Higher-order Dispersion Research Articles

Near-zero-dispersion soliton and broadband modulational instability Kerr microcombs in anomalous dispersion

The developing advances of microresonator-based Kerr cavity solitons have enabled versatile applications ranging from communication, signal processing to high-precision measurements. Resonator dispersion is the key factor determining the Kerr comb dynamics. Near the zero group-velocity-dispersion (GVD) regime, low-noise and broadband microcomb sources are achievable, which is crucial to the application of the Kerr soliton. When the GVD is almost vanished, higher-order dispersion can significantly affect the Kerr comb dynamics. Although many studies have investigated the Kerr comb dynamics near the zero-dispersion regime in microresonator or fiber ring system, limited by dispersion profiles and dispersion perturbations, the near-zero-dispersion soliton structure pumped in the anomalous dispersion side is still elusive so far. Here, we theoretically and experimentally investigate the microcomb dynamics in fiber-based Fabry-Perot microresonator with ultra-small anomalous GVD. We obtain 2/3-octave-spaning microcombs with ~10 GHz spacing, >84 THz span, and >8400 comb lines in the modulational instability (MI) state, without any external nonlinear spectral broadening. Such widely-spanned MI combs are also able to enter the soliton state. Moreover, we report the first observation of anomalous-dispersion based near-zero-dispersion solitons, which exhibits a local repetition rate up to 8.6 THz, an individual pulse duration <100 fs, a span >32 THz and >3200 comb lines. These two distinct comb states have their own advantages. The broadband MI combs possess high conversion efficiency and wide existing range, while the near-zero-dispersion soliton exhibits relatively low phase noise and ultra-high local repetition rate. This work complements the dynamics of Kerr cavity soliton near the zero-dispersion regime, and may stimulate cross-disciplinary inspirations ranging from dispersion-controlled microresonators to broadband coherent comb devices.

Dynamics of Dark Pulse Affected by Higher-Order Effects in Microresonators

We theoretically investigate dynamics of dark pulse and Raman-Kerr microcombs generation influenced by higher-order effects, including high-order dispersion (HOD), stimulated Raman scattering (SRS) and self-steepening (SS) effects in silicon microresonators. These three effects cause the delay of dark pulse individually, or interact with each other to alter the drift velocity and direction of pulses. HOD effect can change pulse shift direction and even cause bifurcation. The temporal drift induced by SS or SRS effects could be balanced by the simultaneous third-order dispersion (TOD) engineering. In spectral domain, stable Raman-Kerr frequency comb will be generated due to the competition between strong SRS and Kerr effects. The Raman comb components are suppressed when HOD effect coexists, while SS effect has ignorable effect on the distribution of the Raman comb. Furthermore, the SS effect will increase the total energy of the spectrum by shifting the dispersive wave (DW) generation to the longer wavelength side. Our findings could deepen the understanding of intracavity nonlinear dynamics and provide theoretical guidance to precisely control the stabilization of dark pulse and the generation of broadband mid-infrared (MIR) microcomb.

The modulation instability of shallow wake flows based on the higher-order generalized cubic-quintic complex Ginzburg–Landau equation

In the context of the parallel flow hypothesis, we derive a higher-order generalized cubic-quintic complex Ginzburg–Landau (GCQ-CGL) equation to describe the amplitude evolution of shallow wake flow from the dimensionless shallow water equations by using multi-scale analysis, perturbation expansion, and weak nonlinear theory. The evolution model includes not only the slowly changing envelope approximation but also the influence of higher-order dissipation, dispersion, and cubic and quintic nonlinear effects. We give the analytical solution of the higher-order GCQ-CGL equation based on the ansatz and coordinate transformation methods, and we discuss the influence of the higher-order dissipation coefficient on the amplitude and frequency of the wake flow by means of three-dimensional diagrams, contour maps, and plane graphs. The subsequent linear stability analysis gives a theoretical basis for the modulation instability (MI) of plane waves, and the linear theory predicts the instability of any amplitude of the main waves. Finally, we focus on the MI of shallow wake flows. Results show that the MI gain function is internally related to the background wave number, disturbance wave number, background amplitude, disturbance expansion parameter, and dissipation coefficient. The area of the MI decreases as the higher-order dissipation coefficient decreases.

