Propagation Of Optical Pulses Research Articles

Nonlinear dispersion of backward-wave four-wave mixing in a photorefractive semiconductor and its effect on group velocity

Photorefractive backward-wave four-wave mixing may be configured for the amplification of the phase conjugate output and the attenuation of the transmitted output. The nondegenerate-in-frequency interaction is studied in such a configuration, realized in a semiconductor CdTe crystal. The spectra measured at different outputs show the gain and attenuation resonances. The preliminary study of optical pulse propagation demonstrates that, due to different nonlinear dispersions at different outputs of the selected wave mixing configuration, a slowing down of light is observed at the phase conjugate output, while an acceleration of light is detected at the transmitted output for the same input pulse at the same interaction.

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Impact of higher order dispersion in the propagation of optical pulse in the photonic crystal fibers - A Projection Operator approach

Optical Pulse Generation with Programmable Positions in an Actively Mode-locked Optical Cavity

Optical Pulse Generation with Programmable Positions in an Actively Mode-locked Optical Cavity

Direct-modulation optoelectronic oscillator for optical pulse and frequency comb generation

We report the generation of an optical pulse train with a 10 GHz repetition rate in a dual loop direct-modulation optoelectronic oscillator (OEO). Pulse generation is achieved using nonlinear compression in the OEO 5-km-long optical delay line. 3 ps pulses with a timing jitter of 13 fs are reported, while the OEO maintains a phase noise of −133dBc/Hz at 10 kHz from the carrier. Two architectures are compared experimentally and theoretically. A frequency comb with a 1.2 THz linewidth at −30dB is generated.

Propagation of broadband mid-infrared optical pulses in atmosphere

We study and describe the reshaping of ultrashort and broadband mid-IR optical pulses in an ambient atmosphere. While all pulse propagation undergoes dispersion and absorption, which causes pulse reshaping, the effects are strongly pronounced for broadband radiation in the mid-IR due to the orders of magnitude greater oscillator strengths of molecular constituents of our atmosphere. A noticeable macroscopic impact is a transition of the measured autocorrelation function from squared hyperbolic secant to Lorentzian, which we fully explain based on pulse propagation, including molecular free induction decay. Electro-optical sampling directly reveals the light wave response to atmospheric molecular free induction decay, and a Kramers–Kronig-based propagation model thoroughly explains the observation. The findings are essential for applications in sensing, standoff detection, high-energy pulse propagation, and energy delivery.

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.

Various exact solutions to the time-fractional nonlinear Schrödinger equation via the new modified Sardar sub-equation method

We aim to investigates the nonlinear Schrödinger equation including time-fractional derivative in (3+1)-dimensions by considering cubic and quantic terms The modified Sardar sub-equation method is used that lead to the discovery of a unique class of optical solutions. To transform the suggested nonlinear equation into an ordinary differential equation, we applied wave transformations, resulting in a set of nonlinear equations that offer diverse solution scenarios. The derived solutions encompass dark, wave, bright, mixed dark-bright, bell-shape, kink-shape, and singular soliton solutions. To enhance our understanding of the dynamic behavior exhibited by these solitons under varying time parameter values, visual simulations through a variety of graphs is presented. Furthermore, a comprehensive comparison is conducted, exploring a range of values for the conformable fractional order parameter. This comparison aims to highlight on the influence of fractional order variations on the solutions, contributing valuable insights into the nuanced dynamics of the system. Overall, this study serves to advance our understanding of nonlinear processes, and its potential applications in real-life phenomena. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons.

Power efficient UAV-assisted FSO communication: novel 4-PAM optical pulse generation and performance analysis in foggy environment

Power efficient UAV-assisted FSO communication: novel 4-PAM optical pulse generation and performance analysis in foggy environment

Dynamic interplay: unveiling inelastic breather collisions and modulation instability enhancement in a periodically gained inhomogeneous fiber optic communication system across temporal frequencies

Examining the impact of inhomogeneity on the propagation of femtosecond ultrafast optical pulses in fiber, we delve into the realm of the modified Hirota nonlinear Schrödinger equation (NLS) with inhomogeneity of variable coefficients (MIH-vc). Employing the Hirota bilinear method, we derive two soliton solutions for the modified Hirota NLS equation and analyze the effect of variable coefficients. The dynamical properties of these soliton solutions come to light as we meticulously analyze the corresponding plots. In our exploration, a noteworthy revelation unfolds as we witness the inelastic collision between two breathers, unleashing profound changes in the trajectory of femtosecond pulses. Furthermore, we showcase a detailed modulation instability analysis, unraveling the gain spectrum for our theoretical model. Through graphical illustrations, we elucidate how inhomogeneous functions intricately shape the modulation instability (MI) gain spectrum. A groundbreaking observation surfaces as, for the first time, we discern the periodic gain enhancement in relation to Group Velocity Dispersion along the fiber and its dynamic interactions.

