Instability Gain Research Articles

Analysis of free carrier effects on modulational instability in silicon-on-insulator nano-waveguides

We have numerically studied the effect of free-carrier-induced loss and dispersion on the modulational instability (MI) gain at low input powers in silicon-on-insulator (SOI) nanowaveguides with normal and anomalous second-order dispersion. We have shown that the free carriers affect the gain spectra even at low input powers. First time we have reported the gain in normal SOI nanowaveguides even in the absence of higher order dispersion parameters, which is due to the interaction of free-carrier-induced dispersion and nonlinearity. The MI gain in an anomalous SOI nanowaveguide vanishes even at a few milliwatt range of input power due to this interaction. We have shown that the gain could be achieved in an anomalous nanowaveguides by reducing the free carrier lifetime.

Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines.

We experimentally generate high-coherence primary Kerr combs with multiple sub-lines by using dual pumps and demonstrate the application of a primary comb state in multichannel communications. We find that more than 10 primary comb lines can be generated within the spectrum of modulation instability gain in our microring resonator. The generation is also verified by numerical simulations and the measured linewidth confirms the high coherence of the generated primary comb lines. We also demonstrate the high-coherence characteristics in a coherent communication experiment, in which each comb line is encoded with 20 Gbaud quadrature phase-shift-keyed signals.

A theoretical study on threshold conditions of modulation instability in oppositely directed couplers

We theoretically investigate threshold conditions to observe modulation instability (MI) in a two-core nonlinear oppositely directed coupler (ODC) with a negative-index material (NIM) channel. Using linear stability analysis, we obtain an expression for the instability gain. The analysis shows, with two discrete instability regions, that the band at lower values of f (ratio of the backward to forward-propagating waves amplitude) is a result of the nonlinear positive index material (PIM) channel while the broader range band is a consequence of the nonlinear NIM channel. Both bands are highly sensitive to system parameters. We demonstrate that MI has a threshold-like condition in the normal dispersion regime. This study also shows that gain increases proportionally to power increases and the two instability regions approach each other, thereby narrowing the stability region. Furthermore, we report that the effect of pump power and the coupling coefficient on instability gain have an opposite relationship. Similarly, study of the influence of the nonlinear coefficient on critical power (Pc) shows that Pc gradually decreases as the nonlinear coefficient increases. Thus, a comprehensive study on the influence of various physical effects on MI is reported in this paper.

Single gain peak from modulation instability in As2Se3 chalcogenide glass photonic crystal fiber

With the As2Se3 photonic crystal fiber (PCF), the effect of pump power and wavelength on modulation instability (MI) gain is studied in detail. Due to high Raman scattering effect and high nonlinearity of As2Se3 PCF, ultra-broadband MI gain is obtained when appropriate pump power and wavelength is chosen, and the optimal MI gain bandwidth reaches 2812 nm. More importantly, competing between Raman scattering and four-wave mixing results in a single gain peak observed in the anti-Stokes region of As2Se3 PCF when pump power is higher than about 3000 W, while there is no gain spectrum in the fiber Stokes region. The phenomenon is found for the first time, and the obtained single gain peak mainly results from Raman scattering effect.

Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model

Under investigation in this paper is a generalized mixed nonlinear Schrödinger equation (GMNLSE) which arises in several physical areas including the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. The linear stability analysis is performed and the instability zones as well as the modulational instability gain are obtained and discussed. Higher–order rogue waves (RWs) in terms of the determinants for the GMNLSE model are constructed by the N-fold Darboux transformation. Several patterns of the RWs are illustrated, such as the fundamental pattern, triangular pattern, circular pattern, pentagon pattern, circular–triangular pattern, and circular-fundamental pattern. Effects of the nonlinear parameters on the RWs are discussed. It is found that the nonlinear terms affect the widths and velocities of the RWs, although the amplitudes of these waves remain unchanged. The semirational RW solution, which is a combination of rational and exponential functions, is derived to describe the interaction between the RW and multi-breather.

