Effect Of Group Velocity Dispersion Research Articles

The nondegenerate solitons solutions for the generalized coupled higher-order nonlinear Schrödinger equations with variable coefficients via the Hirota bilinear method

In this paper, the generalized coupled higher-order nonlinear Schrödinger equations (GCHNLSEs) with variable coefficients, describing the propagation of femtosecond pulse with high peak power in birefringence fibers and inhomogeneous media, are researched by the Hirota bilinear method. The nondegenerate two-solitons and nondegenerate N-solitons solutions for these equations are obtained successfully for the first time. Then, we attain the v-shape, u-shape and wave-type double-hump solitons by adjusting the group velocity dispersion, cross-phase modulation and group velocity effect. Finally, through selecting the appropriate complex wave parameters, we change the distances between solitons and analyze the dynamic behaviors of the collisions.

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

Dynamical characteristics and physical structure of cusp-like singular solitons in birefringent fibers

In this paper, we explore optical nonlinear waves in a birefringent fiber by investigating the dynamics of a coupled nonlinear Schrödinger system with four-wave mixing factors. Utilizing the Jacobi elliptic function approach, we achieve this goal by building cusp-like singular soliton solutions in this optical system. Depending on the characteristics of the focusing and defocusing optical medium, we investigate four different physical possibilities. We identify numerous cusp-type singular soliton profiles in these settings, namely cusp-like bright, dark, kink, and antikink solitons. Group velocity dispersion, spatio-temporal dispersion, and four-wave mixing effects are further evaluated in terms of their influence on the constructed singular soliton solutions. We show that the intensity of the singular soliton profiles can be suppressed or enhanced by altering the dispersion values. We also witness interesting transitions: when four-wave mixing parameters are tuned, cusp-like kink-type solitons can become cusp-like antikink solitons and vice versa. These novel findings about singular solitons in birefringent fibers have great promise for experimental uses in the realm of optics, as well as for advancing our knowledge of four wave mixing and nonlinear propagation.

Chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating upwards in the atmosphere

The chirp characteristics and the effect of chirp on the beam quality of laser pulses propagating from the ground through the atmosphere to the space orbit are studied. The analytical expressions of the additional chirp caused by group-velocity dispersion (GVD) and self-focusing effects in the atmosphere are derived, respectively. It is shown that the behavior of the additional chirp caused by GVD effect is quite different from that caused by self-focusing effect. On the other hand, it is found that there exists a minimum of pulse width on the target when a certain negative initial chirp arrives. In particular, it is demonstrated that the beam quality on the target can be optimized (i.e., the target intensity can be improved and the temporal pulse splitting on the target can be avoided) by the preliminary chirp method.

(3+1)-dimensional Sasa–Satsuma equation under the effect of group velocity dispersion, self-frequency shift and self-steepening

Purpose:The aim of this study is to examine the effects of the coefficients of group velocity dispersion, self-frequency shift and self-steepening terms on the optical solitons of the (3+1)-dimensional Sasa–Satsuma equation which is important for modeling many physical events and it has recently been introduced to the literature. Methodology:To get desired results we have used the solution approach as following. The first step is defining the wave transform and applying it to the nonlinear partial differential equation (NLPDE). Then we have obtained the ordinary differential equation (ODE). Afterwards it is introduced and applied the new Kudryashov method (nKM) and unified Riccati equation expansion method (UREEM) to obtain the algebraic equation system. Finally, by determining the parameters from the solution of algebraic system we have substituted them in the solution function. Findings:By using the solution function we have obtained interesting soliton graphics under different parameter values. In addition to the basic solitons of the (3+1)-dimensional Sasa–Satsuma equation (SSE), V-shaped and periodic singular type solitons have also been obtained. Originality:The findings of the soliton behaviors under the parameter values effect has not been studied before. The results presented in the article are reported for the first time.

Chirped optical soliton propagation in birefringent fibers modeled by coupled Fokas-Lenells system

The propagation of ultrashort light pulses in a birefringent optical fiber exhibiting spatiotemporal dispersion, cross- and self-phase modulation, self-steepening, and group-velocity dispersion effects is addressed. The evolution of light pulses in such system is described by the coupled Fokas-Lenells equations which offer an accurate description of pulse dynamics in the femtosecond range when certain terms of the next asymptotic order beyond those necessary for the nonlinear Schrödinger equation are sustained. We report the first analytical demonstration of the propagation of chirped solitons in a birefringent fiber medium governed by the coupled Fokas-Lenells equations. The formation of those nonlinearly chirped solitons in the optical material may be attributed to the presence of self-steepening process. The results show that the frequency chirp associated with each of the two field components is directly proportional to the total intensity of the pulse. The chirped solitons for the system including the dark-dark and bright-bright soliton pairs in the presence of all fiber parameters are retrieved. The chirps accompanying the soliton pairs are also determined. The existence constraints of these chirped solitons are presented. In addition, the stability of the chirped solutions with respect to the finite perturbations is studied numerically.

