Propagation Of Femtosecond Light Pulses Research Articles

Soliton unveilings in optical fiber transmission: Examining soliton structures through the Sasa–Satsuma equation

The exploration of higher-order and multicomponent extensions of the nonlinear Schrödinger equation holds significant importance across diverse applications, notably within the field of optics. Among these equations, the integrable Sasa–Satsuma equation stands out for its captivating soliton solutions. The Sasa–Satsuma equation serves as a mathematical representation for describing the propagation of femtosecond light pulses through optical fibers. The breather, multiwave, combined dark–bright, singular, dark, bright and periodic singular optical soliton solutions are derived in this paper by using the 1φ(ϑ),φ′(ϑ)φ(ϑ) and multivariate generalized exponential rational integral function approach. Furthermore, the paper emphasizes the essential fiber parameters essential for the emergence of these structures and offers visual representations of chosen solutions to elucidate their physical characteristics. The novelty of this work lies in the inaugural application of these methods to the Sasa–Satsuma equation and gives a significant advancement in the understanding of optical phenomena. This study not only opens avenues for further research but also introduces a fresh perspective on the Sasa–Satsuma model in the field of nonlinear physics with its applications in optical systems.

Periodic and localized waves in parabolic-law media with third- and fourth-order dispersions.

Considering the higher-order nonlinearity is essential in a broad range of real physical media as it significantly influences the wave dynamics in these systems. We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such a system is governed by a higher-order nonlinear Schrödinger equationincorporating second-, third-, and fourth-order dispersions as well as cubic and quintic nonlinearities. The periodic and solitary wave solutions are identified using the equationmethod. Results presented indicated the potentially rich set of periodic waves in the system under the combined influence of higher-order dispersive effects and cubic-quintic nonlinearity. The velocity of these structures is uniquely dependent on all orders of dispersion. Conditions on the optical fiber parameters for the existence of these exact stable solutions are found by analytical stability analysis.

Propagation of periodic and solitary waves in a highly dispersive cubic–quintic medium with self-frequency shift and self-steepening nonlinearity

We study the dynamics of femtosecond light pulse propagation in a cubic–quintic medium exhibiting dispersive effect up to the fourth order as well as self-frequency shift and self-steepening nonlinearity. A rich variety of periodic and solitary wave solutions are derived for the governing generalized higher-order nonlinear Schrödinger equation in the presence of self-frequency shift and self-steepening effects. It is found that the frequency shift, inverse velocity, amplitude and wave number of both periodic and solitary waves depend on dispersion coefficients and nonlinearity parameters as well. The conditions on optical fiber parameters for the existence of these structures are presented. The stability of these periodic and solitary wave solutions is studied numerically by adding white noise. It is proved by using the numerical split-step Fourier method that the derived exact solutions are stable by Lyapunov criteria.

The stability issues in problems of mathematical modeling

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

On optical solitons: the nonlinear Schrödinger equation with self-steepening and self-frequency shift

This article studies the dynamics of optical solitons in cubic-quintic nonlinear Schrodinger model that describes the propagation of femtosecond light pulses in optical fibers. The model is considered with self-steepening and self-frequency shift. As a result, the dark and singular optical solitons are extracted using \((G^{\prime }/G)\)-expansion scheme. Additionally, the constraint conditions for the existence of these solutions are also listed.

Imaging the propagation of light through scenes at picosecond resolution

We present a novel imaging technique, which we call femto-photography , to capture and visualize the propagation of light through table-top scenes with an effective exposure time of 1.85 ps per frame. This is equivalent to a resolution of about one half trillion frames per second; between frames, light travels approximately just 0.5 mm. Since cameras with such extreme shutter speed obviously do not exist, we first re-purpose modern imaging hardware to record an ensemble average of repeatable events that are synchronized to a streak sensor, in which the time of arrival of light from the scene is coded in one of the sensor's spatial dimensions. We then introduce reconstruction methods that allow us to visualize the propagation of femtosecond light pulses through the scenes. Given this fast resolution and the finite speed of light, we observe that the camera does not necessarily capture the events in the same order as they occur in reality: we thus introduce the notion of time-unwarping between the camera's and the world's space--time coordinate systems, to take this into account. We apply our femto-photography technique to visualizations of very different scenes, which allow us to observe the rich dynamics of time-resolved light transport effects, including scattering, specular reflections, diffuse interreflections, diffraction, caustics, and subsurface scattering. Our work has potential applications in artistic, educational, and scientific visualizations; industrial imaging to analyze material properties; and medical imaging to reconstruct subsurface elements. In addition, our time-resolved technique has already motivated new forms of computational photography, as well as novel algorithms for the analysis and synthesis of light transport.

