Propagation Of Ultrashort Optical Pulses Research Articles

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.

Mean-field equation for phase-modulated optical parametric oscillator

The widely established techniques for the generation of ultrashort optical pulses rely on passive mode locking of lasers, with the output pulse duration and emission spectrum determined by the intrinsic lifetime of laser transition in the gain medium. Due to the instantaneous nature of nonlinear gain, optical parametric oscillators (OPOs) are capable of generating optical radiation in all timescales from continuous-wave (cw) to ultrashort femtosecond regime, if driven by laser pump sources in the corresponding time domain. In the ultrashort timescale, operation of OPOs conventionally relies on mode-locked pump lasers, with the concomitant disadvantages of large footprint and high cost. At the same time, the lack of gain storage mandates the use of synchronous pumping, resulting in increased complexity. In this paper, we present the concept of phase-modulated OPO driven by cw pump laser. The approach overcomes the traditional drawbacks of ultrafast OPOs, enabling femtosecond pulse generation without the need for synchronous pumping, resulting in a simplified, compact, and cost-effective architecture using cw input pump lasers. We derive a mean-field equation for a degenerate χ(2) OPO driven by a cw laser with intracavity electro-optic modulator (EOM), and also including dispersion compensation. The equation predicts the formation of stable femtosecond pulses (<200fs), in both normal and anomalous dispersion regimes, with a controllable repetition rate determined by the frequency of the EOM. The remarkable functionality of the proposed scheme paves the way for the development of an alternative class of widely tunable coherent femtosecond light sources in both bulk and integrated format based on χ(2) OPOs using cw pump lasers. Published by the American Physical Society 2024

Spectral stability of elliptic solutions to the short-pulse equation

The short pulse (SP) equation describes the propagation of ultrashort optical pulses in nonlinear media and possesses a Lax pair of the Wadati–Konno–Ichikawa (WKI) type. In this paper, using integrability, we examine the spectral stability of elliptic solutions to the SP equation. Firstly, we analytically give an explicit description of the spectrum of the WKI-Lax operator to the SP equation for elliptic potentials. Then, by constructing the squared-eigenfunction connection between the non-standard linear stability problem (LZ=ΛZ′) and the Lax spectral problem, we prove that the elliptic solutions are spectrally stable with respect to subharmonic perturbations.

Effect of dispersion and nonlinearity on ultrashort optical pulse propagation in long-period fiber grating: An analytical investigation

Long-period fiber grating is widely used as an optical component in photonics communication technology. The optical pulse propagation in grating has been studied mostly numerically and some number of studies carried out experimentally. The detailed analytical investigation has not been reported due to the complexity of the mathematical equations. Here, we have investigated analytically the effect of dispersion and nonlinearity on ultrafast optical pulse propagation in long-period fiber grating and derived the expression for transmitted optical pulses because the detailed analytical investigation has not been reported by any authors. The results of the study show how grating-induced overall dispersion and nonlinearity-induced self-phase modulation (SPM) modify the shape of the ultrashort optical pulses when it’s propagating through a length of the grating. The combined effects of dispersion and SPM on the optical pulse evaluation are also analyzed. From the plotted graphs it is investigated that the dispersion of the grating distorted the pulse shape whereas SPM shifts the pulse towards the higher time scale. It is also investigated that the distorted optical pulse due to dispersion is reshaped by the nonlinearity introduced in the medium due to the combined effect of dispersion and SPM. Optical pulse compression, optical limiting and pulse reshaping are also illustrated as a function of excitation intensity.

Exact soliton solutions and stability analysis to (3 + 1)-dimensional nonlinear Schrödinger model

In this research, a dynamical (3 + 1)-dimensional nonlinear Schrödinger model (NLSM) is under consideration which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This aforementioned model has been widely applied in Bose–Einstein condensates, nonlinear optical fiber communication plasma physics, hydrodynamics, elastic media and other diversified areas of mathematical physics and engineering. This study has two main objectives. Firstly, to obtain some novel solutions in the shape of singular, dark, periodic and plane wave solutions that are innovative and not previously found in the literature. Secondly, an amended extended tanh-function method with modulation instability (MI) is used for this model. As far as we know, this has never been investigated in this manner. The 2-D, 3-D and contour plots have been defined using the required parametric values to support the results of physical compatibility. According to the examined results, the method used in this study to retrieve consisting and conventional solutions is efficient and more immediate in computing and can be thought of as a useful tool in resolving more difficult problems that arise in the field of engineering, physics, mathematics and fiber optics.

