Normal Dispersion Regime Research Articles

Propagation dynamics of elliptical super-Gaussian bullets in nonlinear metamaterial waveguide

The characteristics of an optical beam propagating in a medium should be preserved for many applications related to fiber optic communication. The phenomenon of self-trapping due to adequate balance among linear and nonlinear effects may preserve the characteristics of an optical beam. In this work, we perform a theoretical investigation on the propagation of a spatiotemporal elliptical super-Gaussian beam in a Kerr nonlinear metamaterial waveguide. We follow the Lagrangian variational method and numerical analysis using the appropriate trial function for the input elliptical super-Gaussian beam and analyze the self-trapping and deformation of the propagating beam in metamaterials. We obtain special conditions to observe the self-trapping and stabilize the dynamics of the elliptical super-Gaussian beam in both negative and positive index regimes of the metamaterial. It is found that in the negative index regime of metamaterial, the phenomenon of self-trapping may exist in the normal dispersion regime with defocusing Kerr nonlinearity. However similar to the conventional medium, the robust balance among the anomalous dispersion and focussing Kerr nonlinearity supports the self-trapping in the positive index regime. There is a critical optical power for the input beam to observe the pulse trapping phenomena. This power is found to be a function of the super-Gaussian parameter as well as the ellipticity of the input beam. The period of self-trapping is also a function of the super-Gaussian parameter and the ellipticity of the input beam.

Build-up dynamics of different pulse types in a dispersion-managed Yb-doped fibre laser

We present a dispersion-managed mode-locked ytterbium fibre laser based on the nonlinear polarization evolution technique. Four single-pulse states could be generated by changing group delay dispersion values from anomalous (−0.0038 ps2) to normal (0.051 ps2) with a grating pair. In the normal dispersion regime, the pulse width was gradually decreased with the decrease of the net dispersion. In the anomalous dispersion region, the typical soliton was obtained, which time-bandwidth product could be calculated as 0.526. In addition, the dynamics of four states were also investigated by using the dispersive Fourier transformation technique. Different pulse evolution dynamics were observed from chaotic state to mode-locking.

Temporal characteristics of stationary switching waves in a normal dispersion pulsed-pump fiber cavity.

Kerr cavities driven in the normal dispersion regime are known to host switching waves. These consist of a traveling wavefront that connects separate regions associated with high- and low-intensity steady states of the cavity. In this Letter, we drive a 230-m custom built fiber ring cavity with strong normal dispersion using nanosecond pulses, allowing us to directly resolve the fine structure of individual switching waves, including resonant oscillations occurring over periods of the order of ∼10 ps. We demonstrate the intimate connection between the temporal and spectral features of the dispersive waves associated with switching waves, while also investigating how these dispersive waves evolve with cavity parameters, namely the frequency detuning and pump desynchronization. Furthermore, by applying a localized and temporary perturbation to our driving field in the presence of a phase modulation trapping potential, we are able to generate a stable and persistent dark pulse, allowing us to directly observe and model the interlocking of two stationary switching waves under quasi-CW pumping conditions. These results further verify the accuracy of the dispersive wave formalism used, and show that their temporal modulation frequency and decay rate in a pulsed-pumped cavity are accurately captured from theory previously applied to CW-pumped systems.

Coherent Combining for High‐Power Kerr Combs

AbstractKerr frequency combs enable the miniaturization of comb sources for applications such as data communications and spectroscopy. However, due to the high field confinement and effective nonlinearity, Kerr combs typically operate with low output comb powers. While nonsolitonic Kerr combs operating in the normal group velocity dispersion (GVD) regime can access high pump‐to‐comb conversion efficiencies and relatively flat spectral profiles, many frequency comb applications require even higher comb‐line powers that are otherwise fundamentally unattainable without the use of optical amplifiers. A high efficient coherent beam combining of Kerr combs is demonstrated via on‐chip synchronization to greatly enhanced comb‐line powers. Two normal GVD Kerr combs are coherently combined for a 2.9 dB increase in comb power compared to a single comb while maintaining a high total pump‐to‐comb conversion efficiency of 26%. Lastly, it is shown that via spectral engineering of two normal GVD combs, it should be possible to significantly increase the spectral flatness of a combined comb. This platform enables fully integrated systems with powers that can readily exceed that of an individual comb system by more than an order of magnitude.

