Modulation instability scenario in negative index materials

We present an investigation of the critical frequency windows permitting modulation instability in negative index materials. The principal motivation for our analysis stems from the impact of the inevitable presence of the effective dispersive magnetic permeability in addition to the effective dielectric permittivity determining the propagation model for ultrashort pulses in negative index materials. We emphasize the influence of nonlinear dispersion terms, arising out of the combinatorial effect of the dispersive permeability with the nonlinear polarization, over the MI phenomena, the outcome of its development achieved by using linear stability analysis. Gain spectrum investigation has been carried out for both anomalous and normal dispersion regime in the focusing and defocusing cases of nonlinearity and near zero dispersion regime where higher order linear dispersive effects emerge. The results of linear stability analysis have been validated by direct numerical simulation of the governing equation using the split-step Fourier transform method. We show that second-order nonlinear dispersion opens up distinct MI windows with their appropriate conditions and unlike the first-order nonlinear dispersion term, the sign of it has got deep consequences in the modulation instability scenario.     

Spectral evolution of an optical pattern generated by spatial modulation instability in a reorientational Kerr nonlinear medium

An experimental investigation is reported on the role of molecular reorientational nonlinearity in the spectral evolution of multifilamentation patterns induced by spatial modulation instability (MI) in a nonlinear Kerr medium. The influence of molecular reorientational Kerr nonlinear response on the spatial MI is analyzed theoretically by the standard stability analysis. The spatial MI gain spectra obtained by experimental measurements were found to agree with the theoretical derivation. In addition, by changing the launch average power, we also analyze the spatial spectral behavior of the optical pattern in such media. It is shown that, for higher launch average power, there will be secondary spatial stripes, manifesting as the original spatial modulation frequency doubling in the spatial frequency domain, which originated from the molecular reorientational Kerr nonlinearity response.     

Novel high gain regimes of spatio-temporal modulational instability for a single-cycle pulse in metamaterials

We derive a generalized expression for the spatio-temporal modulational instability (MI) gain in a metamaterial incorporating linear dispersion terms up to fourth order and nonlinear dispersion terms up to second order and study the influence of the varying input pulse widths and carrier frequency on MI gain. For a single-cycle pulse we have found new regimes of spatio-temporal MI, symmetrically located with respect to the central gain maximum at q?=?0 (q being the transverse spatial frequency of the perturbation). The gain in these new branches of MI is much higher compared to the central branch.     

Modulational instability in metamaterials with saturable nonlinearity and higher-order dispersion

Modulational instability (MI) in negative refractive metamaterials with saturable nonlinearity, fourth-order dispersion (FOD), and second-order nonlinear dispersion (SOND) is investigated by using standard linear stability analysis and the Drude electromagnetic model. The expression for the MI gain spectrum is obtained, which clearly reveals the influence of the saturation of the nonlinearity, FOD, and SOND parameters on the temporal MI. The evolution of the MI in negative refractive metamaterials is numerically investigated. Special attention is paid to study the effects of the higher-order dispersion terms on the formation and evolution of the solitons induced by MI. It is shown that as the third-order dispersion term increases, the solitons travel toward the right. Moreover, the magnitude of the FOD term influences considerably the number of wave trains induced by MI.     

Higher order dispersion effects in the noninstantaneous nonlinear Schrödinger equation

We present a systematic analysis of the effects, of higher-order dispersion, noninstantaneous nonlinear response, as well as stochastic coefficients in optical fiber. This study is motivated by recent experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber. Analytical expression of pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order as well as fourth-order dispersion effects involved. The influence of stochasticity, as well as the delayed Raman response in the nonconventional sidebands obtained due to the fourth-order dispersion, is considered. We note that the shape of the spectrum, and in particular the relative intensities of the higher order harmonics, is highly sensitive to the initial presence of classical noise, and can therefore be taken as a signature that the MI is seeded by vacuum fluctuations. Some direct simulations to see the evolution of different continuous wave states are reported. These show the formation of modulation instability pulses as well as transitions from lower amplitude continuous wave states to higher amplitude continuous wave states. The present results fit well with recent experimental investigations.     