Soliton interactions and Yang–Baxter maps for the complex coupled short‐pulse equation

AbstractThe complex coupled short‐pulse equation (ccSPE) describes the propagation of ultrashort optical pulses in nonlinear birefringent fibers. The system admits a variety of vector soliton solutions: fundamental solitons, fundamental breathers, composite breathers (generic or nongeneric), as well as so‐called self‐symmetric composite solitons. In this work, we use the dressing method and the Darboux matrices corresponding to the various types of solitons to investigate soliton interactions in the focusing ccSPE. The study combines refactorization problems on generators of certain rational loop groups, and long‐time asymptotics of these generators, as well as the main refactorization theorem for the dressing factors that leads to the Yang–Baxter property for the refactorization map and the vector soliton interactions. Among the results obtained in this paper, we derive explicit formulas for the polarization shift of fundamental solitons that are the analog of the well‐known formulas for the interaction of vector solitons in the Manakov system. Our study also reveals that upon interacting with a fundamental breather, a fundamental soliton becomes a fundamental breather and, conversely, that the interaction of two fundamental breathers generically yields two fundamental breathers with a polarization shifts, but may also result into a fundamental soliton and a fundamental breather. Explicit formulas for the coefficients that characterize the fundamental breathers, as well as for their polarization vectors are obtained. The interactions of other types of solitons are also derived and discussed in detail and illustrated with plots. New Yang–Baxter maps are obtained in the process.

Transition mechanisms of breather molecules in the Hirota equation

The transition dynamics of the breather molecules are investigated for the Hirota equation, which describes the propagation of ultrashort optical pulses in optical fibers. Based on the two-breather solution, the breather molecules and breather complexes are obtained. The half-transition mechanism of the breather molecules is unveiled and a series of the transformed wave molecules and the corresponding complexes are generated. The superposition mechanisms of breather molecules and transformed wave molecules are explained through the nonlinear superposition principle. It should be noted that the full transition of the breather molecules does not exist in the Hirota equation. The effects of the phase parameters on the transformed wave molecules are discussed. Besides, the collisions for breather molecules and transformed wave molecules are investigated. The distances between atoms in the molecules and the shapes of the transformed waves are changed after the collisions. By means of the phase shift analysis, the nature of shape-changed collisions is shed light on. Finally, the stability of the propagation of molecule waves under small perturbations is performed.

On complex wave solutions for the variable-coefficient fourth-order nonlinear Schrödinger system in an inhomogeneous optical fiber

In this paper, the variable-coefficient fourth-order nonlinear Schrödinger system, which is used to depict the simultaneous propagation of ultrashort optical pulses in an inhomogeneous optical fiber, is probed by two approaches. As an achievement, heaps of complex exact solutions, including some complex solitary, soliton and elliptic wave solutions as well as some complex trigonometric, hyperbolic trigonometric and rational solutions, are derived in the light of the unified and improved F-expansion methods separately. Additionally, the movement mechanisms of partial solutions that we gain are graphically discussed with appropriate parameters. And one thing should be mentioned is that we choose one solution from every foregoing category of solutions to draw the 2D, 3D and contour images to realize the wave propagation more systematically and deeply.

Nonlinear Wave Molecules for the Lakshmanan–Porsezian–Daniel Equation in Nonlinear Optics and Biology

AbstractThe nonlinear wave molecules of the Lakshmanan–Porsezian–Daniel (LPD) equation describing the propagation of ultrashort optical pulses through optical fibers and Davydov soliton in α‐helical proteins are investigated. Based on the analysis of characteristic lines, the breather molecules consisting of two, three, or even four different breather atoms are derived, and the synthesis modes of molecules by adjusting the values of the phase parameters are generated. The state conversion of the breather molecules is studied and a variety of converted wave molecules are produced. In particular, it is reported that the full conversion of the breather molecules does not exist in the LPD equation. The formation mechanisms of different types of nonlinear wave molecules through the nonlinear superposition are further explored and the influence of higher‐order effects on the breather molecules is discussed. Finally, the intricate interactions between the molecules and nonlinear waves are considered. It is found that the distances between atoms in the molecules as well as the shapes of the converted waves change after the interactions, and the essence of such shape‐changed interactions is revealed.

Gain-switching in CsPbBr3 microwire lasers

All-inorganic perovskite microwire lasers, which have intrinsic high material gain and short cavity, especially favor the generation of ultrashort optical pulses via gain switching for various potential applications. Particularly, the ultrashort gain-switched pulses may extend perovskite microwires to previously inaccessible areas, such as ultrafast switches, and chipscale microcombs pumping souces in photonic integrated circuits. Here, we show 13.6-ps ultrashort single-mode green pulses from the gain-switched CsPbBr3 microwire lasers under femtosecond optical pumping. The gain-switching dynamics is experimentally investigated by a streak camera system. The excitation fluence dependences of pulse width, delay time and rise time of the output pulses show good agreements with the rate equation simulations with taking gain nonlinearities and carrier recombination ABC model into account. Our results reveal that perovskite microwire lasers have potential for ultrashort pulse generation, while the low transient saturated gain, which may result from the high transient carrier temperature under femtosecond pumping is a significant limitation for further pulse shortening.

