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.     

Enhancing coherent nonlinear-optical processes in nonmagnetic backward-wave materials

Novel concepts of nonlinear-optical (NLO) photonic metamaterials (MMs) are proposed. They concern with greatly enhanced coherent NLO energy exchange between ordinary and backward waves (BWs) through the frequency-conversion processes. Two different classes of materials which support BWs are considered: crystals that support optical phonons with negative group velocity and MMs with specially engineered spatial dispersion. The possibility to replace plasmonic NLO MMs enabling magnetic response at optical frequencies, which are very challenging to engineer, by the ordinary readily available crystals, are discussed. The possibility to mimic extraordinary NLO frequency-conversion propagation processes attributed to negative-index MMs (NIMs) is shown in some of such crystals, if optical phonons with negative group velocity and a proper phase-matching geometry are implemented. Here, optical phonons are used as one of the coupled counterparts instead of backward electromagnetic waves (BEMWs). The appearance of BEMWs in metaslabs made of carbon nanotubes, the possibilities and extraordinary properties of BW second harmonic generation in such MMs is another option of nonmagnetic NIMs, which is described too. Among the applications of the proposed photonic materials is the possibility of creation of a family of unique BW photonic devices such as frequency doubling metamirror and Raman amplifiers with greatly improved efficiency.     

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.     

饱和非线性下零色散附近的交叉相位调制非稳

从光纤中扩展的耦合非线性薛定谔方程组出发,在饱和非线性光纤零色散附近,研究了不同二、四阶色散参量下交叉相位调制不稳定性增益谱及其临界扰动频率、谱宽和谱峰随两光波入射功率的演化特点.研究表明,随色散参量不同,增益谱随两光波入射功率的增大可能出现三种演化形式：一是始终是两个分离的谱区;二是由开始时的两个合成一个,最后再分离成两个;三是始终是一个谱区.饱和非线性的存在则使每个谱区的谱宽、谱峰及远离零点的临界扰动频率,随两光波入射功率的增大可能呈现出先增大后减小的特点,使第二谱区靠近零点的临界扰动频率呈现先减小后增大的特点,从而可能出现两个不同的输入功率对应同一个增益峰值和谱宽的情形.色散参量对增益谱的谱峰影响小,对谱宽影响大.越靠近零色散区,每个谱区谱宽越大,越易连成一个谱区.     

Stationary soliton states in couplers with saturable nonlinearity

We find the possible stationary states for nonlinear couplers formed from materials that have saturable nonlinearities. We also determine the effect of saturation on the asymmetric state bifurcation point and the energy required for switching.     

色散磁导率对异向介质中的调制不稳定性的影响

基于Drude模型研究了异向介质的色散磁导率对调制不稳定性的影响. 结果表明,在反常色散情形,赝五阶非线性在异向介质的负折射区中增大了调制频谱的范围及增益值,这与常规正折射介质中出现的现象正好相反;自陡峭效应在异向介质中有可能为负值,但无论正负,也无论在正折射区还是负折射区,它都抑制调制不稳定性的产生;二阶非线性色散效应在正、负折射区中分别促进和抑制调制不稳定性的产生. 在正常色散情形,由于二阶非线性色散效应的作用,使本来在常规正折射介质中不可能出现的调制不稳定性现象也能出现,这一特性为在正常色散区形成孤 关键词： 异向介质 调制不稳定性 色散磁导率 二阶非线性色散     

负折射介质中超短脉冲的反常分裂现象

对超短脉冲在负折射介质中的传输特性进行了研究,着重分析其不同于常规介质的反常脉冲分裂现象。结果表明:由于负的折射率影响,介质将通过反常群速度色散与自散焦非线性的相互作用机理来诱导脉冲的对称分裂。同时,分析由色散磁导率所导致的可控自陡效应对脉冲分裂的影响,发现负折射介质中正负的自陡效应都会引脉冲非对称分裂。其中负的自陡效导致脉冲裂变后其后沿比前沿高,这与常规介质自陡效应（恒为正）情形相同;而负折射介质正的自陡效应对脉冲分裂影响刚好与前者相反,即裂变后脉冲后沿比前沿低。     