Comparison of Solutions of the General Nonlinear Amplitude Equation and a Modified Schrӧdinger Equation

We review the dynamics of narrow and broad-band optical pulses in nonlinear dispersive media. A major problem that arises during the development of theoretical models, which describe accurately and correctly the behavior of these pulses, is the limited application of the nonlinear Schrӧdinger equation. It describes very well the evolution of nanosecond and picosecond laser pulses. However, when we investigate the propagation of femtosecond and attosecond light pulses, it is necessary to use the more general nonlinear amplitude equation. We show that in this equation two additional terms are included and they have a significant impact on the phase of the pulse. We perform numerical simulations and show the temporal shift of the position of fundamental solitons. This effect depends on the initial duration of the laser pulses. To clarify the influence of the additional terms on the parameters of the optical pulses, we consider the nonlinear amplitude equation, which is a modified nonlinear Schrӧdinger equation.

New Exact Solutions for High Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.

Femto-photography

We present femto-photography , a novel imaging technique to capture and visualize the propagation of light. With an effective exposure time of 1.85 picoseconds (ps) per frame, we reconstruct movies of ultrafast events at an equivalent resolution of about one half trillion frames per second. Because cameras with this shutter speed do not exist, we re-purpose modern imaging hardware to record an ensemble average of repeatable events that are synchronized to a streak sensor, in which the time of arrival of light from the scene is coded in one of the sensor's spatial dimensions. We introduce reconstruction methods that allow us to visualize the propagation of femtosecond light pulses through macroscopic scenes; at such fast resolution, we must consider the notion of time-unwarping between the camera's and the world's space-time coordinate systems to take into account effects associated with the finite speed of light. We apply our femto-photography technique to visualizations of very different scenes, which allow us to observe the rich dynamics of time-resolved light transport effects, including scattering, specular reflections, diffuse interreflections, diffraction, caustics, and subsurface scattering. Our work has potential applications in artistic, educational, and scientific visualizations; industrial imaging to analyze material properties; and medical imaging to reconstruct subsurface elements. In addition, our time-resolved technique may motivate new forms of computational photography.

Optical solitary wave solutions for the higher order nonlinear Schrödinger equation with self-steepening and self-frequency shift effects

In this paper, we have obtained the optical solitary wave solutions for the nonlinear Schrödinger equation which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method was used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses were determined. Using the 1-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa-Satsuma cases. We have also constructed some periodic wave solutions of the higher order nonlinear Schrödinger equation by reducing it to quartic anharmonic oscillator equation and by using projective Ricatti equations. Moreover by using He's semi-inverse method, variational formulation was established to obtain exact soliton solutions. The 1-soliton solutions of time dependent form of this equation was also obtained. To visualize the propagation characteristics of dark-bright soliton solutions, few numerical simulations are given.

DARK AND BRIGHT SOLITARY WAVE SOLUTIONS OF THE HIGHER ORDER NONLINEAR SCHRÖDINGER EQUATION WITH SELF-STEEPENING AND SELF-FREQUENCY SHIFT EFFECTS

In this paper, we obtain the exact bright and dark soliton solutions for the nonlinear Schrödinger equation (NLSE) which describes the propagation of femtosecond light pulses in optical fibers in the presence of self-steepening and a self-frequency shift terms. The solitary wave ansatz method is used to carry out the derivations of the solitons. The parametric conditions for the formation of soliton pulses are determined. Using the one-soliton solution, a number of conserved quantities have been calculated for Hirota and Sasa–Satsuma cases and finally, we have constructed some periodic wave solutions by reducing the higher order nonlinear Schrödinger equation (HNLS) to quartic anharmonic oscillator equation. The obtained exact solutions may be useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a HNLS model equation.

Solitary wave solutions for a higher order nonlinear Schrödinger equation

We consider a higher order nonlinear Schrödinger equation with third- and fourth-order dispersions, cubic–quintic nonlinearities, self steepening, and self-frequency shift effects. This model governs the propagation of femtosecond light pulses in optical fibers. In this paper, we investigate general analytic solitary wave solutions and derive explicit bright and dark solitons for the considered model. The derived analytical dark and bright wave solutions are expressed in terms of the model coefficients. These exact solutions are useful to understand the mechanism of the complicated nonlinear physical phenomena which are related to wave propagation in a higher-order nonlinear and dispersive Schrödinger system.

Digital Light-in-Flight Recording by Holography by Use of a Femtosecond Pulsed Laser

We succeeded in digital light-in-flight recording by holography by use of a femtosecond pulsed laser. We recorded and reconstructed a moving picture of femtosecond light pulse propagation on a diffuser plate on which a test chart pattern was printed. A mode-locked Ti:sapphire laser was used as a femtosecond pulsed laser. The center wavelength and the duration of the light pulse were 800 nm and 96 fs, respectively. We conducted a numerical simulation in order to validate the proposed technique. We confirmed that the technique was capable of recording the moving picture of femtosecond light pulse propagation. In addition, we experimentally demonstrated the technique and successfully observed femtosecond light pulse propagation for 576 fs. The experimental results agreed well with the simulation results.