Engineering nonautonomous chirped rogue waves in coupled nonlinear Schrödinger equations with external potentials in normal dispersion regimes

Engineering nonautonomous chirped rogue waves in coupled nonlinear Schrödinger equations with external potentials in normal dispersion regimes

Modulational instability and soliton trains in optical fiber media with real and imaginary Raman gains

We consider a higher-order nonlinear Schrödinger amplitude equation with real and imaginary Raman gain terms. This equation is shown to govern the propagation of femtosecond pulses in optical fiber media. We investigate on the modulational instability of continuous wave solution of this amplitude equation and show that the gain exist in both the anomalous and normal dispersion regimes, provided the complex intrapulse Raman terms are considered. However, when the dissipation induced by Raman process in the optical fiber is neglected; periodic bright solitary waves can only be identified in the anomalous dispersion regime. Nonlinear periodic trains of optical pulses are analytically obtained using the ansatz technique which incorporates the direct integral method. The observation of an optical shock front moving at the group velocity, is attributed to the Raman dissipation process in the optical fiber. Finally, results of numerical simulations equally underscores the influence of Raman gain terms on the evolution of optical soliton trains.

Cavity-birefringence-based manipulation of long-duration optical pulses in a passively mode-locked fiber laser with large normal dispersion.

Optical pulse manipulation in the large normal dispersion regime through intracavity birefringence management is demonstrated experimentally in an erbium-doped fiber (EDF) laser, for the first time to the best of our knowledge. The EDF laser is passively mode-locked based on a nonlinear amplifying loop mirror (NALM) in a figure-of-eight (f-8) configuration. Different lengths of the same type of polarization-maintaining fiber (PMF) are incorporated into the NALM to vary the net cavity birefringence. For each length of PMF, various polarization states and pump powers were tested and compared to achieve a pulse duration tuning range as large as possible. For comparison, these polarization states and pump powers were also studied by incorporating the PMF into the unidirectional loop of the f-8 cavity. Our results reveal some new features for the management of cavity birefringence that can enable long-duration pulse manipulation in the large normal dispersion regime.

Quintic Dispersion Soliton Frequency Combs in a Microresonator

AbstractChip‐scale optical frequency combs have attracted significant research interest and can be used in applications ranging from precision spectroscopy to telecom channel generators and lidar systems. In the time domain, microresonator based frequency combs correspond to self‐stabilized soliton pulses. In two distinct regimes, microresonators are shown to emit either bright solitons in the anomalous dispersion regime or dark solitons (a short time of darkness in a bright background signal) in the normal dispersion regime. Here, the dynamics of continuous‐wave‐laser‐driven soliton generation is investigated in the zero‐group‐velocity‐dispersion regime as well as the generation of solitons that are spectrally crossing different dispersion regimes. In the measurements, zero‐dispersion solitons with multipeak structures (soliton molecules) are observed with distinct and predictable spectral envelopes that are a result of fifth‐order dispersion of the resonators. Numerical simulations and the analysis of bifurcation structures agree well with the observed soliton states. This is the first observation of soliton generation that is governed by fifth‐order dispersion, which can have applications in ultrafast optics, telecom systems, and optical spectroscopy.