Copropagation of two pulses of different frequencies and modulation instabilities induced by cross-phase modulation in metamaterials

Nonlinear coupled equations describing the copropagation of two light pulses of different central frequencies in metamaterials (MMs) are derived. Based on the derived equations and the Drude model for dispersive MMs, the modulation instabilities (MIs) induced by cross-phase modulation (XPM) for different combination of the signs of refractive index experienced by the two optical pulses, respectively, are analyzed. It is shown that, in the absence of group-velocity mismatch, the property of MI only depends on the sign of group-velocity dispersion the two pulses experience, irrespective of the sign of refractive index. The group-velocity mismatch plays an important role in the occurrence of MI, especially when the central frequencies of the two pulses near the electric or magnetic plasma frequency of the MM. The theoretical results are confirmed by numerical simulations.     

Phase-dependent spectral control of pulsed modulation instability via dichromatic seed fields

We investigated experimentally and numerically the spectral control of modulation instability (MI) dynamics via the initial phase relation of two weak seed fields. Specifically, we show how second-order MI dynamics exhibit phase-dependent anti-correlated growth rates of adjacent spectral sidebands. This effect enables a novel method to control MI-based frequency conversion: in contrast to first-order MI dynamics, which exhibit a uniform phase dependence of the growth rates, second-order MI dynamics allow to redistribute the spectral energy, leading to an asymmetric spectrum. Therefore, the presented findings should be very attractive to different applications, such as phase-sensitive amplification or supercontinuum generation initiated by MI.     

Observation of two state behavior in the instability spectra of saturable nonlinear media

We investigate the modulational instability (MI) in the saturable nonlinear system (SNL). We identified the unique behavior of MI in the SNL system, which we called as the two state behavior. Unlike the case of Kerr type nonlinearity the so called critical modulational frequency does not monotonously increases, rather behaves in such way, that the increase in power increases the CMF upto the saturation power, and further increase in power decreases the CMF. This behavior is identified to be unusual in the context of MI and thus makes the study of MI interesting.     

Flexible alteration of optical nonlinearities of iodine charge-transfer complexes in solutions

The type of donor used is found to influence greatly the optical nonlinearities of iodine charge-transfer (CT) complexes in solutions for several solvents. The magnitude and sign changes of nonlinear absorption of iodine CT complexes for different solvents as donors are observed, which implies the transition from saturable absorption to reverse saturable absorption. Compared with C60 in toluene, iodine CT complexes with toluene and benzene demonstrate larger reverse saturable absorption. Meanwhile, flexible alteration of optical nonlinearities is easily obtained by adjusting the mixture ratio of different solvents, yielding a prospective means of constructing a nonlinear medium with a large nonlinear coefficient.     

Self-trapping of bright rings

We present experimental observations of self-trapped rings carrying zero topological charge, along with simulations that display the self-focusing dynamics of the rings and their stability features in materials with saturable nonlinearities.     

A theoretical investigation of soliton induced supercontinuum generation in liquid core photonic crystal fiber and dual core optical fiber

The supercontinuum generation (SCG) in liquid core photonic crystal fiber (LCPCF) with versatile nonlinear response and the spectral broadening in dual core optical fiber is presented. The analysis is presented in two phase, phase I deals with the SCG in LCPCF with the effect of saturable nonlinearity and re-orientational nonlinearity. We identify and discuss the generic nature of the saturable nonlinearity and reorientational nonlinearity in the SCG, using suitable model. For the physical explanation, modulational instability and soliton fission techniques is implemented to investigate the impact of saturable nonlinear response and slow nonlinear response, respectively. It is observed that the saturable nonlinearity inevitably suppresses the MI and the subsequent SCG. On the other hand, the re-orientational nonlinearity contributes to the slow nonlinear response in addition to the conventional fast response due to the electronic contribution. The phase II features the exclusive investigation of the spectral broadening in the dual core optical fiber.     