Jacobian-elliptic-function and rogue-periodic-wave solutions of a high-order nonlinear Schrödinger equation in an inhomogeneous optical fiber

Optical fiber communication plays an important role in the modern communication. Under investigation is a high-order nonlinear Schrödinger equation with the additional high-order dispersion and nonlinear terms in an inhomogeneous optical fiber. We give the Jacobian-elliptic-function solutions of that equation. Based on the nonlinearization of the existing Lax pair, we obtain the values of the spectral parameters corresponding to that Lax pair. We construct the linearly-independent and non-periodic solutions of that Lax pair. We take the Jacobian-elliptic-function solutions as the seed solutions, and substitute the linearly-independent and non-periodic solutions into the Darboux transformation to obtain the rogue-periodic-wave solutions. For the one-fold rogue-dn-periodic wave, when the parameter γ of the equation increases, we find that the period and maximum amplitude of the one-fold rogue-dn-periodic wave remain unchanged, while the minimum amplitude decreases. When the parameter η of the equation increases, we find that the maximum amplitude of the one-fold rogue-dn-periodic wave remains unchanged, while the period becomes the smaller. For the one-fold rogue-cn-periodic wave, the same conclusions can be observed. For the two-fold rogue-cn-periodic wave, when the parameter γ of the equation increases, we find that the period and maximum amplitude of the two-fold rogue-cn-periodic wave remain unchanged, while the minimum amplitude rises. When the parameter η of the equation increases, we find that the maximum amplitude of the two-fold rogue-cn-periodic wave remains unchanged, while the period becomes the smaller.

Higher-Order Dispersive and Nonlinearity Modulations on the Propagating Optical Solitary Breather and Super Huge Waves

The nonlinearity form of the Schrödinger equation (NLSE) gives a sterling account for energy and solitary transmission properties in modern communications with optical-fiber energ- reinforcement actions. The solitary representation during fiber transmissions was regulated by NLSE coefficients such as nonlinear Kerr, evolutions, and dispersions, which controlled the energy changes through the model. Sometimes, the energy values predicted from the NLSEs computations may diverge due to variations in the amplitude and width caused by scattering, dispersive, and dissipative features of fiber materials. Higher-order nonlinear Schrödinger equations (HONLSEs) should be explored to alleviate these implications in energy and wave features. The unified solver approach is employed in this work to evaluate the HONLSEs. Steepness, HO dispersions, and nonlinearity self-frequency influences have been taken into consideration. The energy and solitary features were altered by higher-order actions. The unified solver approach is employed in this work to reform the HONLSE solutions and its energy properties. The steepness, HO dispersions, and nonlinearity self-frequency influences have been taken into consideration. The energy and soliton features in the investigated model were altered by the higher-order impacts. Furthermore, the new HONLSE solutions explain a wide range of important complex phenomena in wave energy and its applications.

Highly Nonlinear Composite-Photonic Crystal Fibers with Simplified Manufacturing Process and Efficient Mid-IR Applications

This paper reveals special design features of the proposed highly nonlinear circular-lattice-silicon-core and silica-doped-with-fluorine (1%) cladding-composite photonic crystal fiber (PCF) in the Mid-infrared region of the spectrum. A region of small negative group velocity dispersion (GVD), managed higher order dispersions (HODs), and unique nonlinearity of silicon have been used to demonstrate a supercontinuum broadening from 1500 nm to 4700 nm with consumption of low input power of 400 W over short fiber distances. It will be also shown that the fiber’s high-level engineered structure finally results in a simple manufacturing process compared with other designed nano-sized silicon PCFs. The designed fiber could have massive potential in gas sensing, soliton effect pulse compression, spectroscopy, material processing, etc.

Modeling coarse-grained van der Waals interactions using dipole-coupled anisotropic quantum Drude oscillators.

The Quantum Drude Oscillator (QDO) model is a promising candidate for accurately calculating the van der Waals (vdW) interaction. Anisotropic QDO models have recently been used to represent quantum fluctuations of molecular fragments rather than that of single atoms. While this model promises accurate calculation of vdW energy, there is significant room for improvements, such as incorporating a proper fragmentation method, higher-order dispersion corrections, and so forth. The present work attempts to gauge dipole-dipole interactions' ability without fragmentation. A suitable anisotropic damping function is also introduced to work with anisotropic QDO. This revised model accurately predicts the binding energies of vdW complexes for most of the systems considered. This work indicates the limit of dipole approximation for an anisotropic QDO-based model.

