Modulation instabilities in randomly birefringent two-mode optical fibers

Modulation instabilities in the randomly birefringent two-mode optical fibers(RB-TMFs) are analyzed in detail by accounting the effects of the differential mode group delay(DMGD) and group velocity dispersion(GVD) ratio between the two modes, both of which are absent in the randomly birefringent single-mode optical fibers(RB-SMFs). New MI characteristics are found in both normal and anomalous dispersion regimes. For the normal dispersion, without DMGD,no MI exists. With DMGD, a completely new MI band is generated as long as the total power is smaller than a critical total power value, named by Pcr, which increases significantly with the increment of DMGD, and reduces dramatically as GVD ratio and power ratio between the two modes increases. For the anomalous dispersion, there is one MI band without DMGD. In the presence of DMGD, the MI gain is reduced generally. On the other hand, there also exists a critical total power(Pcr), which increases(decreases) distinctly with the increment of DMGD(GVD ratio of the two modes) but varies complicatedly with the power ratio between the two modes. Two MI bands are present for total power smaller than Pcr, and the dominant band can be switched between the low and high frequency bands by adjusting the power ratio between the two modes. The MI analysis in this paper is verified by numerical simulation.     

Graph-based complex network features for the auscultation of mitral incompetence

The paper unravels the potential of graph theory in the heart murmur auscultation by constructing a complex network from the single murmur time-series signals. In this study, forty-eight murmur signals of mitral incompetence (MI) and healthy heart (NM) are subjected to complex network and wavelet analyses. For the complex network analysis, the correlation coefficient is fixed as 0.8 and the time series is segmented based on the time delay obtained from the autocorrelation function. The signals are classified based on graph features, reflecting the haemodynamic through the mitral valve, using unsupervised principal component analysis and supervised k-nearest neighbour classifier. The appearance of many frequency components in the murmur due to MI is understood from the wavelet analysis. The graphs of NM and MI are found to show two well-defined clusters. When the graph of NM shows a large number of uncorrelated nodes due to the absence of signal in the systolic region that of MI shows interconnected nodes. The improper closing of the mitral valve and the regurgitation of blood in MI results in sound signals in the systolic region, responsible for the increased number of edges compared to NM. The present economical and sensitive graph-based method opens up the plausibility of remote auscultation in primary health centres in the context of the outbreak of pandemic COVID 19.     

Magnetoimpedance in soft magnetic amorphous and nanostructured wires

The surface impedance tensor approach has been used to review the impedance response in a variety of amorphous and nanocrystallized wires. An experimental study on the torsion annealing effect on the magnetoimpedance (MI) behaviour for positive and negative magnetostriction amorphous wires of FeSiB and CoSiB compositions, respectively, has been carried out. Moreover, the influence of the onset nanocrystallization on the MI behaviour in Finemet-type alloys, with particular attention focussed on the case that the wires are annealed under applied torsional stress, is also presented. The analysis of the MI and torsion-impedance (TI) effects allows us to compare the different magnetic characteristics observed in a variety of wires. Special attention is paid to new results of the off-diagonal MI huge responses of these ferromagnetic samples, which are also a very useful source of information on the magnetic properties of the wires.     

Modulation instability in metamaterials with fourth-order linear dispersion,second-order nonlinear dispersion,and three kinds of saturable nonlinearites

The linearized nonlinear propagation equation and its coefficients, gain spectrum of modulation instability (MI) in metamaterials (MMs) with fourth-order linear dispersion, second-order nonlinear dispersion, and three kinds of saturable nonlinearites, are analytically deduced by utilizing the linear stability analysis and Drude electromagnetic model. Then variations of gain spectra of MI with the normalized angular frequencies and the optical power densities are calculated in real units. In the negative refractive region, two kinds of gain spectra are discovered. The first (second) one is close to (far from) the zero perturbation frequencies and it corresponds to the lower (higher) normalized angular frequencies. Moreover, the second one has higher cutoff frequency, which is obviously beneficial to generation of high-repetition-rate pulse trains. While in the positive refractive region, only the first kind of gain spectra is found. With increase of the optical power densities, the peak gains and the spectral widths of MI increase before decrease, but they vary the most rapidly (slowly) for the exponential (conventional) saturable nonlinearities. The MI characteristics and their corresponding applications can be adjusted by several methods.     