Modulation instability in a nonlinear oppositely directed coupler with saturable nonlinearities and higher-order effects

The influence of a saturable nonlinearity on the modulation instability in oppositely directed coupler in the presence of high-order effects is investigated. By using the standard linear stability analysis, we obtain the instability gain that exhibits a significant change in the bands of instability due to the effects of a saturable nonlinearity. We also show that even in the presence of saturation there is no change in instability gain when we compare the results obtained for both channels not influenced by self-steepening effect or for both channels influenced by self-steepening effect but opposite in sign. Regarding the Raman effect, there is reflection symmetry (asymmetry) to the gain at zero perturbation frequency when the values of the Raman coefficients in each directional coupler are equal and with same (opposite) sign. For the anomalous group velocity dispersion regime we observe that the growth of the saturation parameter is followed by an increase in the null gain region near {\Omega} = 0, enlarging the separation of the instability bands close to this point. Finally, we show that an efficient control of the modulation instability can be realized by adjusting self-steepening effect and intrapulse Raman scattering, even in the presence of a saturable nonlinearity.

Propagation of envelope bright breather coupled wave modes in Ablowitz–Ladik chains

We investigate a model of a two coupled Ablowitz–Ladik (AL) lattices which admits the integrable AL model, when it is reduced to symmetric states. We compute the discrete modulational instability gain analytically and verified numerically. The play-role of the coupling parameter ϵ which is the back-bone of the two coupled AL chain is analyzed. We perform molecular dynamics (MD) simulations and elucidate the short time as well as the long time instability of AL chain. We demonstrate that the AL chain supports the formation of bright breather coupled wave modes spanning over 36 lattice sites on either side of the bond-center. We explore a kink solitary profile of solutions for the AL chains by invoking the extended tangent hyperbolic function method (ETHF) embedded with symbolic computation. Spectral stability of the exact solutions is determined by the eigenvalues of the discrete spectrum. We demonstrate the onset of chaos that leads the quasi-periodic dynamics of AL chains through the period-doubling bifurcation route to chaos.

Supercontinuum and rogue soliton generation by induced modulational instability in photonic crystal fibre

We present an approach that enables active control of supercontinuum (SC) and rogue soliton (RS) generation through the modulation of a 500 fs input pulse by numerical simulations. The induced modulational instability contributes to the initial comb-like SC generation, which is fundamentally different from SC initiated by high-order soliton fission. The output spectrum shows great dependence on modulation frequencies and depths. It is interesting that we can manipulate the RS generation by adjusting the modulation parameters. And we also demonstrate the conditions which can be beneficial to RS generation: (i) very weak or large values of modulation depth; (ii) seeding in the vicinity of the peak of the modulational instability gain spectrum. Although RS degrades the smoothness of the SC, it is of great significance in the generation of tailored SC.

Analytical model and experimental verification of the critical power for modulation instability in optical fibers.

Modulation instability is thoroughly investigated and a simple analytical model for its power critically modifying the wave properties in terms of system parameters is derived and experimentally validated. The differences on the modulation instability gain spectrum in lossless and lossy optical fibers are analyzed based on theoretical models and numerical simulations. In particular the impact of background noise on the behavior of modulation instability is studied analytically and verified by measurements and simulations. The proposed analytical model is experimentally validated by monitoring the wave propagation along an optical fiber using a Brillouin optical time-domain analyzer. This way, the evolution of the optical signal traveling through optical fibers, especially, the pump depletion and the recurrence phenomenon are investigated.

Triply resonant coherent four-wave mixing in silicon nitride microresonators.

Generation of multiple tones using four-wave mixing (FWM) has been exploited for many applications, ranging from wavelength conversion to frequency comb generation. FWM is a coherent process, meaning that its dynamics strongly depend on the relative phase among the waves involved. The coherent nature of FWM has been exploited for phase-sensitive processing in different waveguide structures, but it has never been studied in integrated microresonators. Waveguides arranged in a resonant way allow for an effective increase in the wavelength conversion efficiency (at the expense of a reduction in the operational bandwidth). In this Letter, we show that phase shaping of a three-wave pump provides an extra degree of freedom for controlling the FWM dynamics in microresonators. We present experimental results in single-mode, normal-dispersion high-Q silicon nitride resonators, and numerical calculations of systems operating in the anomalous dispersion regime. Our results indicate that the wavelength conversion efficiency and modulation instability gain in microcavities pumped by multiple waves can be significantly modified with the aid of simple lossless coherent control techniques.