Optical solitons and stability analysis for the new (3+1)-dimensional nonlinear Schrödinger equation

This paper explores the new [Formula: see text]-dimensional nonlinear Schrödinger equation which is used to model the propagation of ultra-short optical pulses in highly-nonlinear media. This equation is newly derived based on the extended [Formula: see text]-dimensional zero curvature equation. An effective technique, namely, the extended sinh-Gordon equation expansion method is applied to find optical soliton solutions and other solutions for this model. As a result, dark, bright, combined dark–bright, singular, combined singular soliton solutions, and singular periodic wave solutions are obtained. The stability of the model is investigated by using the modulation instability analysis which guarantees that the model is stable and all solutions are stable and exact. Physical explanations of the obtained solutions are presented by using 3D and 2D plots. The reported outcomes are useful in the empirical application of fiber optics.

New single traveling wave solution in birefringent fibers or crossing sea waves on the high seas for the coupled Fokas–Lenells system

The main work of this paper is focused on construction the single traveling wave solution of the coupled Fokas–Lenells system, which is usually used to simulate the propagation of ultrashort optical pulses in birefringent fibers or crossing sea waves on the high seas. Firstly, the coupled Fokas–Lenells system is simplified into a nonlinear ordinary differential equation by traveling wave transformation and linear transformation. Then, using the well-known complete discriminant system of third-order polynomials, some single traveling wave solutions of the coupled Fokas–Lenells system are obtained including implicit solutions, rational function solutions and Jacobian function solutions.

Influence of nonlinear absorption on the propagation of ultrashort optical pulses in an anisotropic optical medium with carbon nanotubes

We study the features of the evolution of a pulse in a dielectric medium (crystal) with optical anisotropic properties taking into account pumping. The medium contains semiconductor carbon nanotubes of a fixed orientation directed at an angle to one of the principal axes of the crystal. We analyze the influence of pumping and resistance to disturbances. Our study shows that the effects of pumping and nonlinear absorption suppress the dispersive pulse spreading caused by the optically anisotropic properties of the medium.

Dark soliton solutions for a variable coefficient higher-order Schrödinger equation in the dispersion decreasing fibers

Under investigation in this paper is a variable coefficient higher-order Schrödinger equation with the effects of third-order dispersion, self-steepening and stimulated Raman scattering, which describes the propagation of ultrashort optical pulses in the dispersion decreasing fibers. Via the symbolic computation and Hirota method, the bilinear forms, dark one- and two-soliton solutions are derived. Propagation and interaction for the dark solitons are illustrated graphically: the shape of the dark solitons is affected by the third-order dispersion, self-steepening and stimulated Raman scattering, while the amplitude and velocity of those are influenced by the gain coefficient Γ. With the increase of the parameter Γ, the amplitude of the dark soliton pulse increases, and the velocity of that changes exponentially in the same propagation distance. For the elastic interaction, the anti-bell- and two parabolic-shape dark solitons are discussed respectively, where the amplitudes and shapes remain unchanged after interaction except for certain phase shifts.

Evolution of temporal broadening of ultrashort optical pulse propagation in general ocean turbulence.

Theoretical and experimental explorations have demonstrated that both anisotropy and unstable stratification exist in general ocean turbulence. Recent analyses of temporal broadening of ultrashort optical pulses in oceanic turbulence have adopted the assumptions that the propagation path in the z direction was isotropic, or turbulent cells are simply premised on circular symmetry in the xy plane. In this paper, circular symmetry of turbulent cells in the xy plane is no longer maintained, and two anisotropic factors describing the anisotropic scales in the xy plane are introduced to study the temporal broadening of ultrashort optical pulses. Moreover, unstable stratification of oceanic turbulence indicates the eddy diffusivities of temperature and salt are no longer equal. By Rytov approximation and the temporal-moments method, a new model is proposed for the temporal broadening of ultrashort optical pulse propagation in general ocean turbulence. We focus on the effects of asymmetric turbulent cells, unstable stratification, and other characteristics in general ocean turbulence on the temporal broadening. This work provides a theoretical basis for improving the transmission quality of ultrashort optical pulses and the performance of underwater optical communication systems.