Modulational instability in optical fiber with stochastic parameters and noninstantaneous response

We investigate analytically and numerically the modulational instability (MI) in optical fiber, where the effect of noninstantaneous nonlinear response as well as stochastic coefficients are taken into account. Applying the linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant matrix. In the limiting cases of small fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we derive an explicit form of the effective matrix and compute numerically the maximal eigenvalue. The moment MI peak is enhanced and the delayed Raman response reduces the maximum MI gain caused by stochasticity both in anomalous and normal dispersion regimes. Numerical simulations of the full stochastic nonlinear Schródinger equation show that, the phenomenon of MI gives rise to periodic pulse arrays of waves train, as well as to a chain of peaks with continuously growing amplitudes.     

光晶格中双组分偶极玻色-爱因斯坦凝聚体的调制不稳定性

利用线性稳定性分析的方法,对光晶格中双组分偶极玻色-爱因斯坦凝聚体(Bose-Einstein condensates,简称BECs)的调制不稳定性进行了研究.得到了光晶格中双组分偶极BECs原子系统调制不稳定性区域的分布与在位相互作用和由偶极-偶极相互作用所导致的格点间BECs相互作用之间的关系.结果显示,格点间BECs的相互作用对光晶格中双组分偶极BECs的调制不稳定性有较大的影响,这可为实际应用中如何操控双组分偶极BECs提供有用的信息. 关键词： 光晶格 双组分玻色-爱因斯坦凝聚体 调制不稳定性 偶极-偶极相互作用     

Investigation of dispersion characteristic in MI- and MII-type single mode optical fibers

Dispersion characteristic of MI and MII type single mode optical fibers is analytically investigated. For this purpose modal analysis of these fibers to obtain possible wave vectors for given system parameters are done. Then using numerical evaluation of the presented analytical relations, chromatic and waveguide dispersions are calculated. The effects of geometrical and optical parameters of the fibers on dispersion characteristics are investigated. In this analysis, we show that with increase of Δ (optical parameter) for MI structure the slope of dispersion curve is decreased and the case is reversed for MII structure. Also, with rising of Q (geometric parameter) for MI structure the slope of dispersion curve is decreased and the situation is reversed for MII structure. Finally, we show that with boosting of R₂ for MII structure the slope of dispersion is increased. As a final result, our simulations show that small values for optical parameters are better in MII structure for multi-channel optical communications. In MI structure to obtain small dispersion slope, Q can be increased that is easy for fabrication in practice. Finally, Q and R₂ are suitable parameters for control of dispersion in the proposed structures.     

Analysis of functional networks involved in motor execution and motor imagery using combined hierarchical clustering analysis and independent component analysis

Cognitive experiments involving motor execution (ME) and motor imagery (MI) have been intensively studied using functional magnetic resonance imaging (fMRI). However, the functional networks of a multitask paradigm which include ME and MI were not widely explored. In this article, we aimed to investigate the functional networks involved in MI and ME using a method combining the hierarchical clustering analysis (HCA) and the independent component analysis (ICA). Ten right-handed subjects were recruited to participate a multitask experiment with conditions such as visual cue, MI, ME and rest. The results showed that four activation clusters were found including parts of the visual network, ME network, the MI network and parts of the resting state network. Furthermore, the integration among these functional networks was also revealed. The findings further demonstrated that the combined HCA with ICA approach was an effective method to analyze the fMRI data of multitasks.     

