Propagation Of Optical Solitons Research Articles

Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion

The vector-coupled nonlinear Schrödinger equation, which can be applied to describe the propagation of Thirring optical solitons in birefringent fibers with Kerr law nonlinearity, detuning, intermodal dispersion and spatiotemporal dispersion, has been studied analytically. By means of the complex envelope function ansatz, exact Thirring bright-dark combosolitons are reported, and the properties of these solitons are discussed.

Exact solitons in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity

This work studies the optical solitons in the physical model that describes the propagation of optical solitons in a medium with competing weakly nonlocal nonlinearity and parabolic law nonlinearity via the [Formula: see text]-expansion scheme, exact dark and singular one-soliton solutions, along with the constraint conditions, are reported.

Bright, dark, and singular solitons in optical fibers with spatio-temporal dispersion and spatially dependent coefficients

Investigated in this work is the nonlinear Schrödinger equation with space-dependent parameters, which models the propagation of optical solitons in spatially inhomogeneous optical fiber with detuning, spatiotemporal dispersion, intermodal dispersion, and fiber gain or loss. Through the ansatz scheme, analytical bell, kink, and singular soliton solutions under certain coefficient constraints are obtained.

Analytical study of solitons in magneto-electro-elastic circular rod

The nonlinear longitudinal wave equation, describing the propagation of optical solitons in magneto-electro-elastic circular rod, is investigated analytically. Two integration tools that are traveling wave hypothesis and G\(^{\prime }\)/G expansion scheme are recruited to extract explicit soliton solutions. The existence conditions are derived.

Angle-resolved photoemission spectroscopy with 9-eV photon-energy pulses generated in a gas-filled hollow-core photonic crystal fiber

A recently developed source of ultraviolet radiation, based on optical soliton propagation in a gas-filled hollow-core photonic crystal fiber, is applied here to angle-resolved photoemission spectroscopy (ARPES). Near-infrared femtosecond pulses of only few μJ energy generate vacuum ultraviolet radiation between 5.5 and 9 eV inside the gas-filled fiber. These pulses are used to measure the band structure of the topological insulator Bi2Se3 with a signal to noise ratio comparable to that obtained with high order harmonics from a gas jet. The two-order-of-magnitude gain in efficiency promises time-resolved ARPES measurements at repetition rates of hundreds of kHz or even MHz, with photon energies that cover the first Brillouin zone of most materials.

Analytical study of Thirring optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

This paper presents for the first time an analytic study on Thirring optical solitons in birefringent fibers with parabolic law nonlinearity and spatio-temporal dispersion. The dynamical model for the propagation of Thirring optical solitons is given by the vector coupled nonlinear Schrodinger equation, which is investigated analytically using two different ways. These algorithms, that are the traveling wave hypothesis and the P6 model scheme are employed to obtain bright, dark as well as singular solitons. The integrability conditions are also exhibited.

Continuous Solitons in a Lattice Nonlinearity.

We study theoretically and experimentally the propagation of optical solitons in a lattice nonlinearity, a periodic pattern that both affects and is strongly affected by the wave. Observations are carried out using spatial photorefractive solitons in a volume microstructured crystal with a built-in oscillating low-frequency dielectric constant. The pattern causes an oscillating electro-optic response that induces a periodic optical nonlinearity. On-axis results in potassium-lithium-tantalate-niobate indicate the appearance of effective continuous saturated-Kerr solitons, where all spatial traces of the lattice vanish, independently of the ratio between beam width and lattice constant. Decoupling the lattice nonlinearity allows the detection of discrete delocalized and localized light distributions, demonstrating that the continuous solitons form out of the combined compensation of diffraction and of the underlying periodic volume pattern.

Bilinearization of the generalized coupled nonlinear Schrödinger equation with variable coefficients and gain and dark-bright pair soliton solutions.