Modulational instability in PT -symmetric Bragg grating structures with saturable nonlinearity

We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system, which gives rise to an additional degree of freedom, due to the concept of $\mathcal{PT}$ symmetry. We obtain the nonlinear dispersion relation of the saturable model and discover that such dispersion relations for both the conventional and $\mathcal{PT}$-symmetric cases contradict the conventional Kerr and saturable systems by not displaying the typical signature of loop formation in either the upper branch or lower branch of the curve drawn against the wave number and detuning parameter. We employ a standard linear stability analysis to study the MI dynamics of the continuous waves perturbed by an infinitesimal perturbation. The main objective of this paper is twofold: We investigate the dynamics of the MI gain spectrum at the top and bottom of the photonic band gap followed by a comprehensive analysis carried out in the anomalous and normal dispersion regimes. As a result, this perturbed system driven by the saturable nonlinearity and gain or loss yields a variety of instability spectra, which include the conventional sidebands, monotonically increasing gain, the emergence of a single spectrum in either of the Stokes wave-number regions, and so on. In particular, we observe a remarkably peculiar spectrum, which is caused predominantly by the system parameter, though the perturbation wave number boosts the former. We also address the impact of all the physical parameters considered in the proposed model, which include the coupling coefficient, dispersion parameter, and saturable nonlinearity on the phenomenon of MI for different $\mathcal{PT}$-symmetric regimes ranging from the unbroken one to the broken one in greater detail.

Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network

We deploy a supervised machine-learning model based on a neural network to predict the temporal and spectral reshaping of a simple sinusoidal modulation into a pulse train having a comb structure in the frequency domain, which occurs upon nonlinear propagation in an optical fibre. Both normal and anomalous second-order dispersion regimes of the fibre are studied, and the speed of the neural network is leveraged to probe the space of input parameters for the generation of custom combs or the occurrence of significant temporal or spectral focusing.

Third-harmonic generation in silica wedge resonators

Whispering-gallery-mode microcavities are known to have a high optical quality factor, making them suitable for nonlinear optical interactions. Here, third-harmonic generation is observed using a relatively small radius wedge silicon oxide optical microcavity. The small radii wedge microdisks can be dispersion-tailored to obtain either normal or anomalous group velocity dispersion. In our case, we operated in the normal dispersion regime preventing frequency comb generation by suppressing IR cascading four-wave mixing. This approach allowed for a clean third-harmonic generation at phase-matched visible optical modes. Tunability of the third-harmonic emission was obtained due to a combination of thermo-optical and Kerr effects. An additional thermal control of the phase-matching condition allows the optimization of the third-harmonic generation, and an agreement between this process and the couple-mode theory was demonstrated.

Dissipative Solitons and Switching Waves in Dispersion-Modulated Kerr Cavities

We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose spectrum encompasses an integrated dispersion that exceeds the cavity free-spectral range. We are able to access this regime in low-dispersion photonic chip-based microresonators by employing synchronous pulse driving, which increases the peak power over the continuous-wave-driving regime. Exploring this dispersion-folded regime, we demonstrate that the presence of periodically varying dispersion can excite higher-order comb structures, which we explore in both the normal and anomalous dispersion regimes. In the former, we observe the coexistence of switching wave fronts with Faraday instability-induced period-doubling patterns. They manifest as strong satellite microcombs highly separated either side of the core microcomb, at an offset close to half the repetition rate but while sharing the same repetition rate. In the latter, for dissipative Kerr solitons in anomalous dispersion, we observe the formation of higher-order phase-matched dispersive waves (“Kelly-like” sidebands), where the folded dispersion crosses the frequency comb grid. We observe up to the fifth higher-order dispersive wave in our experiments and show that these higher-order dispersive waves coherently extend the soliton frequency comb bandwidth significantly. For both cases, we show that our results can be understood by considering four-wave mixing in a two-dimensional Fourier transform representation. The results demonstrate the rich novel nonlinear dynamics of driven dissipative nonlinear cavities with periodically varying dispersion in the dispersion-folded pumping regime.2 MoreReceived 19 June 2022Accepted 14 February 2023DOI:https://doi.org/10.1103/PhysRevX.13.011040Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasPattern formationSpatiotemporal chaosPhysical SystemsCoherent structuresFloquet systemsFront propagationNonlinear wavesSolitonsSynchronizationNonlinear Dynamics

Non-linear dynamics of multimode semiconductor lasers: dispersion-based phase instability and route to single-frequency operation.

