Propagation Of Ultrashort Light Pulses Research Articles

The dynamic behaviors between double-hump solitons in birefringent fibers

In this paper, we research the fractional coupled Hirota equations with variable coefficients describing the collisions of two waves in deep oceans and the propagation of ultrashort light pulses in birefringent fibers and successfully acquire the double-hump one-soliton, two-solitons and N-solitons solutions via the Hirota bilinear method. At the same time, the Bäcklund transformation and the corresponding soliton solutions are also obtained. Based on the precise forms of the solitons solutions, we gain double-hump solitons images with different shapes including U-shape, V-shape and wave-type by assigning proper functions to the group velocity dispersion and the third-order dispersion and analyze the interaction dynamics of double-hump solitons. It is worth noting that the Hirota bilinear operators involved here are fractional rather than integer, which has never appeared in previous literatures.

H 2-solutions for an Ostrosky–Hunter type equation

The Ostrosky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth, for the evolution of nonlinear propagation of optical pulses of a few oscillations duration in dielectric media, and for the evolution of the propagation of ultra-short light pulses in silica optical fibers. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Exploring the Dynamics of Dark and Singular Solitons in Optical Fibers Using Extended Rational Sinh–Cosh and Sine–Cosine Methods

Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method

This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The equation models the propagation of ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solution and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as dark, periodic, singular periodic, combined bright-dark. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to the optic fiber industry.

Darboux Transformation for the Hirota Equation

The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and then construct its quasideterminant solutions. The multisoliton and breather solutions of the Hirota equation are given explicitly.

Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system

The propagation of ultrashort light pulses in a birefringent optical fiber exhibiting spatiotemporal dispersion, cross- and self-phase modulation, self-steepening, and group-velocity dispersion effects is addressed. The evolution of light pulses in such system is described by the coupled Fokas-Lenells equations which offer an accurate description of pulse dynamics in the femtosecond range when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrödinger equation are sustained. We report the first analytical demonstration of the propagation of chirped solitons in a birefringent fiber medium governed by the coupled Fokas-Lenells equations. The formation of those nonlinearly chirped solitons in the optical material may be attributed to the presence of self-steepening process. The results show that the frequency chirp associated with each of the two field components is directly proportional to the total intensity of the pulse. The chirped solitons for the system including the dark-dark and bright-bright soliton pairs in the presence of all fiber parameters are retrieved. The chirps accompanying the soliton pairs are also determined. The existence constraints of these chirped solitons are presented. In addition, the stability of the chirped solutions with respect to the finite perturbations is studied numerically.

Chirped self-similar solitary waves in optical fibers governed with self-frequency shift and varying parameters

We demonstrate that when self-frequency shift effect is the dominant higher-order nonlinear process affecting ultrashort light pulse propagation in an inhomogeneous optical fiber media, a novel class of self-similar solitary waves that are characterized by a nonlinear chirp existed. The solitary wave profiles are of bright, dark, kink, and gray type, illustrating the potentially rich set of chirped self-similar pulses in the inhomogeneous fiber system. Compared with the cubic nonlinear Schrödinger equation with distributed coefficients, the phase of these chirped pulses exhibits a nonlinear structure which makes them more suitable for diverse physical applications. The application of obtained chirped self-similar pulses is also discussed in a periodic distributed amplification system. The results show that one may control the propagation dynamics of the presented nonlinearly chirped pulses by an appropriate choice of the dispersion and nonlinearity parameters.

Recordable-Time Extension of Digital Light-in-Flight Recording by Holography Using a Polarization-Imaging Camera

Digital light-in-flight recording by holography is a powerful tool for observing ultrashort light pulse propagation as a motion picture. However, the recordable time of the technique has been limited by the lateral length of the image sensor used for the recording of the hologram, and no technique for extending the recordable time has been reported yet. Then, to extend the recordable time of digital light-in-flight recording by holography, we proposed a technique that records two holograms as a single hologram using double reference light pulses with an image sensor. In this technique, the image sensor is spatially divided into multiple micro-areas. Each micro-area consists of 2 × 1 pixels and records 1 pixel of each of the two holograms. We employed a polarization-imaging camera in order to implement the proposed technique to extend the recordable time. This technique is a new application of the polarization-imaging camera. We experimentally succeeded in extending the recordable time for the first time using the proposed technique. Specifically, we recorded the motion picture of the ultrashort light pulse propagation for 1.04 ps.

