Analysis of ultra short pulse propagation in optical directional coupler structures

We employ an efficient time-domain beam propagation technique to study the effect of the propagation of ultra short pulse duration on the behavior of directional coupler operation. The technique used is based on higher order non-paraxial formulation that takes into account the spatiotemporal coupling effect which is crucial for the proper propagation of ultra short optical pulses. In this work the characterization of pulse spread and broad frequency content interactions of short pulse propagation have been analyzed. We validate in this rigorous analysis that the intermodal dispersion of the structure changes the behavior of the well known operation and breaks up the pulse during propagation which gives rise to distortion.     

Dynamic spatial replenishment of femtosecond pulses propagating in air

We present numerical simulations of nonlinear pulse propagation in air whereby an initial pulse is formed, absorbed by plasma generation, and subsequently replenished by power from the trailing edge of the pulse. This process can occur more than once for high-power input pulses and produce the illusion of long-distance propagation of one self-guided pulse.     

Modeling photonic crystal fiber for efficient soliton pulse propagation at 850 nm

We numerically investigate the dynamics of soliton propagation at 850 nm in chloroform filled liquid core photonic crystal fiber (LCPCF) by using both finite element method (FEM) and split step Fourier method (SSFM). We propose a novel chloroform filled PCF structure that operates as a single mode at 850 nm featuring an enhanced dispersion and nonlinearity for efficient soliton propagation with low input pulse energy and low loss over small distances. We adopt the projection operator method (POM) to derive the pulse parameter equations which clearly describes the impact of fourth order dispersion on the pulse propagation in the proposed PCF. To analyse the quality of the pulse, we perform the stability analysis of pulse propagation numerically and compare our results of the newly designed chloroform filled PCF with that of standard silica PCF. From the stability analysis, we infer that the soliton pulse propagation in modified chloroform filled PCF is highly stable against the perturbation.     

Controlling the propagation velocity of a femtosecond laser pulse with negative index metamaterials

We theoretically study the propagation of a femtosecond laser pulse in negative-index metamaterials, and show that its propagation velocity can be easily controlled at a certain wavelength range simply by changing the initial chirp. This phenomenon may be used as an extremely simple way to control the propagation velocity of a femtosecond laser pulse.     

Exact solution to the problem of nonlinear pulse propagation through random layered media and its connection with number triangles

An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal’s and Catalan’s triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems.     

Group velocity of the light pulse in an open V-type system

We investigate the group velocity of the probe light pulse in an open V-type system with spontaneously generated coherence. We find that, not only varying the relative phase between the probe and driving pulses can but varying the atomic exit rate or incoherent pumping rate also can manipulate dramatically the group velocity, even make the pulse propagation switching from subluminal to superluminal; the subliminal propagation can be companied with gain or absorption, but the superluminal propagation is always companied with absorption.     

Controllable self-steepening of ultrashort pulses in quadratic nonlinear media

By analyzing ultrashort optical pulse propagation in quadratic nonlinear media beyond the slowly varying envelope approximation, we find that the sign and magnitude of self-steepening can be controlled through the wave vector mismatch. As an example of this phenomenon's impact on ultrashort pulse propagation, we show that it may be used to cancel the propagation effects of group-velocity mismatch. We obtain quantitative agreement between theory, simulations, and experiments.     

Photochemical time-domain holography of weak picosecond pulses

We show that weak picosecond optical pulse propagation through an absorbing medium with a photochemically burnedin persistent spectral hologram of a picosecond pulse train makes the sample emit coherently a replica of the pulse train applied in the burning-in cycle.     

Effects of pressure and gas-jet thickness on the generation of attosecond pulse

We investigate how the intensity and duration of an attosecond pulse generated from high-order harmonic generation are affected by the pressure and thickness of the gas jet by taking into account the macroscopic propagation of both fundamental and harmonic fields. Our simulations show that, limited by the propagation effects, especially the absorption of harmonics, the intensity of an attosecond pulse cannot be improved by just independently increasing the gas pressure or the medium length. On the other hand, due to good phase-matching conditions, the duration of a generated attosecond pulse can be improved by changing the gas pressure.     