Emission dynamics of a multimode broadband interband semiconductor laser have been investigated experimentally and theoretically. Non-linear dynamics of a III-V semiconductor quantum well surface-emitting laser reveal the existence of a modulational instability, observed in the anomalous dispersion regime. An additional unstable region arises in the normal dispersion regime, owing to carrier dynamics, and has no analogy in systems with fast gain recovery. The interplay between cavity dispersion and phase sensitive non-linearities is shown to affect the character of laser emission with phase turbulence, leading to regular self-excited oscillations of mode intensity, self-mode locking, and single-frequency emission stabilized by spectral symmetry breaking. Such physical behavior is a general phenomenon for any laser with a slow gain medium relative to the round trip time, in the absence of spatial inhomogeneities.

Modulation instability solitons in oppositely double-doped directed couplers with two negative refractive index material channel and non-Kerr nonlinearity

In a three-core nonlinear contrarily directed coupler with two negative-index material channels, we theoretically explore the instability in the presence of a non-Kerr-like nonlinear refractive-index shift. Through the use of linear stability analysis, we determine an expression for the instability gain. It is discovered that the septic saturation, the ratio of the forward- to backward-propagating wave power, pump power, and nonlinearity all have a substantial impact on the MI in the nonlinear three-core contrarily directed coupler. The septic and saturation nonlinearity is found to improve the MI in the case of forward-to-backward ratio power (f) by boosting the width and gain of the instability profile in both normal and abnormal dispersion regimes. However, septic nonlinearity improves the MI in the case of pumps by boosting both its width gain and in the abnormal dispersion regime alone. Using 2D pictures, we could investigate the MI's dynamic behaviour during an anomalous dispersion regime. We discovered from the contour images that the gain of the instability profile grows as septic and saturation nonlinearity increases in both normal and abnormal dispersion regimes. So, with a focus on a negative refractive material channel in the existence of contamination and saturation nonlinearity, we report new techniques for producing and controlling MI and soliton in three-core contrarily directed couplers.

Modified nonlinear saturable effects on instability characteristics in three-core oppositely directed coupler with Kerr nonlinearity

This work shows that it is possible to observe the modulational instability (MI) zones caused by the modified form of nonlinear saturation effect in triangular design of a three-core oppositely directed coupler. In this design, the first and third channels are made of a material with a low (negative) refractive index, while the second one is made of a high (positive) index. The governing equations are modified coupled nonlinear Schrödinger equations with saturable nonlinearity terms and coupling terms. In the presence of modified saturable nonlinearity, we can determine the dispersion relation for the optical coupler. We use a linear stability approach to investigate the modulation instability characteristic gain in the normal and anomalous group-velocity dispersion regimes. We greatly widened the spectrum of physical system parameters to consider various contingencies. Using nonlinear and power factors, MI can be controlled. Nonlinear saturation effect normally can suppress the MI gain and bandwidth in optical fiber system. But, as compared to conventional saturable nonlinearity, the modified saturation nonlinearity more significantly changes the MI dynamical behaviour. The analytical results show that new instability bands are created in a system parameter's normal and anomalous dispersion regimes. As a result of the effects of modified nonlinear saturation, we describe new methods for creating and managing the soliton through MI in three-core oppositely directed couplers with two negative index material channels.

Dispersion Management Nonlinear Multimode Interference Mode-Locked Ytterbium Fiber Laser.

Dispersion management plays an important role in improving the output performance of a mode-locked fiber laser. Therefore, dispersion management is carried out by introducing the grating pair in our experiment. Through adjusting the distance between the grating pair, mode-locked pulses corresponding to different dispersion regimes can be realized, which typically range from soliton state in the anomalous dispersion regime to the dissipative soliton format in the normal dispersion regime. Furthermore, tunable spectrum distribution can be achieved by adjusting two intra-cavity polarization controllers. The proposed dispersion management method complements mode-locking techniques based on nonlinear multimode interference (NL-MMI). The laser can operate with self-start mode locking stably and is useful for practice applications.