Dynamics of temporal Kerr cavity solitons in the presence of rapid parameter inhomogeneities: From bichromatic driving to third-order dispersion

Temporal Kerr cavity solitons are pulses of light that can persist in coherently driven, dispersive resonators with Kerr-type nonlinearity. Many studies have shown that such solitons can react to parameter inhomogeneities (e.g., variations in the complex amplitude of the driving field) by experiencing a temporal drift. The vast majority of such studies assume that the inhomogeneity varies slowly across the soliton, leading to the prediction that the soliton drift rate is linearly proportional to the gradient of the inhomogeneity at the soliton position. However, the assumption of a slowly varying inhomogeneity may not hold true in all situations, e.g., when using bichromatic driving or in the presence of third-order dispersion that gives rise to an extended dispersive wave tail. Here we report on theoretical and numerical results pertaining to the behavior of dissipative temporal Kerr cavity solitons under conditions where parameter inhomogeneities vary nonlinearly across the width of the soliton. In this case, the soliton velocity is dictated by the full overlap between its so-called adjoint neutral mode and the parameter perturbation, which we show can yield dynamics that are manifestly at odds with the common wisdom of motion dependent solely upon the gradient of the inhomogeneity. We also investigate how the presence of third-order dispersion and the associated dispersive wave tail changes the motion induced by parameter inhomogeneities. We find that the dispersive wave tail as such does not contribute to the soliton motion; instead, higher-order dispersion yields counterintuitive influences. Our results provide new insights into the behavior of temporal cavity solitons in the presence of parameter inhomogeneities and can impact systems employing pulsed or bichromatic pumping and/or resonators with non-negligible higher-order dispersion.

Intermodal dispersive wave generation and soliton linear-wave interaction in optical fibers

The emission of dispersive wave and soliton linear-wave interaction are two of the widely studied nonlinear phenomena in fiber optics. They manifest as the generation of a new spectral component when a strong ultrashort optical pulse with/without a weak linear-wave propagates along an optical fiber in the presence of higher-order dispersions. Recent works have demonstrated that the dispersive wave generation and soliton linear-wave interaction can be interpreted in the spectral domain through the cascade of four-wave mixing processes. We show in this work that the emission of the dispersive wave is a special case of soliton linear-wave interactions, in which the linear-wave is degenerate from the soliton field. By studying the driving field (soliton) and linear-wave in different modes, the role of the soliton is to provide cross-phase modulation to the linear-wave as in the earlier studies, while the fiber dispersion is to detrimentally shape the pure cross-phase modulated linear-wave spectra into the seemingly ’idler component’. We present a theoretical model to approximately calculate the spectral profile of the generated idler/dispersive wave and further verify our model with numerical simulations.

Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model

The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of active research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model describing the evolution of water waves with higher-order temporal dispersion by characterizing the dynamics of lump and soliton waves on different spatially-varying backgrounds. Particularly, we construct some explicit lump wave and kink-soliton solutions for the considered model through its trilinear and bilinear equations with appropriate forms of the polynomial and exponential type initial seed solutions, respectively. Additionally, we obtain hyperbolic and periodic waves through bilinear Bäcklund transformation. We explore their propagation and transformation/modulation dynamics due to different spatial backgrounds through categorical analysis and clear graphical demonstrations for a complete understanding of the resulting solutions. Our analysis shows that the lump solution results into a simultaneous existence of well-localized spike and declining (coupled bright-dark wave) structures on a constant background, while the soliton solution exhibits kink and anti-kink wave patterns along different spatio-temporal domains with controllable properties. When the arbitrary spatial background is incorporated appropriately, we can witness the manifestation of soliton into manipulated periodic and interacting dynamical structures. On the other hand, the lump wave results into the coexistence, interacting wave and breather formation due to periodic and localized type arbitrary spatial backgrounds. The present results will be an important addition to the context of engineering nonlinear waves with non-vanishing controllable backgrounds in higher-dimensional models. Further, the present study can be extended to investigate several other nonlinear systems to understand the physical insights of the variable background in their dynamics.

