All-optical AND gate by use of a Kerr nonlinear microresonator structure

We numerically demonstrate the feasibility of constructing an all-optical AND gate by using a microresonator structure with Kerr nonlinearity. The gate is much smaller than similar AND gates based on Bragg gratings and has lower power requirements.     

各阶克尔非线性折射率对强激光大气传输的影响

用数值方法研究了各阶克尔非线性折射系数对强激光传输的影响,结果显示第7阶克尔非线性系数和第9阶克尔非线性系数协同影响激光传输,当第7阶克尔效应起作用时,忽略第9阶克尔效应的作用会导致光强随传输距离震荡剧烈,传输非常不稳定。要得到稳定传输需要第7阶克尔非线性系数和第9阶克尔非线性系数同时起作用或同时不起作用。在自聚焦阶段第3阶非线性折射率对折射率改变起主要作用,在稳定光丝传输阶段第7阶克尔非线性系数,第9阶克尔非线性系数起主要作用。第5阶克尔系数在整个传输过程中对折射率的改变一直比较小。     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Kerr nonlinear switch based on ultra-compact photonic crystal directional coupler

In this paper, an all optical switch based on nonlinear photonic crystal directional coupler has been simulated and analyzed by the finite difference time domain (FDTD) method. The lunched pump signal increases the refractive indices of the central row of the coupler, due to nonlinear Kerr effect, hence the coupler works in the nonlinear conditions and lightwave guides to the other output port. We have tried to increase the coupling efficiency and reduce the required power in the nonlinear status by optimizing the bends structure and increasing the interaction between dielectric and lightwave signal. Therefore, the input signal beam can be controlled to be exchanged between two output ports to earn the highest output power ratio and the smallest amount of power required for nonlinear performance, the physical length of the coupler is determined to be 20a, where a is the structure lattice constant.     

All-optical circulator based on cross phase modulation in a nonlinear Mach-Zehnder interferometer

We show that by exploiting unequal magnitude of cross phase modulation (XPM) in co-propagating and counter-propagating beams, an all-optical circulator (AOC) using a nonlinear Mach-Zehnder Interferometer (MZI) could be constructed. The proposed circulator is novel, simple and polarization independent.     

圆柱对称光脉冲在负色散克尔介质中的传输

利用变分法得到了任意光脉冲传输的一般特性及高斯光脉冲压缩（或扩展）的必要条件，这说明在一定初始条件下时空非对称的光脉冲也可形成“光子弹”，在某些区域内，通过时空耦合作用，光束的空间会聚可以导至脉宽的压缩。     

Experimental study of solitary waves in a nonlinear transmission line

Several properties of solitary waves were measured on a nonlinear transmission line. These include the transition from a linear dispersive response into a solitary wave response as the amplitude of a narrow voltage impulse is increased, and an observation of the recurrence phenomena of solitary waves. Supported in part by the National Science Foundation.     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

All-optical clock frequency divider using Fabry-Perot laser diode based on the dynamical period-one oscillation

We propose and experimentally demonstrate a frequency divider implemented by an optically injected Fabry-Perot laser diode (FP-LD) based on the nonlinear dynamical period-one oscillation. Injected by optical pulses, the FP-LD will oscillate in unstable dynamical period-one (P1) oscillation. Through changing the injected strength, emitting wavelength and bias current of the FP-LD, the oscillating frequencies of the P1 state can be varied. Once one of the harmonic frequencies is adjusted to match the repetition frequency of injected optical clock pulse, the P1 oscillation will be locked, and then a divided clock at the fundamental frequency of the P1 oscillation can be generated. By utilizing this divider, we can achieve the optical clock frequency division of divide-by-two, -three and -four in a wide input frequency range, for instance, of 9.0 to 20.0 GHz for divide-by-two. The influence of injected optical power on the timing jitter of the divided clock is also investigated. It is expected that this frequency divider can be applied to high frequency division exceeding 100 GHz due to its fast P1 oscillation.     

A numerical formulation for nonlinear ultrasonic waves propagation in fluids

A finite-difference algorithm is developed for analysing the nonlinear propagation of pulsed and harmonic ultrasonic waves in fluid media. The time domain model allows simulations from linear to strongly nonlinear plane waves including weak shock. Effects of absorption are included. All the harmonic components are obtained from only one solving process. The evolution of any original signal can be analysed. The nonlinear solution is obtained by the implicit scheme via a fast linear solver. The numerical model is validated by comparison to analytical data. Numerical experiments are presented and commented. The effect of the initial pulse shape on the evolution of the pressure waveform is especially analysed.     

All-optical switching of solitons in an active nonlinear directional coupler

A numerical study of the all-optical switching properties of an active nonlinear directional coupler is presented. The switching power is reduced for both CW and soliton inputs because of the gain. The switching properties of the coupler are enhanced for solitons, which switch nearly completely. For ultrashort pulses, the effects of the bandwidth of the gain medium are considered by using a general form for the gain band. The gain spectrum of erbium is also considered as a specific example.     