Modulational instability of electromagnetic waves in birefringent fibers with periodic and random dispersion

Modulational instability (MI) of electromagnetic waves in a birefringent fiber with a periodic dispersion (two-step dispersion management scheme) is investigated. The properties of new sidebands are studied. The strong variation of dispersion leads to the decreasing of the main MI region and the suppression of additional resonance. In the random dispersion case the MI of all frequencies of modulation in the normal dispersion region is predicted. In the anomalous dispersion case the decreasing of the main MI peak is calculated and changes in the spectral bandwidth of MI gain are found. The analytical predictions are confirmed by the numerical simulations of the full coupled nonlinear Schr?dinger equations with periodic coefficients.     

Impacts of higher-order dispersions and saturable nonlinearities on modulation instability in negative-refractive metamaterials

On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability(MI) have been analyzed and calculated for negative-refractive metamaterials(MMs).Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.     

Modulational instability of optically induced nematicon propagation

We report the modulational instability （MI） analysis for the modulation equations governing the propagation of coherent polarized light through a nematic liquid crystal （NLC） slab, in the limit of low light intensity and local material response. The linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave vectors （k,l） of the basic states and wave vectors （K,L） of the perturbations as free parameters. We compute the MI gain, and the MI gain peak is reduced and the stable bandwidth is widened with the increase of the strength of the applied electric field. Further, we invoke the extended homogeneous balance method and Exp-function method aided with symbolic computation and obtain a series of periodic solitonic humps of nematicon profiles admitting the propagation of laser light in the NLC medium.     

Spontaneous and induced modulation instability in the presence of broadband spectra caused by the amplified spontaneous emission

Spontaneous and induced modulation instability (MI) in the presence of rather broadband spectra are shown in the conventional single-mode fiber (SMF) for the first time. The broadband spectra are caused by the amplified spontaneous emission (ASE) of the erbium-doped fiber amplifiers (EDFAs). The two kinds of MI are seeded by noise components and a probe beam which results from two EDFAs amplification, respectively. For the spontaneous MI, the MI threshold is shown to be ??170 mW, which contains the laser as well as the ASE component. For the induced MI, an idler beam appears and grows with the peak power of input pulses at first, and then multiple spectral peaks emerge.     

Magnetoimpedance of cobalt-coated silicon steels

Magnetoimpedance (MI) effect of cobalt-coated silicon steels is measured as a function of cobalt thickness (0−45 μm), DC magnetic field (0-2 kOe), frequency (1 kHz-1 MHz) and magnitude (1-20 mA) of AC current. With increase in deposition thickness, the MI ratio and the characteristic frequency are decreased because the samples are magnetically hardened by the coating. Nevertheless, cobalt deposition broadens the frequency-dependent MI curves, and the frequency range with a large MI ratio is extended. The variations of this peak width as well as the characteristic frequency and the MI ratio are explained by the skin effect and crossing effect.     

光晶格中双组分玻色-爱因斯坦凝聚系统的调制不稳定性

利用线性稳定分析的方法,在不满足原子流相等的条件下,对光晶格中双组分玻色-爱因斯坦凝聚原子(BEC)系统的调制不稳定性区域与不同BEC组分的波长和不同的调制波长,以及两组分BEC间相互作用大小之间的关系进行了研究.结果显示,光晶格中双组分BEC系统的调制稳定性的区域在不满足原子流相等的条件下,随不同的波长,不同的调制和相互作用之间的大小会出现了较大的变化.相应结果可为实际应用中如何操控双组分BEC提供有用的信息.     

Modulation Instability in Non-Kerr-like Optical Fibers near the Zero Dispersion Point

Modulation instability (MI) in non-Kerr-like optical fiber near the zero dispersion point is analyzed. Taking into account the fourth order dispersion, new regions of MI are found. The action of the self-steepening is not the same for each region of MI and critical modulation frequency.     

Impact of higher-order dispersion in the modulational instability spectrum of a relaxing coupled saturable media

A theoretical analysis of modulational instability (MI) of optical pulses propagating near the zero dispersion wavelength of a lossless fibre with the effect of delayed saturable nonlinear response is presented. We calculate the exact dispersion relation with the effect of higher dispersion for the harmonic perturbation. We analysed the impact of fourth-order dispersion effects in the MI spectrum. We examine the possibility of MI in both dispersion regimes, regardless of the sign of the group velocity dispersion.     

