Modeling interaction of ultrashort pulses with ENZ materials

In this work, the split-step Fourier method for beam propagation is used to investigate the interaction of ultra-short pulses with epsilon-near-zero materials. The propagation of pulses is governed by the nonlinear Schrödinger equation (NLSE) containing dispersion, gain-bandwidth, self-phase modulation, self-steepening, and absorption parameters. It is found that the intensity profile of the pulse is broadened and the phase of the pulse is shifted by dispersion phenomena. The gain/loss related to the imaginary part of the refractive index causes an increase or decrease in intensity and pulse edge effects. These effects do not favor the steady propagation of the pulse. The self-phase modulation is not noted to appreciably affect the intensity pulse profile. The self-steepening modifies the phase and energy of the pulse during propagation, as well as absorption, which influences the losses by both the linear and nonlinear effects.     

Effective method of characterization of the phase and intensity profiles of asymmetrically distorted light pulses in optical fiber systems

We address the problem of characterization of light pulses that propagate in long-haul high-bit-rate optical communication systems, under strongly perturbed conditions. We show that the conventional technique for characterization of the phase and intensity profile of such pulses becomes qualitatively inconsistent when the pulse’s profile is asymmetrically distorted with respect to its center-of-mass. We resolve these inconsistencies by partially reformulating the conventional technique by means of appropriate pulse parameters, which we call upgraded parameters, which allow a fair characterization of the intensity and phase of all types of light pulses, including those which are asymmetrically distorted. We illustrate the effectiveness of the upgraded parameters by applying them to a meticulous characterization of light pulses in a dispersion-managed optical fiber system in which third-order dispersion is acting as a strong perturbation.     

Integrated Acousto-Optical Temperature Sensor

In this work, we investigate the performance of a novel integrated acousto-optical temperature sensor fabricated in LiNbO₃ and operating with ultrashort light pulses (2 ps). Five parameters (time duration, bandwidth, time intensity maximum, frequency intensity maximum, and output energy on the output pulse converted for the TM mode, as a function of temperature) were observed for the switched pulse at the output of the sensor (TM mode) with and without the presence of an increasing linear self-phase modulation (SPM) profile. Comparing all analyzed parameters, one can conclude that the pulse intensity is presenting the larger variation (100.09%) as a function of the temperature change (24.5 to 400°C) in a configuration without profile. Considering the increasing linear SPM profile, all the analyzed parameters are presenting a significant increase in the percentile variations in the studied range of temperature (24.5 to 400°C). Comparing all the five parameters, in two configurations (with and without the use of linear SPM profile), one can conclude that the time intensity maximum showed to be the most suitable parameter as measurement to be accomplished in a schematic detection for the temperature sensing in the range 24.5 to 400°C. We can conclude that the sensitivity of the AOTS is improving in the configuration with the increasing nonlinearity profile (β = 2) and for higher temperature.     

Integrated Acousto-Optical Temperature Sensor

In this work, we investigate the performance of a novel integrated acousto-optical temperature sensor fabricated in LiNbO₃ and operating with ultrashort light pulses (2 ps). Five parameters (time duration, bandwidth, time intensity maximum, frequency intensity maximum, and output energy on the output pulse converted for the TM mode, as a function of temperature) were observed for the switched pulse at the output of the sensor (TM mode) with and without the presence of an increasing linear self-phase modulation (SPM) profile. Comparing all analyzed parameters, one can conclude that the pulse intensity is presenting the larger variation (100.09%) as a function of the temperature change (24.5 to 400°C) in a configuration without profile. Considering the increasing linear SPM profile, all the analyzed parameters are presenting a significant increase in the percentile variations in the studied range of temperature (24.5 to 400°C). Comparing all the five parameters, in two configurations (with and without the use of linear SPM profile), one can conclude that the time intensity maximum showed to be the most suitable parameter as measurement to be accomplished in a schematic detection for the temperature sensing in the range 24.5 to 400°C. We can conclude that the sensitivity of the AOTS is improving in the configuration with the increasing nonlinearity profile (β = 2) and for higher temperature.     