High-power femtosecond laser generation from an all-fiber linearly polarized chirped pulse amplifier

Abstract An all-fiber high-power linearly polarized chirped pulse amplification (CPA) system is experimentally demonstrated. Through stretching the pulse duration to a full width of approximately 2 ns with two cascaded chirped fiber Bragg gratings (CFBGs), a maximum average output power of 612 W is achieved from a high-gain Yb-doped fiber that has a core diameter of 20 μm with a slope efficiency of approximately 68% at the repetition rate of 80 MHz. At the maximum output power, the polarization degree is 92.5% and the M2 factor of the output beam quality is approximately 1.29; the slight performance degradations are attributed to the thermal effects in the main amplifier. By optimizing the B-integral of the amplifier and finely adjusting the higher-order dispersion of one of the CFBGs, the pulse width is compressed to 863 fs at the highest power with a compression efficiency of 72%, corresponding to a maximum compressed average power of 440.6 W, single pulse energy of 5.5 μJ and peak power of about 4.67 MW. To the best of our knowledge, this is the highest average power of a femtosecond laser directly generated from an all-fiber linearly polarized CPA system.

Sideband-free dispersion-managed Yb-doped mode-locked fiber laser with Gires–Tournois interferometer mirrors

High-order dispersion introduced by Gires–Tournois interferometer mirrors usually causes spectral sidebands in the near-zero dispersion region of mode-locked fiber lasers. Here, we demonstrate a sideband-free Yb-doped mode-locked fiber laser with dispersion-compensating Gires–Tournois interferometer mirrors. Both the simulation and the experiment demonstrate that the wavelength and energy of the sidebands can be tuned by changing the transmission coefficient of the output mirror, the pump power, and the ratio of the net cavity dispersion to the net third-order dispersion in the cavity. By optimizing these three parameters, the laser can generate a sideband-free, Gaussian-shaped spectrum with a 13.56-nm bandwidth at -0.0232 ps2 net cavity dispersion, which corresponds to a 153-fs pulse duration.

Influence of high-order dispersion on output pulse characteristics in passively mode-locked fiber laser

Influence of high-order dispersion on output pulse characteristics in passively mode-locked fiber laser

SPICE-Compatible Equivalent Circuit Models for Accurate Time-Domain Simulations of Passive Photonic Integrated Circuits

Passive photonic integrated circuits (PICs) can be easily characterized in the frequency-domain, but their accurate time-domain performance evaluation is a hurdle for system-level designers, especially when dealing with resonant circuits having highly dispersive behavior, such as ring resonators. In this paper, a new equivalent circuit modeling and simulation approach is proposed, based on the Complex Vector Fitting algorithm, able to perform accurate and robust time-domain simulations of passive PICs directly in standard SPICE simulators. The proposed modeling technique starts from scattering parameters of passive PICs, and is able to capture linear and high order dispersion, backscattering, and wavelength dependent effects. Considering the different nature of optical and electronic signals, a novel concept of equivalent voltage and current for optical waveguides is proposed to simplify the optical to electronic ports conversion and to make it possible to connect and terminate the equivalent circuit models as needed in SPICE simulators, natively supporting bidirectional signal propagation in a waveguide. This work provides a precise and reliable solution to evaluate time-domain characteristics of passive PICs and to access any internal nodes within a circuit, such as the signals inside a ring resonator. Three examples of time-domain simulations of passive PICs in commercial SPICE simulators are presented to demonstrate the flexibility and advantages of the proposed technique.

On the investigation of optical soliton solutions of cubic–quartic Fokas–Lenells and Schrödinger–Hirota equations

Purpose:When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic Fokas–Lenells equation is also one of the recently developed equations, which has importance in the field of telecommunications regarding optical soliton transmission in the absence of chromatic dispersion. In this study, in order to examine the optical solitons, the Schrödinger–Hirota equation in the presence of the chromatic dispersion and the cubic–quartic Fokas–Lenells equation discarding the chromatic dispersion were investigated. For this intent, by obtaining certain soliton types using the unified Riccati equation expansion method (UREEM), optical soliton solutions were obtained for both models and graphical representations and comments were made. Methodology:By developing appropriate computer algorithms and applying UREEM in the following ways, symbolic calculation software was made and analytical optical soliton solutions were obtained. Findings:Through computer algebra software, we plotted the obtained results via 3D, 2D views and we also illustrated the investigation of wave behavior caused by parameter change on 2D graphics. Originality:Different soliton behavior under the parameters effect of the Schrödinger–Hirota equation having chromatic dispersion and the cubic–quartic Fokas-Lenells equation is investigated and the obtained results are reported.