Stationary States and Modulational Instability of Coupled Two-Component Bose-Einstein Condensates in a Ring Trap

We investigate modulational instability (MI) of a coupled two-component Bose-Einstein condensates in a rotating ring trap. The excitation spectrum and the MI condition of the system are presented analytically. We find that the coupling between the two components strongly modifies the MI condition, and the MI condition is phase-dependent. Furthermore, we discuss the effect of MI on both density excitation and spin excitation. If the inter- and intra-component interaction strengths are all equal, the MI causes density excitation but not spin excitation, and if the inter- and intra-component interaction strengths are different, the MI causes both density excitation and spin excitation. Our results provide a promising approach for controlling the stability and excitation of a rotating two-component Bose-Einstein condensates by modulating its coupling strength and interaction strength.     

Dark–bright optical solitary waves and modulation instability analysis with (2 + 1)-dimensional cubic-quintic nonlinear Schrödinger equation

This paper addresses the (2+1)-dimensional cubic-quintic nonlinear Schrödinger equation (CQNLS) that serves as the model to study the light propagation through nonlinear optical media and non-Kerr crystals. A dark–bright optical solitary wave solution of this equation is retrieved by adopting the complex envelope function ansatz. This type of solitary wave describes the properties of bright and dark optical solitary waves in the same expression. The integration naturally lead to a constraint condition placed on the solitary wave parameters which must hold for the solitary waves to exist. Additionally, the modulation instability (MI) analysis of the model is studied based on the standard linear stability analysis and the MI gain spectrum is got. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CQNLS.     

Modulation instability in negative refractive metamaterials with exponential saturable nonlinearity and self-steepening effects

Modulation instability (MI) in negative refractive metamaterials with exponential saturable nonlinearity and the self-steeping effect is investigated by using the standard linear stability analysis and the Drude electromagnetic model. The dispersion relation, instability condition, cut-off frequency, gain spectrum, and their corresponding dimensionless expressions are analytically deduced and then calculated. The results show that, the self-steepening effect will suppress MI by decreasing the cut-off frequency and the maximum gain. And the larger the power density ratio is, more slowly the cut-off frequency and the maximum gain decrease with increase of the self-steepening parameter. Although the sign of the self-steepening parameter does not influence MI but its absolute value must be smaller than a certain value. Depending on different self-steepening parameters, the cut-off frequency and maximum gain may decrease or increase before decrease with increase of the power density ratio. In particular, for large self-steepening parameters, the power density ratio may have a threshold value. When the power density ratio is under this threshold, MI will disappear.     

正三角型三芯光纤中等腰对称平面波的调制不稳定性分析

详细分析了正三角型三芯光纤中等腰对称平面波的调制不稳定性.等腰对称平面波即两芯中场完全相同,第三芯中场入射功率与其他两芯中不同的平面波,其存在的前提是入射光总功率(P)必须大于某最小值(P_(min)),该最小值取决于光纤的线性耦合系数和非线性系数.对一给定的总功率P≥P_(min),令一芯中的入射功率为P_1,其他两芯中入射功率均为P_2,有两种形式的场分布:一种是P_1始终大于P_2,随着P的增加,P_1越来越大,P_2越来越小,依线性稳定性分析方法,该场分布对应的增益谱主要特征与双芯光纤非对称平面波的增益谱相似;另一种是随着P的增加,P_1越来越小,P_2越来越大,使用同样的分析方法,发现该场分布下增益谱与双芯光纤非对称平面波增益谱截然不同,其显著特征是无扰动下,在正常和反常色散区域均可产生不稳定性增益,且在正常色散区域,零扰动频率对应的增益最强;另一方面,耦合系数色散对增益谱的影响在正常和反常色散区域都非常弱,这与其在双芯光纤中的影响截然不同.该结果对基于多芯光纤的模分复用系统非线性效应的研究具有一定的指导意义.