Hysteretic behavior of spectral components of a femtosecond pulse passing through a nonlinear layer

The variation of the frequency at which the spectral intensity is maximal within a given time interval with the amplitude of an applied femtosecond pulse is simulated. The computer simulation is performed in the model of an optically thin layer for a medium with cubic nonlinearity and saturable restoring force. It is shown that the hysteretic dependence of the spectral line frequency on the applied pulse amplitude may take place for both one and several simultaneously generated harmonics.     

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.     

Method for generating solitons sustained by competing nonlinearities by use of optical rectification

We put forward a method for generating engineerable competing quadratic and cubic nonlinearities in suitable settings in which frequency generation is accompanied by optical rectification. The novel scheme is based on the full exploitation of the geometrical conditions that determine the magnitude of the rectified fields and translates the different orientations of an elliptical pump beam into tunable nonlinearities, which can be used to act on the spectral composition and overall features of optical solitons.     

Chaotic Behavior of One-Dimensional Nonlinear Schrodinger Equations Involving High Order Saturable Nonlinear Terms

The non-integrable behavior in one-dimensional generalized nonlinear Schr6dinger equations involving high order saturable nonlinearities, which govern the dynamic behavior in a class of physical systems, is investigated numerically. The numerical results illustrate that the high order saturable nonlinearities would lead to chaos, where the irregular homoclinic orbit (HMO) crossings have been observed in phase space. On the other hand, we show that the periodic solutions and solitary waves may exist in such non-integrable continuum Hamiltonian dynamic systems.     

Analysis of reflectance and modulation spectroscopic lineshapes in optoelectronic device structures

We discuss the spectral lineshapes of reflectance and modulated reflectance (MR) measurements on optoelectronic device structures such as epi-layers, quantum wells (QWs), vertical-cavity surface emitting-lasers (VCSELs) and resonant-cavity light-emitting diodes (RCLEDs). We consider the various methods for the extraction of built-in electric fields and band-gap energies from Franz-Keldysh oscillations (FKO), using the example of a tensilely strained InGaAs QW system, whose InGaAsP barriers yield strong FKO. We describe how critical point transition energies can be easily obtained by eye from Kramers-Kronig (KK) transforms of low field or QW modulation spectra, using the example of the modulated transmittance spectra of dilute-nitrogen InGaAsN p-i-n structures. We also discuss how the ordinary reflectivity spectrum, usually acquired at the same time as the MR signal, may also be exploited to extract layer thicknesses and compositions, and information about the active QW absorption spectrum in VCSEL and RCLED structures.     

Minimization of the pulse's timing jitter in a dispersion-compensated WDM system

We address the problem of the collision-induced crosstalk between pulses in a dispersion-compensated WDM system composed of a periodic array of cells that include two or three fiber segments. Both the cross- and self-phase-modulation nonlinearities are taken into account. A semi-analytical approximation and direct simulations are used to calculate the frequency shift (FS) of colliding pulses, and to search for conditions which provide for minima of the FS and the temporal shift (TS), including the most promising possibility of minimizing both shifts simultaneously. Semi-analytical results, obtained by means of the perturbation theory, are in qualitative agreement with the numerical findings, especially in regimes near the optimum. In searching for the FS and TS minima, we investigate the effect of changing the initial width and chirp of the pulse, position of the amplifier within the dispersion–compensation period, group-velocity difference between the channels, allocation of the group-velocity-dispersion (GVD) inside the cell, and the average GVD. We conclude that a more sophisticated dispersion–compensation map, with three different local values of GVD, may be significantly more efficient than the one based on two different segments. A global FS minimum, with respect to the variation of all the parameters, is found.     

Induced modulational instability in EDFAs in the presence of higher-order nonlinear and dispersive effects

We derive the dispersion equation for erbium doped fiber amplifiers (EDFAs), assuming the supplementary effects of time-derivative nonlinearities including intrapulse Raman scattering and self-steepening incorporated with third order dispersion and product of gain and square of dipole relaxation time parameter, in the extended form of nonlinear Schrödinger equation and investigate their impacts on gain and cut-off frequency of modulational instability (MI) in EDFAs. Also, the influences of those effects on instability of steady-state amplitude, in the form of generation of terahertz pulse train of femtosecond solitons from a weak-modulated signal by induced MI, are numerically simulated and discussed within EDFAs in normalized form.