Optical limiting and pulse reshaping of picosecond pulse trains by fullerene C60

We present a dynamical theory of nonlinear absorption and propagation of a laser pulse train that contains 20 subpulses with an individual pulse width of 100 ps. It is shown that the accumulative nonlinearity and the reverse saturation absorption play important roles in the optical limiting performance and pulse shaping. When the incident field is not too strong, the population transfer reveals a slow response process, and the periodic sequence of short light pulses can be regarded as a continuous long pulse. The general theory is applied to fullerence C₆₀, which is a popular reverse saturable absorption material and a good limiter because of its larger excited-state absorption cross-section compared with that of the ground state. The propagation of the front subpulses is mainly affected by the linear transition between the ground state and the first excited singlet state, while the latter subpulses are attenuated by the excited-state absorption. Moreover, these two different kinds of absorption mechanisms result in different radial distributions for different subpulses. The pulse propagation is studied by solving numerically the coupled rate equations and the propagation equation of the optical pulse intensity, using experimental parameters as input. We suggest a new method to measure the lifetime of the triplet state.     

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.     

Intermediate Self-similar Solutions of the Nonlinear Schrödinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

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.     

What causes the superluminal propagation of light pulses

In this paper, we discuss what causes the superluminal propagation of a pulse through dispersion bysolving Maxwell's equations without any approximation. The coherence of the pulse plays an importantrole for superluminal propagation. When the pulse becomes partially coherent,the propagation changesfrom superluminal to subluminal. The energy velocity is always less than the vacuum velocity.The shapeof the pulse is changed during the propagation.     

Pulse propagation of acoustic waves scattered in a channel

When acoustic waves are scattered by random sound-speed fluctuations in a two-dimensional channel the energy is continually transferred between the propagating modes. In the multiple- scattering region the energy flux assumes an asymptotic form in which there is equal energy flux propagating in each mode. Here we shall make use of this well known result to show how to obtain an asymptotic form for a pulse of acoustic energy propagating in the channel. In the multiple-scattering region the speed of the acoustic waves in the pulse continually changes as the energy is transferred between the modes. The process is basically a diffusion process around the mean speed of propagation. We shall first show, using physical arguments, that the diffusion coefficient is proportional to the square root of the propagation distance times the mean free path of scattering. The theory governing the acoustic propagation in the channel is formulated in terms of modal coherence equations and we shall next give a brief review of the definitions of the coherence functions and a discussion of how the equations governing the propagation of the modal coherence functions are derived. We shall then show how the pulse shape and the relevant parameters may be obtained by solving the basic modal coherence equations at large propagation distances.     

Pulse trains propagating through excitable media subjected to external noise

We study the propagation of periodic pulse trains in excitable media exposed to external spatio-temporal noise using the light-sensitive Belousov-Zhabotinsky reaction with the underlying Oregonator model as representative example. In the weak noise approximation we find noise-induced transitions in the dispersion relation of pulse trains. We discuss noise-enhanced propagation of pulse trains within a certain wave-length range caused by external noise of moderate strength.     

Generation and propagation of subpicosecond pulse train

Higher-order nonlinear Schr\"{o}dinger equation with the Hirota constraint conditions is considered, and an analytic solution, which can describe the modulational instability process, is presented. Based on the solution, a new pulse train without continuous wave (CW) background is generated in quadratures and the propagation of the pulse train is discussed in detail by simulating numerically. The results show that, unlike the propagation of the picosecond pulse train, under the effects of the higher-order terms, the pulse train cannot propagate along the fibre when the energy is very high; however, for some medium energy the pulse train can stably propagate. We also investigate the stability of the pulse train against violation of the Hirota conditions, and the results show that the pulse train can still propagate stably when the Hirota conditions are broken.     

Reverse propagation of femtosecond pulses in optical fibers

We present a numerical technique for reversing femtosecond pulse propagation in an optical fiber, such that given any output pulse it is possible to obtain the input pulse shape by numerically undoing all dispersion and nonlinear effects. The technique is tested against experimental results, and it is shown that it can be used for fiber output pulse optimization in both the anomalous and normal dispersion regimes.     

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.     

Tunable pulse delay in an anisotropic metamaterial slab

We show that large and tunable pulse delays can be obtained at propagation through an anisotropic metamaterial slab. The pulse delay depends not only on frequency but also on the incident/propagation angle and polarization of the electromagnetic field, the last two parameters being much easier to tune than the frequency of the incident field. Although there is a trade-off between large pulse delay values and large tuning ranges, the pulse delay can be modified several times by changing the incidence angle. The results apply to a wide frequency range, from the visible to the THz spectrum.