Propagation Of Short Light Pulses Research Articles

Dynamic Description of soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms

Abstract The article presents an analytical solution for the higher-order nonlinear Schrödinger equation (NLSE), which describes the propagation of short light pulses in monomode optical fibers. Various traveling wave solutions are obtained using the generalized exponential rational function method, a technique with substantial applications in physics and mathematics. Additionally, the parameters leading to the occurrence of optical bright and multipeak solitons in this medium are provided along with their formation conditions. The derived solutions are graphically displayed to enhance the understanding of the model’s physical phenomena. This approach is credible, potent, and successful in solving a wide variety of different models of this kind that arise in the applied sciences. Its robustness, strength, and efficiency make it suitable for addressing various higher-order nonlinear problems in current research fields, extending beyond the models encountered in the applied sciences.

Nonlinear dynamics of short light pulse in birefringent optical fiber

This paper is devoted to the investigation of phase portraits analysis of a vector short pulse equation describing propagation of short light pulses in birefringent optical fiber. Indeed, we introduce transformations that are helpful in decoupling this equation and following the fourth order runge–kutta scheme, we construct phase portraits of the system under interest. The analysis of the phase portrait shows that the system possesses soliton solutions and periodic solutions. We derive Hamiltonian like energy of the system and show that the system is conservative. By double integration, we construct some expressions of the solutions to the system by direct integration which differ from the solutions previously obtained in the literature by the fact that they are difficult to be expressed explicitly as functions of the phase of the wave.

Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative

Abstract This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M- fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa–Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., β=0.1, the magnitude of truncated M-fractional derivative is greater whereas for increasing fractional orders, i.e., β=0.7 and β=0.99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.

Transversally travelling ultrasound for light guiding deep into scattering media

The application of optical methods for tissue diagnosis, activation, and treatment suffers dramatically from the low accessible depths due to strong light scattering in tissues. Here we demonstrate a method to address this issue by utilizing transient ultrasound waves, travelling transversally to the light propagation direction, to guide light into deeper tissue regions. We study the formation of the ultrasound-induced refractive index structures and waveguides using simple ultrasound field configurations and analyze their effects on the propagation of short light pulses. As a proof of concept, we demonstrate using 5 ns pulses of 532 nm light and Intralipid-20%-based phantoms with mu _{mathrm{s}}^prime up to 4.5 cm−1 a waveguide supported light intensity increase up to the depths of at least 90 mean free paths.

Soliton solutions of the Sasa–Satsuma equation in the monomode optical fibers including the beta-derivatives

The main goal of the present paper is to steer an investigation on the dynamics of soliton solutions of a nonlinear model in the monomode optical fibers. In this respect, first, soliton solutions of the model termed as the Sasa–Satsuma (SS) equation describing the propagation of short light pulses are derived in the presence of the beta-derivatives; then, the dynamics of soliton solutions in the monomode optical fibers is analyzed for different values of the parameter β. The soliton solutions presented in this study are categorized in the most common classes of solitons namely bright and dark soliton solutions.

Study of optical soliton fibers with power law model by means of higher-order nonlinear Schrödinger dynamical system

Abstract In this paper, the higher-order nonlinear Schrodinger equation (NLSE) represents description of the propagation of short light pulses in mono-mode optical fibers. The optical solitons and solitary wave solutions of higher-order nonlinear Schrodinger equation mono-mode optical fibers are organized by apply the modified simple equation method to get the exact solutions and possibility of given this solution graphically at a given moment. This solutions help the researchers to study the physical properties of this model and its applications. There are many different types of models that we find in applied science that can be solved by this effective and reliable method. This method can be effective and successful in solving and understanding many of the problems of higher-order non-linear in the various fields of research and advanced.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Optical pulse propagation in monomode fibers with higher order nonlinear Schrödinger equation

In this article, we have discussed the analytical solution to the higher order nonlinear Schrödinger equation representing the propagation of short light pulses in the monomode optical fibers. The so-called bright, dark and singular solutions are founded with solitary wave ansatz method. Moreover, the (1/G′)-expansion and the modified simple equation methods are also applied to extract some new traveling wave solutions.

Optical soliton solutions of higher order nonlinear Schrödinger equation in monomode fibers and its applications

In this article, we have discussed the analytical solution to the higher order nonlinear Schrödinger equation representing the propagation of short light pulses in the monomode optical fibers. A simple transformation is introduced to convert the nonlinear partial differential equation into an ordinary differential equation. A verity of traveling solutions are obtained by employing the auxiliary equation method. The technique can also be functional to other sorts of nonlinear evolution equations in contemporary areas of research.

