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.     

Impact of two-photon absorption on self-phase modulation in silicon waveguides

We study the effects of two-photon absorption on the self-phase modulation (SPM) process in silicon waveguides while including both free-carrier absorption and free-carrier dispersion. An analytical solution is provided in the case in which the density of generated carriers is relatively low; it is useful for estimating spectral bandwidth of pulses at low repetition rates. The free-carrier effects are studied numerically with emphasis on their role on the nonlinear phase shift and spectral broadening. We also consider how the repetition rate of a pulse train affects the SPM process.     

溶胶Cds毫微晶的自聚焦和自位相调制

本文首次报道了氩离子激光在溶胶CdS半导体毫微晶中产生的自聚焦、热自散焦及自位相调制,实验测得此种材料具有很大的克尔(Kerr)非线性系数n_2,比CS_2大10~5倍。并且,文中还分析了这种具有弱吸收的半导体溶胶毫微晶的非线性自位相调制机理及其与热自位相调制的差别。     

Dispersive-scan measurement of the fast component of the third-order nonlinearity of bulk materials and waveguides

A new, simple method to measure the nonlinear refraction and absorption of bulk material and waveguides is proposed. The method relies on the evolution of the intensity and width of femtosecond-pulse spectra, owing to self-phase modulation, as a function of variable chirp and stretching introduced at the input.     

强激光条件下5CB液晶中的激光诱导衍射环现象

强激光经5CB液晶传播时会产生非线性自相位调制现象,利用532 nm和1 064 nmCW激光研究了强激光条件下5CB液晶中的激光诱导衍射环现象,并对强激光在5CB液晶中产生自相位调制的现象和机理进行了讨论.当532 nm激光和1 064 nm激光功率密度分别大于10 kW/cm2和300 W/cm2时,接收白屏上有较明显的衍射环现象|当激光分别持续作用数十毫秒和数百毫秒量级时间时,接收屏上的衍射环现象消失.分别利用基尔霍夫衍射积分公式的菲涅耳近似和夫朗和费近似形式对5CB中激光自相位调制和激光诱导衍射环进行了数值模拟,数值结果与实验结果符合的较好.基于热传导理论定性分析了5CB液晶在不同波长和入射条件下的三阶非线性系数.结果表明：在强激光入射条件下,热效应是自相位调制的主要原因,这种三阶非线性系数除了与液晶的吸收系数和作用时间相关,还与激光作用面积甚至激光诱导指向矢转动过程相关.     

Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission

A novel scheme for postnonlinearity compensation is proposed to reduce the phase jitter in phase-shift keying transmission. A phase modulator is used to modulate the phase of the data pulses in front of the receiver. The magnitude of the phase modulation is proportional to the detected pulse intensity, and the sign is opposite to that of the nonlinear phase shift caused by self-phase modulation. Thus, the nonlinear phase noise induced by amplitude fluctuation and self-phase modulation is partially compensated for. We show by numerical simulations that a differential phase-shift keying dispersion-managed soliton system at 10Gbits/s with such postnonlinearity compensation can provide greater than 3dB of improvement in ultralong-haul dense wavelength-division multiplexing transmissions.     

Nonlinear propagation effects in an AlGaAs Bragg grating filter

We present experimental observations of nonlinear propagation effects in an integrated AlGaAs waveguide filter. We demonstrate pulse shaping, pulse compression, and the production of gap solitons within the stop band of the grating for switching powers of ~130 W . This nonlinear behavior is associated with the counterbalancing effects of self-phase modulation and the large dispersion effects introduced by the grating itself.     

Multiphoton endoscopy

Despite widespread use of multiphoton fluorescence microscopy, development of endoscopes for nonlinear optical imaging has been stymied by the degradation of ultrashort excitation pulses that occurs within optical fiber as a result of the combined effects of group-velocity dispersion and self-phase modulation. We introduce microendoscopes (350-1000 microm in diameter) based on gradient-index microlenses that effectively eliminate self-phase modulation within the endoscope. Laser-scanning multiphoton fluorescence endoscopy exhibits micrometer-scale resolution. We used multiphoton endoscopes to image fluorescently labeled neurons and dendrites.     

Darboux Transformation and Soliton Solutions for InhomogeneousCoupled Nonlinear Schrödinger Equations with Symbolic Computation

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e. Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features ofpicosecond solitons in inhomogeneous optical fibers.     

Propagation of ultrafast pulses in the anomalous-dispersion regime of silicon-on-insulator strip nanowaveguides

The dynamic evolution of ultrafast high-intensity pulses with a 100 fs half-width at 1/e intensity point based on the silicon-on-insulator (SOI) strip nanowaveguides is considered and investigated numerically under the condition of anomalous group-velocity dispersion (GVD) regime. For ultrafast high-intensity pulses propagating in millimeter-long SOI nanowaveguides, the interplay between the dispersion and nonlinear effects such as the two-photon absorption, free-carrier absorption, free-carrier dispersion, and self-phase modulation has to be taken into account, which results in the significant optical wave breaking phenomenon that occurs near the pulse leading edge for an unchirped Gaussian pulse in the anomalous GVD regime. However, when the input Gaussian pulse with linear up-chirp is introduced, the position of the optical wave breaking shifts from the leading pulse edge to its trailing edge along the several millimeters-long SOI nanowaveguides.     

Strong self-phase modulation in planar chalcogenide glass waveguides

Single-mode planar waveguides were fabricated from chalcogenide glass compounds with large Kerr nonlinearities. Strong self-phase modulation of subpicosecond pulses along with low linear and nonlinear absorption losses demonstrates the potential for ultrafast, low-power, all-optical processing applications.     