We investigate coupled nonlinear Schrödinger equations (NLSEs) with variable coefficients and gain. The coupled NLSE is a model equation for optical soliton propagation and their interaction in a multimode fiber medium or in a fiber array. By using Hirota's bilinear method, we obtain the bright-bright, dark-bright combinations of a one-soliton solution (1SS) and two-soliton solutions (2SS) for an n-coupled NLSE with variable coefficients and gain. Crucial properties of two-soliton (dark-bright pair) interactions, such as elastic and inelastic interactions and the dynamics of soliton bound states, are studied using asymptotic analysis and graphical analysis. We show that a bright 2-soliton, in addition to elastic interactions, also exhibits multiple inelastic interactions. A dark 2-soliton, on the other hand, exhibits only elastic interactions. We also observe a breatherlike structure of a bright 2-soliton, a feature that become prominent with gain and disappears as the amplitude acquires a minimum value, and after that the solitons remain parallel. The dark 2-soliton, however, remains parallel irrespective of the gain. The results found by us might be useful for applications in soliton control, a fiber amplifier, all optical switching, and optical computing.

Dynamic behavior of the incoherent optical spatial solitons in a nonlocal nonlinear medium

Dynamic behavior of the propagation of incoherent optical spatial solitons in a nonlocal nonlinear medium is investigated. By means of the Hirota method, we obtain the soliton solutions, based on which we find that is positively related to , but inversely related to and , whereas is independent of them, with as the slowly varying amplitude of the beam, as the refractive index change, , , and as the unperturbed refractive index, frequency of the propagating beam, and beam intensity distribution, respectively. Head-on and bound-state soliton interactions are both given, and one interaction period decreases with and increasing in the bound state one. With the external perturbations taken into consideration, the associated chaotic motions of the perturbed model are studied, and the corresponding power spectra and phase projections are obtained. Both the weak and developed chaotic states are investigated, and the difference between them roots in the relative magnitude of nonlinearities and perturbations. Such chaotic motions can be weakened via increasing and or decreasing . Periodic motion is obtained with the nonlinearities and perturbations balanced.

Exact optical solitons in metamaterials with cubic–quintic nonlinearity and third-order dispersion

This work studies the propagation of optical solitons through nonlinear metamaterials in the presence of spatio-temporal dispersion, parabolic law nonlinearity (cubic–quintic nonlinearity), detuning, inter-modal dispersion, self-steepening, Raman effect, nonlinear dispersion and third-order dispersion. Two integration approaches that are the Riccati equation expansion method and the ansatz scheme are applied to extract exact solitons. Finally, analytical bright, dark as well as singular soliton solutions are reported along with their respective restrictions for the first time.

Bright, dark and singular optical solitons in a cascaded system

This work studies nonlinear dynamics of optical solitons in a cascaded system with Kerr law nonlinearity and spatio-temporal dispersion. The mathematical model that describes the propagation of optical solitons through a cascaded system is given by the vector-coupled nonlinear Schrödinger equation. It is investigated analytically using three integration algorithms. The Jacobian elliptic equation expansion method, Bernoulli equation expansion approach and Riccati equation expansion scheme are the integration tools of this model that are recruited to extract singular, bright and dark solitons. The restrictions that need to hold for the existence of these solitons are derived.

Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.

Rogue-wave interaction of the generalized variable-coefficient Hirota–Maxwell–Bloch system in fiber optics

In this paper, a generalized variable-coefficient Hirota–Maxwell–Bloch system is investigated, which can describe the propagation of optical solitons in an erbium-doped optical fiber. Higher-step generalized Darboux transformation and rogue-wave solutions are obtained. Rogue-wave interaction is analyzed as follows: (1) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the first-step rogue waves for the modulus of the normalized slowly varying amplitude of the complex pulse envelope, modulus of the measure of the polarization of the resonant medium and extant population inversion; (2) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the second-step rogue-wave interaction. Those phenomena can not be attained through the existing Hirota–Maxwell–Bloch system.

Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

The nonlinear Schrödinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.