Dynamics of fractional optical solitary waves to the cubic–quintic coupled nonlinear Helmholtz equation

This work investigates the dynamics of optical waves to the generalized coupled nonlinear fractional Helmholtz equation with quintic and cubic nonlinear effects. The evolution of broad multicomponent self-trapping beams in Kerr-type nonlinear media is described by the coupled Helmholtz equation, which also take into account spatial dispersion due to non-paraxial effects. This phenomena is particularly relevant to the progressive miniaturization of optics, where the optical wavelength is similar to the beam width. It is essential to integrate non-Kerr terms, such as the self-steepening and the self frequency shift, into the coupled Helmholtz system in order to investigate the propagation of ultrashort optical pulses in the non-paraxial domain. For optical wave solutions, nonlinear ordinary equation of the governing model is achieved by applying the fractional transformation. The different types of the solutions like bright, dark, singular and mixed type solitons are extracted by applying advanced integration methods, namely modified Sardar subequation method and new Kudryashov method. These solutions provide very useful information on how the system operates. The applied approaches are highly efficient and have significant computational capability to efficiently tackle the nonlinear systems. Additionally, we include a diverse array of graphs to demonstrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. In the context of the proposed model, these visualizations assist with a comprehensive understanding of the solution’s behavior and characteristics. It is anticipated that these solutions may be significant in the study of wave propagation and related fields.

The integrability and infinite conservation laws of a variable coefficient higher-order Schrödinger equation

In this paper, a variable coefficient high-order Schrödinger equation is studied to describe the propagation of ultrashort optical pulses in dispersion reducing fibers. It has third-order dispersion, self steepening and stimulated Raman scattering effects. Using the Bell polynomial method, the integrability of the variable coefficient higher-order Schrödinger equation is discussed. And the bilinear Bäcklund transformation, Lax pair, and infinite conservation laws of the equation are derived. It can be obtained that the variable coefficient higher-order Schrödinger equation is integrable in the sense of Lax pair. The soliton solutions are constructed from the obtained bilinear Bäcklund transformation and the bilinear form. The obtained results are analyzed in the initial–boundary value problem. It is worth mentioning that this paper, based on the angle of increasing the order, obtained the bilinear Bäcklund transformation of the third order variable coefficient Schrödinger equation by using the Bell polynomial method. On this basis, relevant properties such as Lax pair and infinite conservation laws are also obtained, and analyzed the application in the initial–boundary value problem. This has not been studied in existing literatures.

The impact of Brownian motion on the optical solutions of the stochastic ultra-short pulses mathematical model

The stochastic generalized nonlinear Schrödinger equation (SGNLSE) of third order in the Stratonovich sense is examined here. New elliptic, hyperbolic, trigonometric, and rational stochastic solutions are obtained using a modified mapping method. Because the GNLSE is extensively used in nonlinear optical phenomena, optical fiber communication systems, communication and heat pulse propagation in materials, the obtained solutions may be used to study a broad range of relevant physical phenomena. In order to interpret the effects of multiplicative noise, the dynamic performances of the various obtained solutions are displayed utilizing 3-D and 2-D graphs. We infer that multiplicative noise impacts and stabilizes the behavior of SGNLSE solutions.

Optical soliton solutions of the perturbed fourth-order nonlinear Schrödinger-Hirota equation with parabolic law nonlinearity of self-phase modulation

This article introduces an examination of optical soliton solutions for the perturbed fourth-order nonlinear Schrödinger-Hirota equation, which plays a crucial role in optics. For the first time, it utilizes a novel approach by applying the extended auxiliary equation method. This equation models the propagation of optical pulses through nonlinear media, such as optical fibers, and has been the subject of many studies. Our goal extends beyond merely acquiring a significant number of soliton solutions using the method described in this article; we also aim to investigate the impact of the coefficients of group velocity dispersion, parabolic law, and fourth-order dispersion terms on soliton propagation in the problem examined. The 2D, 3D, and contour plots of the acquired dark and bright solitons, which represent the most fundamental soliton types, are presented. Additionally, all other calculations are performed using symbolic algebraic software. The results provide us with valuable insights, confirming that the introduced model can be analyzed from a physical perspective. It is demonstrated that the proposed technique is not only important but also efficient in analyzing various nonlinear scientific problems.