Propagation of dipole solitons in inhomogeneous highly dispersive optical-fiber media.

We consider ultrashort light pulse propagation through an inhomogeneous monomodal optical fiber exhibiting higher-order dispersive effects. Wave propagation is governed by a generalized nonlinear Schrödinger equation with varying second-, third-, and fourth-order dispersions, cubic nonlinearity, and linear gain or loss. We construct a type of exact self-similar soliton solution that takes the structure of a dipole via a similarity transformation connected to the related constant-coefficients one. The conditions on the optical-fiber parameters for the existence of these self-similar structures are also given. The results show that the contribution of all orders of dispersion is an important feature to form this kind of self-similar dipole pulse shape. The dynamic behaviors of the self-similar dipole solitons in a periodic distributed amplification system are analyzed. The significance of the obtained self-similar pulses is also discussed. By performing numerical simulations, the self-similar soliton solutions are found to be stable under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Numerical analysis of the Hirota equation: Modulational instability, breathers, rogue waves, and interactions.

In this paper, we focus on the integrable Hirota equation, which describes the propagation of ultrashort light pulses in optical fibers. First, we numerically study spectral signatures of the spatial Lax pair with distinct potentials [e.g., solitons, Akhmediev-Kuznetsov-Ma (AKM) and Kuznetsov-Ma (KM) breathers, and rogue waves (RWs)] of the Hirota equation. Second, we discuss the RW generation by using the dam-break problem with a decaying initial condition and further analyze spectral signatures of periodized wavetrains. Third, we explore two kinds of noise-derived modulational instabilities: (i) the one case is based on the initial condition (one plus a random noise) such that the KM and AKM breathers, and RWs can be generated, and they agree well with analytical solutions; (ii) another case is to consider another initial condition (one plus a Gaussian wave with a random noise phase) such that some RWs with higher amplitudes can be found. Moreover, we also investigate the spectral signatures of corresponding periodic wavetrains. Finally, we find that the interactions of two waves can also generate the RW phenomena with higher amplitudes. These obtained results will be useful to understand the RW generation in the third-order nonlinear Schrödinger equation and other related models.

Dispersionless limit of the (1+1)-dimensional Fokas-Lenells equation

Nonlinear dispersionless equations can be obtained as dispersionless limits (quasiclassical limits) of integrable hierarchies of equations or by constructing a system of hydrodynamic type. In this paper, the dispersionless limit of the (1+1)-dimensional Fokas-Lenells equation is found. We present Lax pair for this dispersionless equation. As well known, the Fokas-Lenells equation characterizes the propagation of ultrashort nonlinear light pulses in optical fibers. Exact solutions of the dispersionless version of the Fokas-Lenells equation describe nonlinear shock waves in optical fiber systems. By using the obtained results, one can find shock wave solutions of the dispersionless equation, which have different physical applications.

Extending recordable time of light-in-flight recording by holography with double reference light pulses.

Light-in-flight (LIF) recording by holography is a powerful technique for observing ultrashort light pulse propagation. However, the recordable time of the technique has been limited by the lateral length of the holographic plate. Then, to extend the recordable time of LIF recording by holography, we proposed a space-division multiplexing technique of holograms, which divides the holographic plate longitudinally and uses double reference light pulses. We experimentally demonstrated that the recordable time becomes twice as long as before for the first time, to the best of our knowledge, using the proposed technique. Specifically, we recorded the motion picture of the ultrashort light pulse propagation for 236ps.