五阶非线性光纤中连续谱相位扰动下的光传输与脉冲串产生

根据包含五阶非线性的扩展非线性薛定谔方程,数值研究了高斯型连续谱相位扰动而不是传统单色扰动下基于调制不稳定性的高重复率脉冲串产生.结果表明:脉冲串也能像传统情形那样形成,但却呈现出不同的特性.如脉冲数目有限,且各脉冲的高度、强度及间距不等.脉冲数目随传输距离增加而增加.而五阶非线性能使脉冲宽度和间距变小因而有利于高重复率脉冲串产生,负五阶非线性则相反.对脉冲串形成过程中演变啁啾的数值计算表明,啁啾及其随距离的变化都是高度非单调的,五阶非线性将改变啁啾的范围和量值.     

Propagation of short soliton pulses through a parabolic index fiber with dispersion decreasing along length

A parabolic index dispersion decreasing fiber (DDF) has been designed and optimized to produce high capacity soliton communication system. Variation of different fiber parameters such as core radius, effective core area and GVD factor along the 25 km of DDF length has been carried out to optimize a best possible DDF which can sustain the propagation of fundamental soliton. The variation of non-linearity with length along with the conventional power and GVD factor variation has been included in the generalized non-linear Schrodinger equation (NLSE). This NLSE has been solved numerically by split step Fourier method for shorter pulse propagation, incorporating the term for third order dispersion and intrapulse Raman scattering. Stable soliton pulses in transmission system have been achieved by our simulation, when a correction factor due to Raman induced soliton mean frequency shift is incorporated to the GVD profile predicted by the fundamental soliton condition. The interaction of neighboring soliton pulse pair through the proposed fiber has also been studied.     

拉曼增强型自相位调制再生技术

自相位调制可用于信号脉冲的整形,可实现归零码(RZ)信号的再生。以高非线性光纤(HNLF)为介质,在高非线性光纤中实现了拉曼集总放大和信号脉冲的自相位调制。从理论上分析了同向拉曼泵浦增强信号的自相位调制,大大降低了所需的信号光强度。论证了在色散长度(LD)远大于HNLF长度(L)时由自相位调制(SPM)导致的频谱展宽,它与脉冲的啁啾无关,频谱的功率密度与脉冲的强度无关。因此在高非线性光纤之后加入偏移载波频率的带通滤波器可实现归零码信号的再生。集中拉曼放大可增强再生性能。     

Optical wave breaking of high-intensity femtosecond pulses in silicon optical waveguides

We have investigated numerically the propagation of high-intensity femtosecond optical pulses with pulsewidth of 100 fs (half width at 1/e maximum) on the silicon-on-insulator (SOI) optical waveguide when the central wavelength of the pulse locates in the normal dispersion region. Results show that the combined effects of group-velocity dispersion (GVD), third-order dispersion (TOD), self-phase modulation (SPM), and free-carrier dispersion (FCD) can lead to the phenomenon of optical wave breaking that manifests as an asymmetric profile and oscillation near the trailing edge of the pulse. Moreover, the optical wave breaking will be experienced from generation to disappearance during propagation.     

负折射率介质层中光波的相位和传输特性研究

针对在理解负折射率材料中光波的传播特性时相位的特殊性质 ,详细分析推证了负折射率介质中折射率、波矢k的大小和方向、空间坐标系以及波相相位互之间的关系。分析结果表明负折射率介质层中的波矢k的反常取向是由于其标量值为负 ;在统一的坐标系下 ,由该标量值参与数值计算和分析 ,k则由标量值和单位矢量k0 (k0 >0 )共同决定 ,而不必再考虑左、右手系的区别。在此基础上依据电磁场理论推导了光波在负折射率介质层中的传输矩阵 ,用以分析含有负折射率介质层的复杂薄膜系统的光学性质。初步计算结果显示含有负折射率介质层的膜系对TE和TM波的光谱特性都有显著改变     