Thermal entanglement of a two-level atom and bimodal photons in a Kerr nonlinear coupler

In this paper thermally induced entanglement between a two-level atom and photons inside a bimodal nonlinear coupler is studied. The interaction occurs in the presence of a centrosymmetric medium which couples the two photonic modes via the first and third order susceptibilities. Such effects on the atom–photons interaction, however, are assumed negligible so that the linear Jaynes–Cummings model applies. It is further assumed that the coupler is held at a temperature T$T$, so that each of the combined atom–photon states, with a definite, T$T$ dependent, probability, is present. The partially transposed density matrix and, consequently, the negativity, as a measure of entanglement, are determined as functions of temperature. The negativity so calculated shows that the system of a two-level atom and photons is separable at zero temperature, becomes more entangled, reaching the maximal at a certain temperature and asymptotically disentangles. Effect of medium characteristics on such behavior is also discussed.     

Chirp controllable all-optical router in a nonlinear directional coupler

We analyzed the evolution of chirped optical pulses in a nonlinear directional coupler by coupled nonlinear Schrödinger equations. It is shown that an optical pulses launched into one channel can couple out from either of the two channels of the nonlinear directional coupler, with the routing determined by the chirp of the pulse. This is different from the previous routing mechanism of the nonlinear directional coupler where routing is determined by the peak power of the pulse. Based on the chirp-dependent feature, all-optical router and switch could be implemented by the pulse chirp modulation.     

An iterative method for nonlinear dynamical system of an electrostatically actuated micro-cantilever

This study proposes an iterative method, in which all iterations are linear, for solving the nonlinear dynamical system of an electrostatically actuated micro-cantilever in MEMS. The presented method is further improved, so that the CPU time needed is significantly reduced. This method provides solutions in excellent agreement with numerical ones.     

SPM of nonlinear surface plasmon waveguides

Pulse propagation equation of nonlinear dispersion surface plasmon waveguide is educed strictly from wave equation. The nonlinear coefficient is defined and then used to assess and compare the nonlinear characteristic of three popular 1-D surface plasmon waveguides: the single metal–dielectric interface, the metal slab bounded by dielectric and the dielectric slab bounded by metal. SPM (self-phase modulation) of the typical surface plasmon waveguide is predicted and discussed.     

Numerical simulation of the nonlinear ultrasonic pressure wave propagation in a cavitating bubbly liquid inside a sonochemical reactor

We investigate the acoustic wave propagation in bubbly liquid inside a pilot sonochemical reactor which aims to produce antibacterial medical textile fabrics by coating the textile with ZnO or CuO nanoparticles. Computational models on acoustic propagation are developed in order to aid the design procedures. The acoustic pressure wave propagation in the sonoreactor is simulated by solving the Helmholtz equation using a meshless numerical method. The paper implements both the state-of-the-art linear model and a nonlinear wave propagation model recently introduced by Louisnard (2012), and presents a novel iterative solution procedure for the nonlinear propagation model which can be implemented using any numerical method and/or programming tool. Comparative results regarding both the linear and the nonlinear wave propagation are shown. Effects of bubble size distribution and bubble volume fraction on the acoustic wave propagation are discussed in detail. The simulations demonstrate that the nonlinear model successfully captures the realistic spatial distribution of the cavitation zones and the associated acoustic pressure amplitudes.     

Rapid numerical difference recurrent formula of nonlinear Schrödinger equation and its application

In this paper, a rapid numerical difference recurrent formula, in which it has been taken that the chromatic dispersion and the nonlinearity act together along each fiber segment, is established in the time domain by applying a Maclaurin expansion to the differential form of the nonlinear Schrödinger equation (NLSE) in the frequency domain. The calculated results by using the established formula are contrasted with the known analytical results and the results of the split-step Fourier method (SSFM) and indicated that the rapid numerical difference recurrent formula is very accurate and more reasonable because it abandons an assumption that the dispersive and nonlinear effects can be assumed to act independently as the optical field propagates over each fiber segment. It has been concluded that the established formula in this paper is a scientific, reasonable and effective numerical method for the study of light pulse propagation in a nonlinear optical medium.     

克尔介质中脉冲宽度对瞬态热光非线性效应的影响

在纳秒时域，研究了激光脉冲宽度变化对克尔介质中瞬态热光非 线性效应的影响.通过不同脉冲宽度τp下得到的二硫化碳 苯胺黑溶液的Z_scan实验结果，对瞬态热光非线性效应和光克尔效应的共存过程进行了分析 .随着脉冲宽度的增加，观察到了热光非线性效应从瞬态到稳态变化过程和Z_scan峰谷特性 的转变.同时，从声波的传播方程和光波的非线性传播方程出发，用数值计算方法模拟了这 一非线性过程，结果表明数值模拟结果和实验结果是相符的. 关键词： 瞬态热光非线性效应 脉冲宽度 Z_scan 克尔效应     

All-optical NRZ-OOK-to-RZ-OOK format conversions with tunable duty cycles using nonlinear polarization rotation of a semiconductor optical amplifier

We experimentally demonstrate an all-optical 10 Gb/s format conversion from non-return-to-zero (NRZ) on-off-keying (OOK) to return-to-zero (RZ)-OOK with tunable duty cycle in the whole C-band using nonlinear polarization rotation (NPR) arising in an semiconductor optical amplifier (SOA). The experimental results show that, by tuning the polarizer at the SOA output, an RZ signal with tunable duty cycle from 33% to 66% could be obtained with an extinction ratio(ER) over 10 dB. In addition, we show that the NRZ-to-RZ conversion with duty cycle of 33-66% can be obtained with less than 1 dB power penalty at the bit error ratio (BER) of 10⁻⁹. The device can facilitate the cross-connection between optical transmission networks employing different modulation formats.