Design and development of coherent-OOFDM techniques in wavelength division multiplexing optical network for long-haul communication

Abstract Today, communication is a crucial factor and requires a high data rate for transmission with in an error-free environment, so optical communication has emerged as a best solution to high-speed transmission systems due to its higher bandwidth and higher data rates. Fiber optic transmission integrating with some modern processing and modulator techniques are applied in various areas that need transfer of data from one point to another through reducing an optical affect. Coherent optical orthogonal frequency division multiplexing is a popular technique in optical communication today because of the excessive spectral efficiency, immune to interference, tolerance of the fiber dispersion and it is long-haul application. It employs the OFDM modulation method, which is a type of multicarrier modulation in which data statistics are distributed over a large number of low-cost subcarriers and is a solution to inter-symbol interference. Inter-symbol interference is generated by chromatic dispersion in high-speed optical transmission systems, and it is a severe issue in long-haul systems in the case of higher data rates transmission. The use of standard dispersion compensating devices, such as dispersion compensating fiber, does not completely compensate for high order dispersion, which includes third-order and high dispersion effects and also increase the loses of the system because it is a fiber in itself. This study proposes introducing the concept of coherent optical orthogonal frequency division multiplexing techniques in to the wave division optical network in the case of multiple users, high data rate transmission and long-haul and ultra-long-haul optical link to reduce the optical transmission on related issues and to improve the performance of optical network. The performance of the proposed network can be evaluated by using different parameters such as signal to noise ratio, bit error rate, optical signal to noise ratio, Quality factor and eye-diagram at different distance transmission up to 8000 km by using Optisystem software.

Assorted exact explicit solutions for the generalized Atangana’s fractional BBM–Burgers equation with the dissipative term

In this study, the generalized Atangana’s fractional BBM–Burgers equation (GBBM-B) with the dissipative term is investigated by utilizing the modified sub-equation method and the new G'/(bG' + G + a)-expansion method; with the aid of symbolic computations, many types of new exact explicit solutions including solitary wave solutions, trigonometric function periodic solutions, and the rational function solutions are obtained. Some 3D and 2D plots of these solutions are simulated, which show the novelty and visibility of the propagation behavior and dynamical structure of the corresponding equation. Moreover, with the selection of different values on the parameters and orders, we can deduce many types of exact solutions in special cases. We also discussed the changes and characteristics of these solutions, which can help us further understand the inner structure of this equation. The obtained solutions indicate that the approach is easy and effective for nonlinear models with high-order dispersion terms.

Inverse design of soliton microcomb based on genetic algorithm and deep learning.

Soliton microcombs generated by the third-order nonlinearity of microresonators exhibit high coherence, low noise, and stable spectra envelopes, which can be designed for many applications. However, conventional dispersion engineering based design methods require iteratively solving Maxwell's equations through time-consuming electromagnetic field simulations until a local optimum is obtained. Moreover, the overall inverse design from soliton microcomb to the microcavity geometry has not been systematically investigated. In this paper, we propose a high accuracy microcomb-to-geometry inverse design method based on the genetic algorithm (GA) and deep neural network (DNN), which effectively optimizes dispersive wave position and power. The method uses the Lugiato-Lefever equation and GA (LLE-GA) to obtain second- and higher-order dispersions from a target microcomb, and it utilizes a pre-trained forward DNN combined with GA (FDNN-GA) to obtain microcavity geometry. The results show that the dispersive wave position deviations of the inverse designed MgF2 and Si3N4 microresonators are less than 0.5%, and the power deviations are less than 5 dB, which demonstrates good versatility and effectiveness of our method for various materials and structures.

Cherenkov radiation emitted by Kuznetsov–Ma solitons

Cherenkov radiation emitted by Kuznetsov–Ma soliton (KMS) with an arbitrary propagation constant in the presence of higher-order dispersions is studied analytically and numerically. We show that the third-order dispersion (TOD) yields asymmetric radiated bands, while the fourth-order dispersion (FOD) gives rise to symmetric radiated bands only when the value of FOD is positive. In contrast to radiations emitted by other localized waves, such a radiation emerges periodically in propagation, and can exhibit multi-frequency bands which depends strongly on the propagation constant of the KMS. We presented radiation conditions to calculate different frequency bands, which shows great agreement with numerical simulations. Important radiation features such as radiation frequencies, velocities, and distances are shown in phase diagrams. Our results could be helpful for controllable radiations in nonlinear fiber and other nonlinear 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.