光纤非线性效应对10 Gb/s波分复用色散补偿系统的限制

对信道间距为１００ＧＨｚ的８倍１０Ｇｂ／ｓ波分复用色散补偿系统进行了计算机仿真,分析了光纤的色散和自相位调制（ＳＰＭ）、互相位调制（ＸＰＭ）、四波混频（ＦＷＭ）等非线性效应在具有级联光放大器系统中的作用。四种色散补偿方案是：ＳＭＦ（常规单模光纤）＋ＤＣＦ１（色散斜率为正的色散补偿光纤）、ＳＭＦ＋ＤＣＦ２（色散斜率为负的色散补偿光纤）、ＴＷ１（色散为正的非零色散光纤）＋ＴＷ２（色散为负的非零色散光纤     

Direct time-response measurement of high-speed optical modulators based on stretched-pulse interferometry

A simple technique for the direct measurement of the complex temporal response of a high-speed electro-optic (EO) modulator is proposed. This technique recovers the amplitude and phase temporal profiles of an instantaneous modulation over the duration of a chirped pulse (obtained by linear dispersion) using Fourier-transform interferometry, and it exploits the time-to-frequency mapping induced by the pulse dispersion process. The method can be implemented by using either time- or frequency-domain interferometric detection, allowing the characterization of modulation bandwidths in the tens-of-gigahertz range. The concept is demonstrated by accurately measuring the complex temporal response of a 2.5 Gbps intensity EO modulator.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking(OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity(QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

Evolution of Hyperbolic-Secant Pulses Towards Cross-Phase Modulation Induced Optical Wave Breaking and Soliton or Soliton Trains Generation in Quintic Nonlinear Fibers

The approximate analytical frequency chirps and the critical distances for cross-phase modulation induced optical wave breaking (OWB) of the initial hyperbolic-secant optical pulses propagating in optical fibers with quintic nonlinearity (QN) are presented. The pulse evolutions in terms of the frequency chirps, shapes and spectra are numerically calculated in the normal dispersion regime. The results reveal that, depending on different QN parameters, the traditional OWB or soliton or soliton pulse trains may occur. The approximate analytical critical distances are found to be in good agreement with the numerical ones only for the traditional OWB whereas the approximate analytical frequency chirps accords well with the numerical ones at the initial evolution stages of the pulses.     

A variational approach of nonlinear dissipative pulse propagation

A variational technique to deal with nonlinear dissipative pulse propagation is established. By means of a generalization of the Kantorovitch method, suitable for non-conservative systems, we are able to cope with an extended nonlinear Schr?dinger equation (NLSE) which describes pulse propagation under the influence of nonlinear loss and/or gain, in particular, in the presence of two-photon absorption (TPA). Based on the characteristics of the exact solution of the NLSE in the absence of TPA, we investigate the effects of frequency dispersion of the nonlinear susceptibility associated to the two-photon resonance, obtaining the necessary conditions for a solitary wave solution, even in the presence of a self-steepening term. Received: 4 August 1997 / Received in final form: 25 November 1997 / Accepted: 14 January 1998     

Quantum Dot Versus Quantum Well Semiconductor Optical Amplifiers for Subpicosecond Pulse Amplification

The performance of quantum well and quantum dot semiconductor optical amplifiers was theoretically investigated. The effects on subpicosecond pulse propagation due to gain and refractive index dispersion, calculated using a microscopic polarization equation and a reduced wave equation in the linear regime including the background refractive index dispersion, were used in the comparison. In particular, the spectral shift and phase modulation imposed on the pulse were compared. It is shown that quantum dot amplifiers suffer comparable spectral shifts to the quantum well amplifier, strong linear frequency chirp and large pulse broadening. In quantum dot amplifiers with small inhomogeneous broadening, similar pulse break-up is shown as that calculated for the quantum well amplifier. In quantum dot amplifiers with large inhomogeneous broadening, the background refractive index dispersion makes the linear frequency chirp the dominant feature. In the light of our calculations, the advantages and disadvantages of quantum dot and quantum well amplifiers are discussed.     