Unusual evolutions of pulses and spectra in an Yb-doped intra-cavity cascaded Raman fiber laser

Based on nonlinear polarization rotation, a passively mode-locked Yb-doped intra-cavity cascaded Raman fiber laser was demonstrated, in which the unusual evolutions of spectra and pulses have been observed for the first time. The first-order stimulated Raman scattering (SRS) laser and the second-order cascaded SRS laser have been obtained successively under the different pump powers. Furthermore, due to the interaction of self-phase modulation, SRS, group velocity dispersion and other nonlinear effects, the spectra and pulses of the Raman fiber laser presented a unique anomalous evolution. With the increase in pump power, the decrease in the intensity of the first-order Stokes and the second-order Stokes waves and the narrowing of the pulses were observed for the first time. Finally, a flat broadband spectrum was achieved based on the unusual evolution of laser emission spectrum, which would be of great interest as a new method in generating the broadband continuum source.

From spectral broadening to recompression: dynamics of incoherent optical waves propagating in the fiber

Interplay between dispersion and nonlinearity in optical fibers is a fundamental research topic of nonlinear fiber optics. Here we numerically and experimentally investigate an incoherent continuous-wave (CW) optical field propagating in the fiber with normal dispersion, and introduce a distinctive spectral evolution that differs from the previous reports with coherent mode-locked fiber lasers and partially coherent Raman fiber lasers [Nat. Photonics 9, 608 (2015).]. We further reveal that the underlying physical mechanism is attributed to a novel interplay between group-velocity dispersion (GVD), self-phase modulation (SPM) and inverse four-wave mixing (IFWM), in which SPM and GVD are responsible for the first spectral broadening, while the following spectral recompression is due to the GVD-assisted IFWM, and the eventual stationary spectrum is owing to the dominant contribution of GVD effect. We believe this work can not only expand the light propagation in the fiber to a more general case and help advance the physical understanding of light propagation with different statistical properties, but also benefit the applications in sensing, telecommunications and fiber lasers.

Limitation of THz conversion efficiency in DSTMS pumped by intense femtosecond pulses.

Terahertz (THz) generation via optical rectification (OR) of near-infrared femtosecond pulses in DSTMS is systematically studied using a quasi-3D theoretical model, which takes into account cascaded OR, three-photon absorption (3PA) of the near-infrared radiation, and material dispersion/absorption properties. The simulation results and the comparison with experimental data for pump pulses with the center wavelength of 1.4 µm indicate that the 3PA process is one of the main limiting factors for THz generation in DSTMS at high pump fluences. The THz conversion efficiency is reduced further by the enhanced group velocity dispersion effect caused by the spectral broadening due to the cascaded OR. We predict that for broadband pump pulses with a duration of 30 fs, the THz conversion efficiency can be enhanced by a factor of 1.5 by using a positive pre-chirping that partially suppresses the cascaded OR and the 3PA effects.

Beam Quality of Annular Pulsed Laser Beams Propagating Through the Nonlinear and Dispersive Atmosphere

The Kerr self-focusing and group-velocity dispersion (GVD) effects play important roles when a high-power pulsed laser beam propagates from the ground through the nonlinear and dispersive atmosphere to space orbits. For an annular pulsed laser beam, the Kerr self-focusing and GVD effects on the beam quality on the target is studied in this paper. Due to self-focusing, the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target arrives when the beam power P = P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> is called the optimal beam power), and the intensity on the target will decrease as the beam power P increases further when P > P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> . The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> of nanosecond and picosecond pulsed beams is lower than that of femtosecond pulsed beams, while the maximum intensity I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> on the target of nanosecond and picosecond pulsed beams is higher than that of femtosecond pulsed beams. The P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">opt</sub> and I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> of annular pulsed beams are higher than those of Gaussian pulsed beams. In addition, the B integral and the Strehl ratio are also adopted to describe the beam quality on the target. On the other hand, because of the interplay of Kerr self-focusing and GVD effects, the temporal pulse splitting and self-healing may take place on propagation, and the temporal pulse splitting may take place more than once. The results obtained in this paper are useful for laser ablation propulsion's applications in space.

Dispersion cancellation in a quantum interferometer with independent single photons.

A key technique to perform proper quantum information processing is to get a high visibility quantum interference between independent single photons. One of the crucial elements that affects the quantum interference is a group velocity dispersion that occurs when single photons pass through a dispersive medium. We theoretically and experimentally demonstrate that an effect of group velocity dispersion on the two-photon interference can be cancelled if two independent single photons experience the same amount of pulse broadening. This dispersion cancellation effect can be applied to a multi-path linear interferometer with multiple independent single photons. As multi-path quantum interferometers are at the heart of quantum communication, photonic quantum computing, and boson sampling applications, our work should find wide applicability in quantum information science.