Small-signal analysis of cross-phase modulation instability in lossy fibres

Based on the small signal analysis theory and split-step Fourier method, the complex nonlinear Schrodinger equation (NLSE) with fibre loss can be solved. This procedure is also adapted to the NLSE with the high order dispersion terms (β₃,?β₄). Because the fibre loss is taken into account, experiment demonstrates that the cross-phase modulation instability gain spectrum is more similar to represent the actual systems. The fibre loss decreases the modulation instability (MI) gain and has an effect on SNR which is caused by the cross-phase modulation instability. The MI intensity fluctuation caused by the nonlinear and dispersion effects is directly derived. As a result, the initial stage of MI can be described, and the whole characteristic of MI can also be discussed in this way.     

Dynamics of self-similar sub-10-fs-pulses in an inhomogeneous highly nonlinear fibre amplifier

ABSTRACT

We study the propagation of ultrashort pulses of width around sub-10 femtosecond in an inhomogeneous highly nonlinear single-mode fibre within the framework of a generalized higher-order nonlinear Schrödinger equation with derivative non-Kerr nonlinear terms and spatially inhomogeneous coefficients. Additional effects to the cubic model include the distributed third-order dispersion, self-steepening, self-frequency shift due to stimulated Raman scattering, quintic nonKerr nonlinearity, derivative non-Kerr nonlinear terms, and gain or loss. The exact self-similar brightand dark-solitary-wave solutions of the governing equation are derived via a transformation connected with the constant-coefficient higher-order nonlinear Schrödinger equation with non-Kerr nonlinearity. The constraint relations among the optical fibre parameters for the existence of these self-similar structures are also discussed. Based on these exact solutions, we investigate the dynamical behaviours of self-similar localized pulses in a periodic distributed fibre system for different parameters.     

Modulation instability dynamics of coupling pulses with different powers in nonlinear fibers

In the paper, the modulation instability (MI) of the pulses with different powers is studied based on the modified coupled nonlinear Schrödinger equations in nonlinear fiber. By analyzing MI gain spectrum with different power ratios, it shows that the increase of power ratio leads to the diminution in the range of strongly unstable frequency and the decrease in the gain of MI spectra. With a fixed power ratio, the increased relaxation time is equally suppressing overall MI.     

Effects of nonlinearity in asymmetric adiabatic three-waveguide directional couplers

We study the effects of optical nonlinearity in asymmetric adiabatic three-waveguide directional couplers, that consist of both linear and nonlinear waveguides. We consider several combinations of linear and nonlinear waveguides and show that the different combinations have different switching characteristics. We also find that in the structure where the central waveguide is nonlinear and the two outer waveguides are linear the nonlinearity does not play a role.     

Bright and dark solitons in the normal dispersion regime of inhomogeneous optical fibers

In this letter, under investigation is a nonlinear Schrödinger equation with varying dispersion, nonlinearity and loss for the propagation of ultra-short optical pulses in the normal dispersion regime of optical fibers. By virtue of the modified Hirota's method and symbolic computation, the analytic two-soliton solution is explicitly obtained. Both the bright and dark solitons are observed in the normal dispersion regime of optical fibers with dispersion management. An asymptotic analysis to verify the elastic collision between solitons is performed and the stability of the soliton solutions is investigated. Besides, a new bright solitonic generator for generating high-power and narrow bandwidth pulses is advised. Furthermore, possible applicable soliton control techniques which might be used for the design of optical switch and dispersion-managed systems are proposed.     

Grey and black optical solitary waves,and modulation instability analysis to the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

This paper addresses the nonlinear Schrödinger equation (NLSE) with Kerr law nonlinearity and perturbation terms in optical fibre. A class of grey and black optical solitary wave solutions of this equation are retrieved by adopting an appropriate solitary wave ansatz solution. These types of solitary waves play a vital role in understanding various physical phenomena in nonlinear systems. This lead to a constraint condition on the solitary wave parameters which must hold for the solitary waves to exist. Moreover, the modulation instability (MI) analysis of the model is studied by employing the concept of linear-stability analysis (LSA) and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviours of the equation.     