Compensation of self-phase modulation in fiber-based chirped-pulse amplification systems

We demonstrate a simple, all-fiber technique for removing nonlinear phase due to self-phase modulation in fiber-based chirped-pulse amplification (CPA) systems. Using a LiNbO3 electro-optic phase modulator to emulate a negative nonlinear index of refraction, we are able to remove 1.0 pi rad of self-phase modulation acquired by pulses during amplification and eliminate nearly all pulse distortion. Our technique is high speed, removes nonlinear phase on a pulse-to-pulse basis, and can be readily integrated into existing CPA systems.     

Characterization of nonlinear phase shifts by use of the temporal transport-of-intensity equation

A temporal transport-of-intensity equation is derived to describe the evolution of the instantaneous power of the electric field in a dispersive medium. As its spatial counterpart, which can be used to measure wavefronts using the intensity measured after various amounts of diffraction, the temporal transport-of-intensity equation allows the determination of temporal phase shifts using only intensity measurements in a direct noninterferometric way. The application to the characterization of nonlinear phase shifts induced by self-phase modulation and cross-phase modulation is used to determine the nonlinear coefficient of a highly nonlinear fiber.     

基于自相位调制和交叉相位调制的全光开关特性研究

提出一种优化含有掺铒光纤放大器的非线性Sagnac干涉仪全光开关的新方法,建立了基于自相位调制和交叉相位调制两种解析模型,讨论了掺铒光纤放大器的小信号增益和饱和输出功率对开关性能的影响.分析表明掺铒光纤放大器的性能参量对开关所需要的Sagnac环中光子晶体光纤长度产生限制.当采用相同长度的光子晶体光纤时,基于交叉相位调制方式的全光开关与基于自相位调制方式的全光开关相比能够显著降低开关功率.采用分布傅里叶法数值求解非线性薛定谔方程,优化了开关结构,讨论了重复频率为40 GHz脉宽为5 ps的高斯型信号脉冲在开关时沿Sagnac环的传输特性.模拟结果表明,通过合理选择高非线性光子晶体光纤长度和掺铒光纤放大器的性能参量能够实现超低开关功率（＜1 mW）的开关操作.     

Velocity of the maximum of the envelope of a frequency-modulated Gaussian pulse in an amplifying nonlinear medium

The variation in the velocity of propagation of a narrowband frequency-modulated pulse in a nonlinear medium with dispersion of gain or absorption is studied. It is shown that the self-phase modulation caused by a cubic nonlinearity of the Kerr type can “accelerate” optical pulses of a Gaussian shape up to superluminal velocities even in the case where an initial frequency modulation (chirp) is absent.     

Nonlinear Fabry-Perot resonator with a silicon photonic crystal waveguide

We derive an equation that describes the nonlinear operation of a Fabry-Perot resonator with a large group index waveguide. Specifically, a silicon photonic crystal microcavity with two-photon-excited free carrier nonlinearity and Kerr nonlinearity is assumed. The equation clearly explains the bistability of the device and the reduction of the required pump energy for a specific nonlinear phase shift at an appropriate phase detuning from the resonance. We present a simple procedure to predict the required optical pump energy for the modulation and the resulting modulation depth by use of the equation and the device parameters.     

Multicontrast nonlinear optical microscopy with a compact and rapid pulse shaper

Homodyne detection can dramatically enhance measurement sensitivity for weak signals. In nonlinear optical microscopy it can make accessible a range of novel, intrinsic, contrast like nonlinear absorption and nonlinear phase contrast. Here a compact and rapid pulse shaper is developed, implemented, and demonstrated for homodyne detection in nonlinear microscopy with high-repetition rate mode-locked femtosecond lasers. With this method we generate two-photon absorption (TPA) and self-phase modulation images of gold nanostars in biological samples. Simultaneous imaging of two-photon luminescence and TPA also enables us to produce two-photon quantum yield images.     

Broadband self-phase modulation, cross-phase modulation, and four-wave mixing in 9-mm-long AlGaAs waveguides

We demonstrate efficient self-phase modulation with a nonlinear phase shift of up to 3π, broadband cross-phase modulation, and four-wave mixing with a 14 nm tunability range in AlGaAs waveguides with a specially designed composition. The length of our sample is only 9 mm, but the efficiency of the observed effects is high.     

Reversing intrachannel ghost-pulse generation by midspan self-phase modulation

Intrachannel pulse interactions are the dominating nonlinear effects in modern transmission systems with high modulation speeds. Scaled symmetries have proved to be effective in suppressing amplitude and timing jitter of mark pulses due to nonlinearity but not for ghost-pulse generation into the empty slots. A method of using midspan self-phase modulation to reverse the generation of ghost pulses due to intrachannel four-wave mixing is proposed. Computer simulations demonstrate significant improvement of signal quality by a combination of scaled symmetries and midspan self-phase modulation.     

Analysis of ultrafast nonlinear phenomena��s influences on output optical pulses and four-wave mixing characteristics in semiconductor optical amplifiers

We have analysed the output pulse characteristics of semiconductor optical amplifier (SOA). It is shown that they can be modified due to the variation of input parameters, such as, gain, input pulsewidth, input pulse energy and effects imposed by the medium. Therefore, the influence of these parameters are analysed on the output pulse shape, spectrum, chirp and pulsewidth. We have used the nonlinear propagation equation taking into account the gain spectrum dynamics, gain saturation which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. We have used the finite-difference beam propagation method to simulate the wave evolution both in time and spectral domain in the SOA. We have also simulated the four-wave mixing characteristics between pulses for various input pulses. An accurate output pulse shape can be achieved by controlling the mentioned parameters. To the authors knowledge, pulse shaping in co-propagation regime due to medium effect and input pulse shapes in presence of all nonlinear effects relevant to picosecond regime have been studied comprehensively, for the first time in this work.