Effects of saturable function in three-core PIM-NIM-PIM coupler through modulation instability

We consider a model of three-core PIM-NIM-PIM coupler with Kerr-type saturable nonlinearity to study both analytically and numerically saturation effects on the modulational instability (MI) phenomenon. The analytical results show us that, in presence of saturable parameters in normal and anomalous dispersion regime the instability gain presents significant changes compared to Shafeeque et al. (Phys Lett A 11:223–229, 2015) in absence of saturable parameter. It clearly also shows that Power and nonlinear parameters can be used to control MI. Through numerical simulation, the generations of periodic soliton are obtained in presence of nonlinear saturation. However in absence of saturable parameter, the train of soliton obtained turns into a turbulent state after a certain propagations distance, and in that case, the system is prone to present MI.

Theoretical and experimental investigations of dispersion-managed, polarization-maintaining 1-GHz mode-locked fiber lasers.

High-repetition-rate (up to GHz) femtosecond mode-locked lasers have attracted significant attention in many applications, such as broadband spectroscopy, high-speed optical sampling, and so on. In this paper, the characteristics of dispersion-managed, polarization-maintaining (PM) 1-GHz mode-locked fiber lasers were investigated both experimentally and numerically. Three compact and robust 1-GHz fiber lasers operating at anomalous, normal, and near-zero dispersion regimes were demonstrated, respectively. The net dispersion of the linear cavity is adjusted by changing types of PM erbium-doped fibers (EDFs) and semiconductor saturable absorber mirrors (SESAMs) in the cavity. Moreover, the long-term stability of the three mode-locked fiber lasers is proved without external control. In order to better understand the mode-locking dynamics of lasers, a numerical model was constructed for analysis of the 1-GHz fiber laser. Pulse evolution simulations have been carried out for soliton, dissipative-soliton, and stretched-pulse mode-locking regimes under different net dispersion conditions. Experimental results are basically in agreement with the numerical simulations.

Modulation instability gain and wave patterns in birefringent fibers induced by coupled nonlinear Schrödinger equation

In this work, we studied the behavior of the modulation instability (MI) growth rate and modulated wave (MW) bright and dark-soliton in nonlinear optical fibers (OFs) where both birefringence and four-wave mixing (4WM) terms are employed. We have shown the effects of the 4WM and the group velocity dispersion (GVD) on the MI gain and MI bands as well as on the MWs patterns. For certain conditions on the coupled nonlinear Schrödinger equation (CNLSE) parameters, we exhibited stable and unstable zones of the MI. More precisely, in a normal dispersion regime, we shown how the variation of 4WM can generate additional sides lobes and consequently the formation of new MI bands. Furthermore, it is observed that when the coupling coefficient (CC) increases, its effects could reduce the stability zones by increasing strongly the number of sides lobes in a normal dispersion regime. To seek the behavior of the MWs patterns, we used numerical investigation (NI). From these results, it has been observed the propagation of the MW bright-soliton and dark-soliton with the effects of the 4WM. We noticed that the MWs patterns can preserve high energy on the peak and keep constant its shapes in birefringent OFs. These results show that the 4WM and the GVD behave as being energy sources for MI and MWs. Our finding can help to manufacture OF tools and could open the way for the use of the 4WM and cross-phase modulation (XPM) to generate MI bands and long-live temporal MWs patterns.

µJ-level normal dispersion fiber optical parametric chirped-pulse oscillator based on a collapsed-ends photonic crystal fiber

We demonstrate the generation of broadband tunable and synchronized pulses exceeding the microjoule level using the new concept of fiber optical parametric chirped-pulse oscillation (FOPCPO). The oscillator is based on a collapsed-ends photonic crystal fiber pumped in the normal dispersion regime by a fiber laser.