Weibull-type speckle distributions as a result of saturation in stimulated scattering processes

AbstractDuring the propagation of an optically smoothed laser beam through a warm plasma the speckle field pattern and the corresponding speckle intensity distribution are modified in time and along the laser propagation direction. It is shown here that the laser–plasma interaction can change the character of speckle statistics from an initially exponential-type limit law to a Weibull-type law. The Weibull distribution is characterized by a power-law-type behavior in a limited interval of the random variable, which is, in the present case, the speckle intensity. The properties of the speckle distributions are studied using methods of extremal and order statistics. The scattering instability process (here stimulated Brillouin forward scattering) causing the change in speckle statistics has an onset behavior associated with a “critical gain” value, as pointed out in work by Rose and DuBois (1993b). The saturation of the instability process as a function of intensity explains the limited interval of the Weibull-type speckle distribution. The differences in the type of the speckle statistics are analyzed by using “excess over threshold” methods relying on the generalized Pareto distribution, which clearly brings to evidence the transition from an exponential type distribution to the Weibull-type distribution as a function of the instability gain value, that is, from the regime below critical gain to values above the critical gain.

Suppression of microbunching instability via a transverse gradient undulator

The microbunching instability in the linear accelerator (linac) of a free-electron laser facility has always been a problem that degrades the electron beam quality. In this paper, a quite simple and inexpensive technique is proposed to smooth the electron beam current profile to suppress the instability. By directly adding a short undulator with a transverse gradient field right after the injector to couple the transverse spread into the longitudinal direction, additional density mixing in the electron beam is introduced to smooth the current profile, which results in the reduction of the gain of the microbunching instability. The magnitude of the density mixing can be easily controlled by varying the strength of the undulator magnetic field. Theoretical analysis and numerical simulations demonstrate the capability of the proposed technique in the accelerator of an x-ray free-electron laser.

A numerical study of the generation mechanism of internal solitary waves in the Luzon Strait

The South China Sea (SCS) is a hot spot for oceanic internal solitary waves due to many factors, such as the complexity of the terrain environment. The internal solitary waves in the northern SCS mainly originate in the Luzon Strait. The generation mechanism of the internal solitary waves in the Luzon Strait is discussed using a modulation instability. The energy gain of the modulation instability is derived based on the fully nonlinear Schrodinger equation. The peak value of the gain is calculated under different conditions of stratification, wavelength and the initial amplitude of an internal tidal wave. The characteristics of the modulation instability in the Luzon Strait are investigated. The conditions that make the internal tidal wave evolve into an internal solitary wave in the Luzon strait are also obtained. The results show that the internal tide waves can generate the modulation instability in the Luzon Strait and that the maximum gain occur at the eastern sill of the Luzon Strait, where the internal tide waves start to break up into internal solitary trains. The magnitude and the scope of the peak gain are relevant to the stratification and the initial conditions of the internal tide waves. The numerical simulation results are consistent with the in-situ data.

Nonlinear Label-Free Biosensing With High Sensitivity Using As<sub>2</sub>S<sub>3</sub> Chalcogenide Tapered Fiber

We demonstrate an experimentally feasible fiber design, which can act as a highly sensitive, label-free, and selective biosensor using the inherent high nonlinearity of an As2S3 chalcogenide tapered fiber. The surface immobilization of the fiber with an antigen layer can provide the possibility to selectively capture antibody biomolecules. This increase of the layer thickness directly affects the group velocity dispersion of the fiber and, thus, the modulation instability (MI) gain spectrum changes (location of the anti-Stokes and Stokes wavelengths) when pumping the fiber close to the zero-dispersion wavelength. The sensitivity of the sensor was predicted to be ∼18 nm/nm, defined as the shift in resonance wavelength per nanometer biolayer thickness, which is almost twice the current record sensitivity of nonlinear MI-based fiber optical biosensors. Importantly, due to the strong nonlinearity of As2S3, this high sensitivity can be obtained using a low-power 1064-nm microchip laser.

Ultra-broadband modulation instability gain characteristics in As2S3 and As2Se3 chalcogenide glass photonic crystal fiber**Project supported by the National Natural Science Fundation of China (Grant No. 11404286), the Natural Science Fundation of Zhejiang Province, China (Grant No. LY15F050010), and the Scientific Research Foundation of Zhejiang University of Technology, China (Grant No. 1401109012408).

Based on the designed As2Se3 and As2S3 chalcogenide glass photonic crystal fiber (PCF) and the scalar nonlinear Schrödinger equation, the effects of pump power and wavelength on modulation instability (MI) gain are comprehensively studied in the abnormal dispersion regime of chalcogenide glass PCF. Owing to high Raman effect and high nonlinearity, ultra-broadband MI gain is obtained in chalcogenide glass PCF. By choosing the appropriate pump parameter, the MI gain bandwidth reaches 2738 nm for the As2Se3 glass PCF in the abnormal-dispersion region, while it is 1961 nm for the As2S3 glass PCF.