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

Analyzing the time-fractional (3 + 1)-dimensional nonlinear Schrödinger equation: a new Kudryashov approach and optical solutions

The paper focuses on investigating the time-fractional (3 + 1)-dimensional cubic and quantic nonlinear Schrödinger equation. We adopt the novel Kudryashov method to generate a distinct class of optical solutions for the current conformable fractional derivative problem. Our method explores various solution forms, including dark, wave, mixed dark-bright, and singular solutions. The soliton solutions we construct are visually represented to illustrate the influence of the fractional order derivative. Further, we elucidate the influence of solution parameters on the wave envelope, providing clear interpretations through 2D graphics presentations. The results underscore the efficacy of our approach in discovering exact solutions for nonlinear partial differential equations, especially in cases where alternative methods prove ineffective. The significance of the present paper lies in its contribution to advancing the understanding of the behavior of optical solutions in nonlinear systems, providing valuable insights for both theoretical and practical applications. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons.

A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave

In the current paper, a generalized nonlinear Schrödinger (gNLS) equation with logarithmic nonlinearity is studied as a model for the propagation of optical pulses. More precisely, after applying a specific hypothesis for the solution of the governing equation, its Gaussian solitary wave is retrieved using the ansatz method. Some numerical simulations in two- and three-dimensional postures are presented to investigate the impact of different physical parameters on Gaussian solitary wave’ dynamics. Results confirm that the physical parameters of the gNLS equation have a key role in controlling the dynamics of the Gaussian solitary wave.

Localized wave solutions to coupled variable-coefficient fourth-order nonlinear Schrödinger equations

This study investigates higher-order localized waves for coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which are used to describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the seed solutions and Lax pair, the Nth-order localized wave solutions are constructed. The interactions of rogue waves with dark–bright solitons are graphically analyzed via numerical simulation. The results are helpful for studying localized wave phenomena in nonlinear optics.

Study on soliton behaviors of the complex nonlinear Fokas–Lenells equation utilizing different methods

In this paper, we study the Fokas–Lenells equation, which is a derivation form of the nonlinear Schrödinger equation and can be used to describe nonlinearity in the propagation of optical pulses. To seek solutions for this nonlinearity, the Logistic method has been proposed in order to drive acceptable and understandable results regarding physical meaning. This method is defined based on the summation of an ordinary differential equation. Moreover, for further study, the Bernoulli [Formula: see text]-expansion method is used by considering hypothetical solutions as a function of the Bernoulli equation. Subsequently, solutions of the Fokas–Lenells equation are successfully acquired, displaying efficient results in hyperbolic, trigonometric, and exponential equations. The importance of these results appears in the definition of the wave function under the consideration of the appropriate coefficients. Hence, computer simulation is used for better understanding of the generated results. The dynamic behaviors of these solutions are demonstrated in 3D graphs, contour maps, and line plots, under applying various parameters, solutions of the waves show different soliton behaviors, including bright-dark, bright, and breather solitons. The results indicate that the exerted methods are novel, reliable, and effective approaches which can be employed in a wide range of nonlinear differential equations. These methods and their begotten results are far from the complexities of mathematical structures and therefore go beyond previous efforts in the literature.

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

This paper was organized to examine the analytical solutions of the improved perturbed parabolic-law nonlinear Schrodinger equation including non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion. This model mostly makes use of studying the propagation of optical pulses in fiber optic communication systems. We performed the Sinh-Gordon equation expansion method so that we produce the analytical solutions of the model under consideration. It was confirmed that the acquired solutions satisfy the main model. Therefore, bright and dark soliton solutions were retrieved; besides, various 3D and 2D graphical illustrations of the solitons were demonstrated via appropriate values of the parameters. Furthermore, this manuscript focused on the parameters’ effect on the acquired solitons behavior.

On the optical soliton solutions to the fractional complex structured (1+1)-dimensional perturbed gerdjikov-ivanov equation

In this work, we examine the complex structured Fractional Perturbed Gerdjikov-Ivanov equation (FPGIE), which describes the propagation of optical pulses with perturbation effects. This model finds applications in optical fibers, especially in photonic crystal fibers. We are discovered novel and unique optical soliton solutions using the modified Extended Direct Algebraic Method (mEDAM), which has never been used with this model previously. As a result, a hierarchy of traveling wave solutions including singular kink, periodic, solitary kink, and rogue-shaped soliton solutions, etc., are derived. Some obtained solutions are discussed graphically based on numerical values of some parameters related to the solution. The results add new and unique soliton types to the model and demonstrate how they interact and impact the system’s overall dynamics.