Moving picture recording and observation of femtosecond light pulse propagation using a rewritable holographic material

We succeeded in recording and observing femtosecond light pulse propagation as a form of moving picture by means of light-in-flight recording by holography using a rewritable holographic material, for the first time. We used a femtosecond pulsed laser whose center wavelength and duration were 800 nm and ∼120 fs, respectively. A photo-conductor plastic hologram was used as a rewritable holographic material. The femtosecond light pulse was collimated and obliquely incident to the diffuser plate. The behavior of the cross-section between the collimated femtosecond light pulse and the diffuser plate was recorded on the photo-conductor plastic hologram. We experimentally obtained a spatially and temporally continuous moving picture of the femtosecond light pulse propagation for 58.3 ps. Meanwhile, we also investigated the rewritable performance of the photo-conductor plastic hologram. As a result, we confirmed that ten-time rewriting was possible for a photo-conductor plastic hologram.

Moving Picture Recording and Observation of Visible Femtosecond Light Pulse Propagation

We succeeded in recording and observing a spatially and temporally continuous moving picture of visible femtosecond light pulse propagation by using light-in-flight recording by holography, for the first time. We applied second-harmonic generation (SHG) to a NIR femtosecond light pulse from a mode-locked Ti:sapphire laser to generate a visible femtosecond light pulse. The center wavelength and duration of the generated light pulse were 400 nm and ∼100 fs, respectively. We acquired a moving picture of a visible and collimated femtosecond light pulse that propagated on a diffuser plate for 145 ps.

Moving Picture Recording and Observation of Visible Femtosecond Light Pulse Propagation

We succeeded in recording and observing a spatially and temporally continuous moving picture of visible femtosecond light pulse propagation by using light-in-flight recording by holography, for the first time. We applied second-harmonic generation (SHG) to a NIR femtosecond light pulse from a mode-locked Ti:sapphire laser to generate a visible femtosecond light pulse. The center wavelength and duration of the generated light pulse were 400 nm and ∼100 fs, respectively. We acquired a moving picture of a visible and collimated femtosecond light pulse that propagated on a diffuser plate for 145 ps.

Moving picture recording and observation of femtosecond light pulse propagation by use of rewritable holographic material

We succeeded in recording and observation of the femtosecond light pulse propagation as a form of moving picture by means of light-in-flight recording by holography that used a rewritable holographic material, for the first time. We used a femtosecond pulsed laser whose center wavelength and duration were 800 nm and ∼120 fs, respectively. A photo-conductor plastic hologram was used as a rewritable holographic material. The femtosecond light pulse was collimated and obliquely incident to the diffuser plate. The behavior of the cross-section between the collimated femtosecond light pulse and the diffuser plate was recorded on the photo-conductor plastic hologram. We experimentally obtained a spatially and temporally continuous moving picture of the femtosecond light pulse propagation for 58.3 ps. Also, we investigated the rewritable performance of the photo-conductor plastic hologram. As a result, we confirmed that ten-time rewriting was possible for a photo-conductor plastic hologram.

A simple ansatz for obtaining exact solutions of high dispersive nonlinear Schrödinger equations in fiber Bragg gratings

We present solitary wave solutions for the perturbed nonlinear Schrödinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrödinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe bright and dark Bragg solitons properties in the same expressions and their amplitude may approach nonzero when the time variable approaches infinity. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in fiber Bragg grating.

Moving picture recording and observation of three-dimensional image of femtosecond light pulse propagation

We recorded and observed, for the first time, three-dimensional image of femtosecond light pulse propagation as continuous moving picture using light-in-flight recording by holography. We present the moving pictures of collimated and converging light pulses and some images extracted from them. We also discussed inherent feature appearing in the images. Such a discussion is essential to determine the actual shape of the propagating light pulse. This technique provides the means for observation of a temporally and spatially continuous moving picture of light itself and also enables the analysis of various kinds of ultrafast phenomena.

Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation

We consider the higher-order dispersive nonlinear Schrödinger equation including fourth-order dispersion effects and a quintic nonlinearity. This equation describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. By adopting the ansatz solution of Li et al. [Zhonghao Li, Lu Li, Huiping Tian, Guosheng Zhou. New types of solitary wave solutions for the higher-order nonlinear Schrödinger equation. Phys Rev Lett 2000;84:4096], we find two different solitary wave solutions under certain parametric conditions. These solutions are in the form of bright and dark soliton solutions.