Spatiotemporal localizations of light in quadratically nonlinear media with transversal inhomogeneity

In the current study with the help of mathematical modeling we investigate the generation of second optical harmonic provided various group velocity dispersion (GVD) and third order dispersion effects taken into account. Varying values and signs of the third-order dispersion at quasi-zero values of GVD we reveal the conditions of light bullet formation and stable propagation. To this end we use a generalization of the well-known system of the second harmonic generation in quasi-optical approach. Particular attention is paid to the case when GVD at the second harmonic is close to zero. In addition, we investigate these cases using both focusing and defocusing waveguide which means the presence of transversal inhomogeneity.

Dispersion engineering of W2 steeple-house-defect waveguide photonic crystal

An epitome for dispersion and buffering in a photonic crystal was set forth. Slots in the form of a line of contacted steeple-houses are implanted in a two-line photonic crystal waveguide (2LPCW) to form an irregular slot of steeple-house defect PCW (SDPCW) to realize bandwidth expanding and a significant regulator for group delay (GD), group velocity dispersion (GVD) and group delay dispersion (GDD) effects. The SDPCW was compared with other types of defects reported in this study and in the literature previously, we fulfilled the highest favorable value of buffering capacity about 210.256 bits. Furthermore, low GDD is achieved in the range from 1ps2to 10ps2 for 1 mm delay line length. The SDPCW may be appropriate for the workable application, which has a utility in coupling enhancement between the cavities as it was observed from the field distribution detected over confined spatial light along the propagation path for enhancing the transmission bandwidth, buffering properties and outstanding tolerance to fabrication errors. Moreover, stopping and/or slowing the light has an excessive advantage in the store of quantum states of light for an adequately long time to make quantum operations. Besides, the SDPCW achieved high electro-optical (EO) sensitivity about 244.42 nm/RIU. Thus, the proposed SDPCW can be used for enhancing the interaction between light and the sensing medium.

Optical solitons and closed form solutions to the (3+1)-dimensional resonant Schrödinger dynamical wave equation

This paper investigates the new solitons and closed form solutions to [Formula: see text] dimensional resonant nonlinear Schrödinger equation (RNLSE) that explains the behavior of waves with the effect of group velocity dispersion and resonant nonlinearities in the optical fiber. The soliton solutions in single and combined forms like dark, singular, and dark-singular in mixed form are extracted by means of two innovative integration norms namely extended sinh-Gordon equation expansion and [Formula: see text]-expansion function methods. Moreover, kink and closed form solutions are also observed under different constraint conditions. By choosing the suitable selection of the parameters, three dimensional, two dimensional, and contour plots are sketched. The obtained outcomes show that the applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations.

Harmonic instability in a quantum cascade laser with Fabry–Perot cavity

A new state of instability called harmonic instability, which is characterized by the appearance of side modes separated by multiple of free spectral range from each other, was discovered in quantum cascade lasers (QCLs) a few years ago. However, a detailed analysis using a model beyond the two-level density-matrix (DM) equations as well as incorporating phenomena such as the detuning of the primary-mode frequency from the line-center frequency and the frequency dependence of the background refractive index, resulting in group velocity dispersion (GVD), has not been performed yet. In this paper, we present a comprehensive analysis of harmonic instability in a QCL with a Fabry–Perot (FP) cavity. Starting from three-level DM equations, which include the resonant tunneling phenomenon and scattering rates between all three states, and then by using Maxwell's equation, we derive a closed-form expression for the gain of the side modes, from which quantities pertinent to instability can be determined. We also take the aforementioned phenomena into account in our theory. By using our theory, we show the way of determining primary-mode detuning from the line center. Furthermore, we study the effects of GVD on instability in detail, showing that the output from an FP QCL demonstrates the characteristic of a frequency-modulated wave up to a certain value of dispersion. Above this value, because of the significant deviation of the side-mode amplitude ratio from unity, the output shows neither frequency-modulated-like nor amplitude-modulated-like behavior.

Futuristic elongated-hexagonal photonic crystal waveguide for slow light

The capability of photonic crystal waveguides (PCWs) to reduce the device footprint, extend the bandwidth, and control the group velocity dispersion effects, has prompted many researchers to propose new models of slow-light PCWs. An unpretentious figure of merit (FoM) to evaluate the intrinsic performances of slow-light structures, e.g., maximum buffer capacity and delay time with modest dispersion engineering, is the normalized-delay-bandwidth-product (NDBP). We proposed a unique platform from an elongated-hexagonal (e-hexagonal) lattice PCW for multi-modes and its performance has been investigated. The proposed e-hexagonal PCW has an ultra-wide bandwidth compatible with a high group index and a high FoM around 0.6456 within the flat band of slow light. We observed periodic oscillations in the field pattern of spatially confined light along the path of propagation, indicating a strong coupling among the cavities of defects. The e-hexagonal PCW is an outstanding initial point for further slow-light engineering in PCWs alongside a promising application for random-access memories and all-optical signal processors.