Switching between positive and negative permeability by photoconductive coupling for modulation of electromagnetic radiation

We introduce a modulation mechanism for negative index materials (NIM) in the GHz frequency range by means of photoconductive coupling. This leads the way to a monolithically integrated modulable NIM achieved by conventional microfabrication techniques. The photosensitive material is deposited in the gap of the split ring resonator (SRR) structure and the response in terms of S-parameters is simulated using a high frequency structure simulator (HFSS^TM) program. Only a single SRR particle is simulated to demonstrate total suppression of resonance amplitude and without any loss of generality the concept is applicable to a NIM comprising of both negative permeability and negative permittivity. This simple modulation of refractive indices can lead to novel optical device developments with the potential to dramatically improve the performance of existing phased array antennas, optical beam-forming networks, antenna remoting and transportation of RF power through fiber. PACS 42.60.Fc; 42.82.Cr; 81.05; 73.50.Pz     

Wave refraction in negative-index media: always positive and very inhomogeneous

We present the first treatment of the refraction of physical electromagnetic waves in newly developed negative index media (NIM), also known as left-handed media (LHM). The NIM dispersion relation implies that group fronts refract positively even when phase fronts refract negatively. This difference results in rapidly dispersing, very inhomogeneous waves. In fact, causality and finite signal speed always prevent negative wave signal (not phase) refraction. Earlier interpretations of phase refraction as "negative light refraction" and "light focusing by plane slabs" are therefore incorrect, and published NIM experiments can be explained without invoking negative signal refraction.     

Performance limit of a multi-frequency probe based coherent optical time domain reflectometry caused by nonlinear effects

The nonlinear effects that limit the performance of the multi-frequency probe(MFP)based coherent optical time domain reflectometry(C-OTDR)are investigated.Based on theoretical analysis and experimental results,compared with conventional C-OTDR,when the probe pulse has power gradient within the pulse width,self-phase modulation(SPM)and cross-phase modulation(XPM)are strengthened in the new C-OTDR scheme.The generation of four-wave mixing(FWM)is dependent on SPM and XPM,and with modulation frequency of phase modulator higher than 40 MHz,the stimulated Brillouin scattering(SBS) threshold can be enhanced by more than 5 dB,which benefits the maximum dynamic range of the MFP C-OTDR.     

Simple and highly sensitive optical pulse-characterization method based on electro-optic spectral signal differentiation

A very simple self-referenced, linear pulse-characterization technique based on spectral phase reconstruction by frequency-domain signal differentiation is introduced. This technique can be implemented using electro-optic intensity modulation of the pulse under test with a synchronized RF sinusoid. The pulse spectral phase profile can be accurately and unambiguously reconstructed from only two measured energy spectra, i.e., at the input and at the output of the modulator, using a direct analytic equation. The method is experimentally demonstrated by precisely characterizing microwatt-power picosecond pulses after linear dispersion through short sections (50-700 m) of conventional single-mode fiber.     

保偏光纤中相近频率传输区域的调制不稳定性

利用激光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了保偏光纤中两相近频率的线偏振光，其偏振方向相互正交且平行于光纤的双折射轴，且偏振方向沿两个双折射轴的分量强度相等时，在同为反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区都能产生调制不稳定性；在正常色散区存在不同的调制不稳定性功率区域，对应不同的功率区域，导致增益谱表现出明显的不同，并且当输入功率一定时，波长差(或频率差)的变化导致增益谱的变化. 关键词： 相近频率传输区域 双折射 保偏光纤 调制不稳定性