Impacts of cross-phase modulation on modulation instability of Airy pulses

The modulation instability (MI) of Airy pulses with the influence of cross-phase modulation is studied based on the coupled nonlinear Schrödinger equations in nonlinear media. The main lobe of Airy pulses can be manifested as breakup of MI under interaction with higher power pumped solitons, although the power of Airy pulses is small. By comparing the main lobe’s gain spectrum of MI, the gain spectrum has gradually improved with the increase of power of pumped solitons. The gain spectrum of MI of the main lobe is inversely proportional to the truncation coefficient, and then it gradually approaches to that of Gauss pulses with the truncation coefficient increasing to 1. For the side lobes of Airy pulses, there are similar MI but smaller gain spectrum than the main lobe when the pumped solitons is overlapping with corresponding ones of Airy pulses.     

Dispersion relations for testing the validity of linear and nonlinear optical spectra

We exploit efficient dispersion relations, which were developed for terahertz spectroscopy, to show their validity for testing linear and nonlinear optical spectra. As an example, we deal with the measured data for complex reflectivity of a KCl crystal and complex nonlinear susceptibility of a polysilane. It is suggested that the spectral data presented in the literature both for the KCl and the polysilane are consistent with the presented spectra analysis method.     

Chirped self-healing Airy pulses compression in silicon waveguides under fourth-order dispersion

Abstract

We present the compression of Airy pulses in silicon-on-insulator (SOI) waveguides under the fourth-order dispersion (FOD) using the variational approach that involves Rayleigh’s dissipation function (RDF). All the pulse characteristics are under the influence of the two-photon and the frequency-carrier absorptions. In a quasi-linear approximation, the pulse compression conditions induced by the interaction of the group-velocity dispersion (GVD), the chirp and the FOD are derived. In the nonlinear case, the self-phase modulation (SPM), the two-photon absorption (TPA) and the free-carrier absorption (FCA) reduce the length of compression in a propagation regime of normal GVD, positive chirp and a negative value of FOD. The TPA reduces the maximal power reached than the SPM while the FCA rather increases its value. These results are confirmed in the general case where they all interact with the linear dispersion terms of the SOI waveguide.     

Normal-mode splitting and output-field squeezing in a Kerr-down conversion optomechanical system

An investigation is reported of the effects of a Kerr-down conversion nonlinear crystal inside an intrinsically nonlinear optomechanical cavity on the dynamics of the oscillating mirror, the intensity and the squeezing spectra of the transmitted field. We show that in comparison with a bare optomechanical cavity, the combination of the cavity energy shift due to the weak Kerr nonlinearity and increase in the intracavity photon number due to the nonlinear gain medium can increase the normal mode splitting in the displacement spectrum of the oscillating mirror. Our study demonstrates that at high temperatures, when the thermal fluctuations in the system are important, the optomechanical and nonlinearity-induced resonances are distinguishable in the output field spectrum. However, at low temperatures, the presence of both nonlinearities enhances the amplitude of the mechanical-mode contribution to the spectrum and leads to the occurrence of normal-mode splitting in the transmitted field spectrum even for low values of the input power. Also, at low temperatures, the Kerr-down conversion nonlinearity increases the radiation pressure contribution to the degree of squeezing of the transmitted field more than that of a bare optomechanical cavity or a nonlinear cavity (in the absence of optomechanical coupling). Furthermore, we find that for the blue-detuned laser the Kerr nonlinearity extends the domain of the stability of the system and leads to the normal-mode splitting of the movable mirror and noise reduction in the range of frequencies in which a bare cavity is not stable.     