Improving the Link Availability of an Underwater Wireless Optical Communication System Using Chirped Pulse Compression Technique

The effect of frequency chirping on the link availability of an underwater wireless optical communication (UWOC) system is studied theoretically using a simple and realistic model. It is observed, both theoretically and numerically, that a light pulse can be compressed in temporal axis when propagating in the water medium and can attain the minimum value at a prespecified location by appropriately choosing the initial pulse chirp parameter. The pulse compression takes place due to the interplay between the initial frequency chirp and the group velocity dispersion (GVD) effect. An increase in peak intensity, due to pulse compression, at the prespecified receiver location results in an improvement in the link availability compromised due to both attenuation and turbulence. The link availability is quantified by estimating the fading probability for various cases of initially chirped (+ve, 0, and -ve) Gaussian pulses under the influence of attenuation and turbulence and the results are compared for different scenarios. To have a complete channel description, the effect of particulate scattering on the GVD-induced pulse compression and hence on the fading probability is studied and quantified using the Monte Carlo numerical simulation technique. It is shown that, for the same system and channel parameters, the fading probability of a UWOC system is a few orders of magnitude lower (at a prespecified location) for the case with the negatively chirped pulse than for the cases when the initial pulse chirp is either zero or positive. In addition, the analytical expressions for estimating the focus distance and minimum pulse length, as functions of the channel properties, incident pulse length, and initial chirp parameters, are presented and discussed.

Health monitoring of long-haul fiber communication system using chaotic OTDR

A novel chaotic optical time-domain reflectometry (OTDR)-based approach was proposed for monitoring long-haul fiber communication systems with multiple fiber segments. The self-phase modulation and group velocity dispersion effects of the optical cable was considered in demonstrating the proof-of-concept experiment and simulation. In experiments, the correlation peaks are clearly obtained from the correlation trace between the reference and reflected (or scattered) light signals propagating in three optical-fiber segments. The technique affords a high spatial resolution of 2 m, and further long-haul fiber simulations indicate that the sensing distance can be more than 3300 km. Thus, the new proposed technique can be effectively applied for health monitoring of long-haul fiber communication systems.

Investigation of optical solitons in birefringent polarization preserving fibers with four-wave mixing effect

The paper studies the optical solitons with coupled nonlinear Schrödinger system (CNLSS) that describes the propagation of waves in birefringence polarization-preserving fibers with four-wave mixing effect. The system is discussed with the effects of group velocity dispersion, self-phase and cross-phase modulations. The mechanism that is used to investigate is the extended Fan-sub equation method. It is observed that this system exhibits a collection of rich solitons (single and combined) for different values of parameters. The 3D figures are also plotted to show the physical behavior of obtained solutions under different constraint conditions.

Pulse Dynamics of an All-Normal-Dispersion Ring Fiber Laser Under Four Different Pulse Regimes

Based on the coupled Ginzburg-Landau equations and Jones matrices of the waveplates considered, a numerical model of an all-normal-dispersion fiber laser mode-locked by nonlinear polarization rotation has been proposed. The operating characteristics of the fiber laser discussed were studied numerically. It has been found that the proposed all-normal-dispersion mode-locked fiber laser (AND-MLFL) could deliver dissipative solitons (DSs) with a M-shaped and U-shaped spectrum, the splitting pulse with a divided spectrum and the amplifier similaritons. The evolution of the intra-cavity pulse and spectrum has been calculated under different regimes and the effects of group velocity dispersion (GVD) and nonlinearity are analyzed. When the fiber laser delivers DSs or causes pulse splitting, nonlinear effects dominate the pulse evolution. With the increase of the accumulated nonlinear phase shift, the operation states change from DS with a M-shaped spectrum to a U-shaped spectrum, and then to the splitting pulse. In the case of amplifier similaritons, both the GVD and nonlinearity play important roles in pulse evolution. The effect of nonlinear polarization rotation and filtering on the pulse reshaping has been analyzed. When the fiber laser delivers DSs with a M-shaped spectrum, the filter has a very weak effect on the pulse and on spectral reshaping. However, when the fiber laser operates in the amplifier similariton state, the filter plays a key role in pulse and spectral reshaping, whereas the nonlinear polarization rotation become less dominant. The dependence of the operational states on the filter bandwidth, fiber length, small signal gain coefficient and orientation of waveplates has also been calculated. A Yb-doped doubled-cladding fiber laser, mode-locked by nonlinear polarization rotation, has also been demonstrated and all of the four pulse regimes are obtained experimentally.