Propagation of short lightpulses in microring resonators: Ballistic transport versus interference in the frequency domain

The propagation of short lightpulses in waveguiding structures with optical feedback, in our case optical microresonators, has been studied theoretically and experimentally. It appears that, dependent on the measurement set-up, ballistic transport or interference in the time domain of fs and ps laser pulses can be observed. The experiments are analyzed in terms of characteristic time scales of the source, the waveguide device and the detector arrangement and are related to Heisenberg’s uncertainty principle. Based on this analysis, a criterion is given for the upper bit-rate for error free data transmission through optical microresonators.

Least-squares support vector machines modelization for time-resolved spectroscopy

By use of time-resolved spectroscopy it is possible to separate light scattering effects from chemical absorption effects in samples. In the study of propagation of short light pulses in turbid samples the reduced scattering coefficient and the absorption coefficient are usually obtained by fitting diffusion or Monte Carlo models to the measured data by use of numerical optimization techniques. In this study we propose a prediction model obtained with a semiparametric modeling technique: the least-squares support vector machines. The main advantage of this technique is that it uses theoretical time dispersion curves during the calibration step. Predictions can then be performed by use of data measured on different kinds of sample, such as apples.

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 μm and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems. Our simulations studies three different profiles, linear, hyperbolic, and constant. One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show any oscillation in the CE value ( log η ), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C i for the generated FWM signal at ω 3 was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems.

Propagation of exciton polaritons in inhomogeneous semiconductor films

A theoretical study of the propagation of short light pulses in semiconductor slabs containing excitons has been performed using the scattering-state technique and the steepest-descent method. These methods have allowed us to calculate numerically and to describe analytically the temporary behavior of the dielectric polarization inside the films as well as the time-resolved optical transmission spectra. The inhomogeneous broadening of exciton resonances has been taken into account within a local model. The appearance of a grating of the dielectric polarization in a semiconductor film illuminated by a short light pulse is predicted. This grating, which is due to interfering exciton polaritons, moves backward with respect to the light-propagation direction. We have shown that reabsorption and re-emission of photons by excitons in quantum wells and semiconductor films have a crucial effect on the coherent time-resolved spectra of these structures. The time-resolved transmission decay rate is found to depend on the thickness of semiconductor films with inhomogeneously broadened exciton resonances, which is not the case for a purely homogeneously broadened exciton. This fact, which follows from the energy dependence of the polariton damping in the former case, has also been explained in terms of multiple reabsorption--re-emission of photons by excitons.

Optical Solitary Waves in the Higher Order Nonlinear Schrödinger Equation

We study solitary wave solutions of the higher order nonlinear Schrodinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the equation to a two-parameter canonical form. Solitary wave (1-soliton) solutions exist provided easily met inequality constraints on the parameters in the equation are satisfied. Conditions for the existence of N-soliton solutions (N>1) are determined; when these conditions are met the equation becomes the modified KdV equation. A proper subset of these conditions meet the Painleve plausibility conditions for integrability.

The influence of the atomic relaxation on the resonant propagation of short light pulses

The propagation of strong and short laser pulses in a medium of two-level atoms is numerically investigated. The spontaneous and collisional relaxation rates are taken into account. The behavior of the pulse envelope and its Fourier transform is studied in connection with the area theorem and formation of the 2nπ-pulses. Particularly, sudden transitions from 2nπ value of the pulse area to 2(n−1)π are predicted. This effect is associated by a sudden change of the energy losses per unit distance.

“Temporal modes” representation of propagating light pulses

A theoretical analysis of the propagation of short light pulses in a dispersive medium is presented. By using the full power series expansion of the dispersive phase, a representation of the propagation radiation as a sum of so called “temporal modes” is obtained. It is shown that the spectral properties of different temporal modes may be used to control the pulse temporal profile.

Bifurcations and stochasticity induced by an external noise in a laser with a nonlinear absorber

A numerical investigation is reported of a five-dimensional dynamic system describing a laser (specifically a CO2 laser) with a nonlinear absorber (in the form of a CO2 cell). Two regions of periodic modulation of the Q factor are found at low and high pressures of the absorbing gas. The laws describing the behavior of the characteristics of a sequence of pulses are based on the general theory of bifurcations and of propagation of short light pulses in amplifying and absorbing media. A mechanism in which an external noise causes stochastization of spontaneous fluctuations is identified and the conditions under which this can occur are investigated.

Transmission of semiconductor laser radiation pulses along an optical fiber

The time of propagation of short light pulses along optical fibers of different lengths was determined. A study was made of the dependence of the passband of an optical fiber on the angle of entry of the beam into the fiber and on the fiber length. The passband decreased with increasing number of bends in the fiber. A study was made of the transmission of a sequence of spikes through a fiber.