Absorption-free superluminal light propagation in a Landau-quantized graphene

In recent years, control of group velocity of light has attracted enormous interest. One of the main challenges is to realize an absorption-free fast or slow light propagation. Here, we study dispersion and absorption properties of a weak probe field in a Landau-quantized graphene and report a gain-assisted superluminal light propagation. Moreover, an attempt is made to develop an analytical expression and necessary parameters for switching the group velocity of the probe field from subluminal to superluminal. It’s worth mentioning that large dephasing rate in graphene offers feasibility of superluminal propagation of ultrashort light pulses. Additionally, dynamical behavior of dispersion and absorption of a weak probe field in a closed-type graphene system is investigated, and it is found that the absorption and dispersion can be dramatically affected by both the relative phase of applied fields and the Rabi frequencies in such a way that a large transient gain can be achieved and a transient absorption can be completely eliminated.

Solitary wave solutions of the Schäfer–Wayne short-pulse equation using two reliable methods

The Schafer–Wayne short-pulse equation, which governs the propagation of ultra-short light pulses in silica optical fibres is analytically investigated. The sine–cosine method and solitary wave ansatz method are used for a reliable treatment of short-pulse equation. It should be noted that the study of this model admitting soliton-type solutions is very useful for future research work.

Well-posedness results for the short pulse equation

The short pulse equation provides a model for the propagation of ultra-short light pulses in silica optical fibers. It is a nonlinear evolution equation. In this paper the wellposedness of bounded solutions for the homogeneous initial boundary value problem and the Cauchy problem associated to this equation are studied.

Pulse propagation in one-dimensional disordered photonic crystals: interplay of disorder with instantaneous and relaxing nonlinearities

Propagation of ultrashort light pulses in disordered multilayers is studied by using numerical simulations in time domain. We consider cases of instantaneous and noninstantaneous Kerr nonlinearities of the structure materials. The competitive nature of disorder and nonlinearity is revealed on the long and short timescales. We also pay special attention to the effect of pulse self-trapping in the photonic crystal with relaxing nonlinearity and show the dependence of this effect on the level of disorder. We believe that the results reported here will be useful not only in the field of optics but also from the standpoint of the general problem of classical waves propagation in nonlinear disordered periodic media.

Ultrashort pulses in an inhomogeneously broadened two-level medium: soliton formation and inelastic collisions

Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.

On the stable propagation of high-intensity ultrashort light pulses

The spatiotemporal dynamics of high-intensity femtosecond laser pulses is studied within a rigorous physical model. The pulse propagation is described by the nonlinear envelope equation. The propagation and the material equations are solved self-consistently at realistic physical conditions. Self-compression of the pulse is found. At certain conditions, transversal width, peak intensity, time duration, and spatiotemporal shape of the pulse remain stable within given propagation range.

Modeling of nonlinear optical activity in propagation of ultrashort elliptically polarized laser pulses

We propose a general model of third-order nonlinear optical susceptibility of isotropic gyrotropic medium with frequency and spatial dispersion. Our model allows for the description of the propagation of ultrashort (several oscillations) elliptically polarized laser pulses in such a medium and does not require smallness of the characteristic nonlocality dimension, unlike the conventional phenomenological model. We implemented our model numerically by means of a modified finite-difference time-domain method with an auxiliary differential equation. We have validated the correctness of our model by the comparison of the results obtained in our numerical simulations with generally known effects observed experimentally and described earlier theoretically for the monochromatic radiation or within the slowly varying envelope approach. We investigated effects accompanying the propagation of ultrashort (several oscillations) light pulses in nonlinear isotropic gyrotropic medium with frequency and spatial dispersion of cubic nonlinearity.

Mathematical simulation of ultrashort light pulse propagation in a highly scattering medium

The problem of probing a nonhomogeneous medium imitating the biological tissue by an ultrashort light pulse is investigated. The pulse propagation in the medium is described by a transient transport equation. A grid algorithm for its solution based on the analytical presentation of the density of the unscattered photon flux is presented as well as a semianalytical algorithm for computing the density of the flux of singly scattered photons. Methodological calculations carried out by the grid method and by the alternative Monte Carlo method are given.