General features of spatiotemporal instability induced by arbitrary high-order nonlinear dispersions in metamaterials

Spatiotemporal instability (STI) in metamaterials (MMs) with a Kerr-type nonlinear polarization is investigated. A general expression for instability gain, taking account of the effects of arbitrary high-order linear and nonlinear dispersions, is derived. Special attention is paid to the general features of instability induced by nonlinear dispersion effects originating from the combination of dispersive magnetic permeability and nonlinear polarization. It is shown that, just like their linear counterparts, all even-order nonlinear dispersions not only deform the original instability regions, but also may lead to the appearance of new instability regions. However, all odd-order nonlinear dispersions always suppress STI irrespective of their signs, quite different from their linear counterparts which exert no influence on instability. Moreover, we find that, unlike the linear dispersions, the nonlinear dispersions lead to the dependence of gain peak on the spatial modulation frequency. The role of the first-order nonlinear dispersion, namely self-steepening (SS), and second-order nonlinear dispersion (SND) in STI is particularly analyzed to illustratively demonstrate the general results.     

Effect of stochasticity on targeted energy transfer from a linear medium to a strongly nonlinear attachment

In this work the problem of targeted energy transfer (TET) from a linear medium to a nonlinear attachment is studied in the presence of stochasticity. Using a Green’s function formulation, complexification-averaging technique and diffusion approximation we derive a complex, nonlinear, Ito stochastic differential equation that governs the slow dynamics of the system. Through the numerical solution of the corresponding Fokker-Planck-Kolmogorov (FPK) equation we study the optimal regime of TET and its robustness to stochasticity for the case of nonlinear interactions of the nonlinear attachment with a single mode of the linear system. The probabilistic analysis reveals that in the presence of stochasticity the optimal TET regime, predicted in the deterministic theory, is not only preserved but also is enhanced due to the interaction of nonlinearity and stochasticity.     

Effects of Nonlinear Micromagnetic Coupling on a Weak-Field Magnetoimpedance Sensor

We present a general harmonic formulation that takes into account, explicitly, the effects of micromagnetics for modeling the magnetic fields in a magnetoimpedance (MI) sensor element. We first relax assumptions commonly made to derive closed form solutions from a decoupled set of linear equations. We then solve numerically (using a meshless method formulated in point-collocation) the Maxwell and the Landau–Lifshitz–Gilbert equations simultaneously for the real and imaginary parts of the magnetic fields and magnetization in the context of a cylindrical amorphous MI sensor element. Comparing our results of the effects of coupling the equations of motion against published experimental data, we found striking differences both quantitatively and qualitatively between the coupled nonlinear and decoupled linear models. The coupled nonlinear harmonic formulation presented here results in improved accuracy and more consistent qualitative behavior in accordance to reported experimental observations, particularly in the weak field regime. Also presented here are spin wave amplitude distributions showing spatial dispersion within MI elements structures, which represents information lost in decoupled formulations.      

Quantum statistics and dynamics of nonlinear couplers

Abstract

We investigate both codirectional and contradirectional nonlinear couplers composed of two nonlinear waveguides operating by second-harmonic generation. We take into account possible mismatches inside the waveguides and between them. We calculate the photon number distribution, its factorial moments, quadrature and integrated intensity variances and quadrature uncertainty product taking into account the effects of transmission of light between waveguides. Incident beams are assumed to be coherent, squeezed and mixed with external noise. Second-harmonic modes are assumed to be pumped with strong coherent beams. We show that non-classical behaviour of beams generated by the nonlinear waveguides can be transferred between them and controlled by linear and nonlinear mismatches. In the contradirectional regime of propagation, asymptotic non-classical states can be generated.     

Effect of competing cubic-quintic nonlinearities on the modulational instability in nonlocal Kerr-type media

We investigate analytically and numerically the modulational instability (MI) of plane waves under competing nonlocal cubic-local quintic nonlinearities. The generic properties of the MI gain spectra are then demonstrated for the Gaussian response function, exponential response function, and rectangular response function. Special attention is paid to competing nonlocal cubic-local quintic nonlinearities on the MI. We observe that the focusing local quintic nonlinearity increases the growth rate and bandwidth of instability contrary to the small values of defocusing local quintic nonlinearity which decrease the growth rate and bandwidth of instability. Numerical simulations of the full model equation describing the dynamics of the waves are been carried out and leads to the development of pulse trains, depending upon the sign the quintic nonlinearity.