Ultra-short optical pulse generation in micro OLEDs and the perspective of lasing

We report experimental and theoretical investigations with an in-house fabricated tris(8‐hydroxyquinoline)‐aluminum (Alq3)-based high-speed micro-organic light-emitting diodes (μ-OLEDs) and demonstrate very promising optical pulse responses as short as 400 ps. With a model for an electrically pumped OLED, we simulate the emission of sub-nanosecond optical pulses. The model includes field-dependent (Poole-Frenkel) Langevin recombination and reabsorption of photons by singlets (Stokes-shifted), and by triplets (TA). The good agreement between the measurement and the simulation is the basis for further study of the prospects on the ps time scale, i.e. stimulated emission and conditions for laser operation. For an Alq3-based micro-OLED with high-Q optical cavity, we predict pulsed laser operation with damped relaxation oscillations in the GHz regime and several orders of magnitude linewidth narrowing, but only during 3 ns at most. The simulated current density threshold values vary from 10 kA cm−2 for Q= 500 to less than 1 kA cm−2 for Q = 1000. No continuous-wave (CW) lasing is found due to the accumulation of triplet excitons for t > 5 ns, which has two deteriorating effects, (a) suppression of the gain-providing singlet excitons due to singlet-triplet absorption and (b) suppression of the photon density due to photon absorption by triplets (TA). Prospects for CW-lasing with other organic molecules are discussed.

Py-fmas: A python package for ultrashort optical pulse propagation in terms of forward models for the analytic signal

We present a flexible, open-source Python package for the accurate simulation of the z-propagation dynamics of ultrashort optical pulses in nonlinear waveguides, especially valid for few-cycle pulses and their interaction. The simulation approach is based on unidirectional propagation equations for the analytic signal. The provided software allows to account for dispersion, attenuation, four-wave mixing processes including, e.g., third-harmonic generation, and features various models for the Raman response. The propagation equations are solved on a periodic temporal domain. For z-propagation, a selection of pseudospectral methods is available. Propagation scenarios for a custom propagation constant and initial field pulses can either be specified in terms of a HDF5 based input file format or by direct implementation using a python script. We demonstrate the functionality for a test-case for which an exact solution is available, by reproducing exemplary results documented in the scientific literature, and a complex propagation scenario involving multiple pulses. Program summaryProgram Title: py-fmasCPC Library link to program files:https://doi.org/10.17632/7s2cv9kjfs.1Developer's repository link:https://github.com/omelchert/py-fmasCode Ocean capsule:https://codeocean.com/capsule/8221780Licensing provisions: MITProgramming language: Python3Supplementary material: Reference manual, extended user guide, and usage examples are hosted on gitHub pages under https://omelchert.github.io/py-fmas.Nature of problem: Solves for the z-propagation dynamics of spectrally broad ultrashort optical pulses in single mode nonlinear waveguides in terms of propagation models for the analytic signal of the optical field [1–3]. The implemented models include, e.g., third-harmonic generation and the Raman effect.Solution method: The initial real-valued optical field is defined on a periodic one-dimensional temporal grid and converted to the complex-valued analytic signal. z-stepping is performed via spectral methods. The software implements a selection of algorithms with fixed or adaptive stepsize, commonly used in nonlinear optics for solving nonlinear Schrödinger type equations.Additional comments including restrictions and unusual features: The range of applicability of the provided software is equivalent to that of the forward Maxwell equation [4]. For reasonably chosen initial conditions, it can be used beyond the unidirectional approximation as a bidirectional model for a complex field, allowing to describe forward and backward waves coupled through nonlinear interactions [1]. The software implements various models for the Raman response and allows to calculate spectrograms, detailing the time-frequency composition of the analytic signal. Additionally, a convenience class for analyzing propagation constants is provided.

Propagation of Ultrashort Optical Pulses in Anisotropic Optical Media with Impurity-Containing Carbon Nanotubes

Propagation of Ultrashort Optical Pulses in Anisotropic Optical Media with Impurity-Containing Carbon Nanotubes

Darboux transformation, generalized Darboux transformation and vector breather solutions for a coupled variable-coefficient cubic-quintic nonlinear Schrödinger system in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide

Non-Kerr media, twin-core nonlinear optical fibers and waveguides are widely applied in optical fiber communications. In order to model the effects of quintic nonlinearity for the ultrashort optical pulse propagation in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide, a coupled variable-coefficient cubic-quintic nonlinear Schrödinger system is investigated in this paper. For the two components of the electromagnetic fields, on the basis of the existing Lax pair, we take a gauge transformation to convert a Lax pair into an Ablowitz-Kaup-Newell-Segur system. Then we acquire a system, which is equal to the original system. The N-fold Darboux transformation is derived based on our Lax pair, where N is a positive integer. Applying Taylor series, we derive the N-fold generalized Darboux transformation. The second- and third-order vector breather solutions are obtained via the generalized Darboux transformation method. All our results depend on the variable coefficients of the original system. Our results might be of some use in a non-Kerr medium, twin-core nonlinear optical fiber or waveguide system.