Effects of fourth-order dispersion on modulational instability in metamaterials with exponential saturable nonlinearity and self-steepening coefficients

We studied the modulational instability in negative index materials with higher-order effects. An expression for the instability gain is derived through the linear stability analysis. We identify and discuss the salient features of the effect, like fourth-order dispersion, self-steepening and saturable nonlinearity on the modulational instability. The results show that the instability gain depends on the sign of the higher-order dispersion and, for anomalous dispersion, the instability regime is constituted of two parts: the conventional gain spectrum and the secondary gain spectrum induced by the fourth-order dispersion. For large values of the fourth-order dispersion, the secondary instability region spectrum vanishes and merges with the ordinary gain. In the normal dispersion regime, an efficient control of the modulation instability is successfully demonstrated by adjusting the fourth-order dispersion, depending on the presence of the self-steepening parameter or the normalized input power.

Influence of self-steepening and intrapulse Raman scattering on modulation instability in oppositely directed coupler.

We investigate the modulation instability in oppositely directed coupler in the presence of higher-order effects. Using linear stability analysis, we obtain an expression for instability gain. Special attention is paid to find out the influence of self-steepening effect and intrapulse Raman scattering on modulation instability. The study shows that in normal dispersion, regime instability gain exists even if perturbation frequency (Ω) is zero. But the instability gain at Ω=0 is zero, when the dispersion is anomalous. Moreover, self-steepening effect and intrapulse Raman scattering form new instability regions and, hence, provide a new way to generate solitons or ultrashort pulses. Further, efficient control of modulation instability by adjusting self-steepening effect and intrapulse Raman scattering also successfully demonstrated.

Rogue-wave pattern transition induced by relative frequency

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

The peripubertal gender-dysphoric child: puberty suppression and treatment paradigms.

Gender-nonconforming youth are emerging at increasingly younger ages, and those experiencing gender dysphoria are seeking medical care at, or sometimes even before, the onset of puberty. Youth with gender dysphoria are at high risk for depression, anxiety, isolation, self-harm, and suicidality at the onset of a puberty that feels wrong. Medical providers would benefit from understanding interventions that help gender-nonconforming children and youth thrive. The use of gonadotropin-releasing hormone (GnRH) agonists to block the onset of an undesired puberty in youth with gender dysphoria is a relatively new practice, particularly in the United States. These medications shut down the hypothalamic-pituitary-gonadal axis (HPG), and the production of either testosterone or estrogen is temporarily halted. Puberty blocking allows a young person to explore gender and participate more fully in the mental health therapy process without being consumed by the fear of an impending developmental process that will result in the acquisition of undesired secondary sexual characteristics. GnRH agonists have been used safely for decades in children with other medical conditions, including central precocious puberty. Potential side effects of GnRH agonists include diminished bone density, injection site problems, emotional instability, and weight gain. Preliminary data have shown GnRH agonists to be very helpful in improving behavioral and overall functioning outcomes. Puberty suppression should ideally begin in the first stages of pubertal development and can be given via intramuscular or subcutaneous injections, or via an implant that is inserted in the upper arm. Monitoring to assure suppression of the HPG axis should occur regularly. Gender-nonconforming youth who remain gender dysphoric can go on to receive cross-sex hormones for phenotypic gender transition when they are older. GnRH agonists have changed the landscape of medical intervention for youth with gender dysphoria and are rapidly becoming the standard of practice.

Microbunching instability suppression via electron-magnetic-phase mixing.

Control of the microbunching instability is a fundamental requirement in modern high-brightness electron linacs, in order to prevent misleading responses of beam optical diagnostics and contamination in the generation of coherent radiation, such as free electron lasers. We present the first experimental demonstration of control and suppression of microbunching instability by means of particles' longitudinal phase mixing in a magnetic chicane. In the presence of phase mixing, the intensity of the beam-emitted optical transition radiation, which is used as an indicator of the instability gain at optical wavelengths, is reduced by one order of magnitude and brought to the same level provided, alternatively, by beam heating. The experimental results are in agreement with particle tracking and analytical evaluations of the instability gain. This article is extended to a discussion of applications of magnetic-phase mixing to the generation of quasicold high-brightness ultrarelativistic electron beams.