,得到一种描述几个周期的等束腰宽度脉冲光束传输的脉冲修正方法。以准单色光束传输的结果为出发点,通过对准单色光束的解进行泰勒级数展开,得到了一种相对简单的修正方法,可以精确的描述具有任意时间波形和横向光束分布的不短于一个周期的超短脉冲光束的传输行为。给出等束腰宽度超短脉冲的近似解,具体研究高斯脉冲光束的传输特性,分析几种不同的频谱对脉冲光束传输行为的影响。     

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 Rectification and Generation of Harmonics Under Condition of Propagation of Few-Cycle Pulses in the Birefringent Medium with Asymmetric Molecules

Without using the approximation of slowly varying envelopes, we investigate spectral transformations of vector few-cycle and quasi-monochromatic solitons under propagation in the birefringent medium of asymmetric molecules possessing permanent dipole moments. We show that when an ordinary pulse enters the medium, the self-modulation effect arises. As a result, the spectrum of the ordinary component undergoes significant changes from the violet shift and the generation of odd harmonics with close frequency satellites to the supercontinuum including zero frequency. The spectrum of the extra-ordinary few-cycle pulse also has the properties of a supercontinuum. When a quasi-monochromatic ordinary pulse enters the medium in the spectrum of an extra-ordinary component, the effect of optical rectification with simultaneous generation of the second harmonics is clearly manifested.     

Analytic study of continuum spectrum pulse dynamics in optical waveguides

It is demonstrated that for femtosecond supercontinuum generation in optical waveguides with nonresonant electronic nonlinearity the squared root-mean-square pulse duration varies near-parabolically with distance, irrespectively of spectrum ultra-broadening scenarios. The derived formulas for parabolic coefficients are applied to find the areas of spectral and energetic parameters of few-cycle pulses propagating in hollow capillaries filled with noble gases, where temporal pulse broadening, compression, or quasi-stationary propagation occur. Each regime is illustrated by the typical changes in the pulse electrical field and spectrum. PACS 42.65.Re     

Dynamics and control of few-cycle ultrashort pulse propagation in an asymmetric coupled-quantum-well nanostructure

The nonlinear propagation of few-cycle ultrashort pulse in an asymmetric coupled-quantum-well (CQW) nanostructure is simulated by solving numerically the full Maxwell-Bloch equations with an iterative predictor-corrector finite-difference time-domain method. The behaviors of electric field profiles for 2π and 4π ultrashort pulses in different propagating zones are predicted in details beyond the slowly varying envelope and rotating-wave approximations. This investigation may provide a guideline for optimizing and controlling ultrashort pulses in solid-state media, which are promising for practical applications in high-speed optical communications.     

Nonlinear pulse propagation in a single- and a few-cycle regimes with Raman response

The propagation equation for a single- and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single- and a 4-cycle pulse, at 0.8 μm wavelength, were studied numerically in one spatial dimension. It was shown that Raman term does influence the propagation characteristics of a single-as well as a few-cycle pulses by counteracting the self-steepening effect.     

An integrable coupled Alice–Bob modified Korteweg de-Vries system: Lax pairs,Bäcklund transformations,residual symmetries and exact solutions

ABSTRACT

A coupled Alice–Bob modified Korteweg de-Vries (mKdV) system is established from the mKdV equation in this paper, which is nonlocal and suitable to model two-place entangled events. The Lax integrability of the coupled Alice–Bob mKdV system is proved by demonstrating three types of Lax pairs. By means of the truncated Painlevé expansion, auto-Bäcklund transformation of the coupled Alice–Bob mKdV system and Bäcklund transformation between the coupled Alice–Bob mKdV system and the Schwarzian mKdV equation are demonstrated. Nonlocal residual symmetries of the coupled Alice–Bob mKdV system are researched. To obtain localized Lie point symmetries of residual symmetries, the coupled Alice–Bob mKdV system is extended to a system consisting six equations. Calculation on the prolonged system shows that it is invariant under the scaling transformations, space-time translations, phase translations and Galilean translations. One-parameter group transformation and one-parameter subgroup invariant solutions are obtained. The consistent Riccati expansion (CRE) solvability of the coupled Alice–Bob mKdV system is proved and some interaction structures between soliton–cnoidal waves are obtained by CRE. Moreover, Jacobi periodic wave solutions, solitary wave solutions and singular solutions are obtained by elliptic function expansion and exponential function expansion.     

Frontend light source for short-pulse pumped OPCPA system

We present the development of a light source for generating optically synchronized seed pulses both for the parametric amplifier chain and the pump-laser chain of the Petawatt Field Synthesizer (PFS), which is currently under construction at MPQ. The PFS system aims at delivering waveform-controlled few-cycle laser pulses with PW-scale peak power using optical parametric chirped pulse amplification (OPCPA). Methods of generating the broadband near-infrared (NIR) seed pulses for the OPCPA chain by spectral broadening using few-cycle pulses are presented. We also demonstrate the generation of a supercontinuum spanning up to three octaves (270–1500 nm) using cascaded hollow-core fibers which supports sub-cycle pulse duration.     

Spatiotemporal propagation dynamics of intense optical pulses in loosely confined gas-filled hollow-core fibers

We numerically study the propagation dynamics of intense optical pulses in gas-filled hollow-core fibers(HCFs). The spatiotemporal dynamics of the pulses show a transition from tightly confined to loosely confined characteristics as the fiber core is increased, which manifests as a deterioration in the spatiotemporal uniformity of the beam. It is found that using the gas pressure gradient does not enhance the beam quality in large-core HCFs, while inducing a positive chirp in the pulse to lower the peak power can improve the beam quality. This indicates that the self-focusing effect in the HCFs is the main driving force for the propagation dynamics. It also suggests that pulses at longer wavelengths are more suitable for HCFs with large cores because of the lower critical power of self-focusing, which is justified by the numerical simulations. These results will benefit the generation of energetic few-cycle pulses in large-core HCFs.     

A Formula of Propagating Beams Driven by Few-Cycle Gaussian Pulse in Dispersive Media

A formula is developed to describe the propagation of beams driven by few-cycle Gaussian pulse in a media with group velocity dispersion （GVD）. With the method, the spatiotemporal evolution of the pulsed beam can be straightforwardly quantified as long as the monochromatic beam solutions in free space, which have been widely investigated in previous works, are known. The method makes it possible to analytically deal with the few-cycle pulsed beams with transverse profiles other than the Gaussian one, which is, to our knowledge, the one mainly investigated previously, in GVD media.