Wavelet based spectral analysis of optical solitons

The propagation of solitons or a pulse or a signal through optical fibers has been a major area of research given its potential applicability in all optical communication systems. In a modern optical communication system, the transmission link is composed of optical fibers and amplifiers. This manifests in noise, clutters and distortion when the signal propagates through optical fibers, consequently affecting the capacity and performance of the optical system. The dynamics of solitons has therefore become an active field of research in nonlinear optics for couple of decades. The nonlinear Schrodinger's equation (NLSE) with log law nonlinearity governs the propagation of optical solitons through optical fibers and its dynamics. Most of the studies reveal that the optical solitons have Gaussian wave profile called Gaussons. This entails the use of wavelet techniques for the processing of optical solitons.Signal processing in optical fiber has two distinct areas of investigations; one, the pulse propagation and the other, signal analysis and synthesis. We, in this work, focus on the later, the signal analysis and synthesis in wavelet spectral framework. For this, new wavelet formalism is proposed for analyzing the Gausson signals transmitted through optical fiber by introducing a nonlinear wavelet-like basis of scaling functions leading to wavelet spectra. The proposed method provides computational algorithm to obtain the Gausson parameters – amplitude and the dispersion, the width and velocity of the traveling soliton, which completely characterize the Gaussian signal. In the end, some of the spectral measures useful for further synthesis of the signal are discussed.

The effect of atomic and optical perturbations on formation and propagation of vortex solitons in a dense atomic media of gas-filled hollow-core optical fibers

We consider the influence of optical and temperature-dependent atomic fluctuations on the formation and propagation of optical vortex solitons in dense media realized as hollow-core optical fibers filled with a cold atomic gas in presence of optical pumping. We show different perturbation-induced scenaria of complete destruction and smooth transformations of the topological characteristics of localized optical structures in hollow-core fiber. The maximum levels of optical and atomic fluctuations at which the soliton regime can be maintained has been determined. The estimates for these levels show an opportunity to observe the optical vortex solitions in the core-filling gas of the fiber for temperatures smaller than the critical temperature for Bose-Einstein condensate.

Propagation properties of soliton solutions under the influence of higher order effects in erbium doped fibers

Under investigation in this paper is the Hirota–Maxwell–Bloch system which governs the propagation of optical solitons in nonlinear erbium doped fibers with higher order effects. By virtue of the Darboux transformation, the Akhmediev breathers, Ma-breathers, localized solitons, bound solitons, two-breathers and localized solutions are generated for the Hirota–Maxwell–Bloch system. Considering the influences of higher order effects, propagation properties of the breathers, modulation instability conditions for the Akhmediev breathers and interaction scenarios between bound solitons and two-breather solutions are discussed.

Optical solitons in birefringent fibers with parabolic law nonlinearity

This paper studies the propagation of optical solitons through birefringent fibers with parabolic law nonlinearity. The Hamiltonian perturbations that are inter-modal dispersion, self-steepening, third-order dispersion and nonlinear dispersions are taken into account. Both, Riccati equation expansion method and Jacobian elliptic equation expansion method are used. Finally, analytical solutions that are Jacobian elliptic periodic traveling wave solutions, periodic solutions, unbounded solutions, singular solutions, bright and dark soliton solutions are obtained under several constraint conditions.

Modulation Instability, Breathers, and Bound Solitons in an Erbium-Doped Fiber System with Higher-Order Effects

We mainly investigate the generalized nonlinear Schrödinger-Maxwell-Bloch system which governs the propagation of optical solitons in nonlinear erbium-doped fibers with higher-order effects. We deduce Lax pair, analyze modulation instability conditions, construct the Darboux transformation, and derive the Akhmediev breathers, Ma-breathers, bound solitons, and two-breather solutions for this system. Considering the influences of higher-order effects, propagation properties of those solitons are discussed.

Potential formalism of optical spatial soliton propagation in a two-photon photovoltaic–photorefractive material under open circuit condition

Propagation characteristics of optical spatial solitons in a two-photon photovoltaic–photorefractive medium under open circuit condition have been investigated using the formalism of a particle in a potential well. Optical nonlinearity has been evaluated using Castro-Camus model. Variational formalism has been employed to investigate the resulting modified nonlinear Schrodinger equation. Potential formalism has been examined to identify localized optical spatial solitons.