Statistical dynamics of parametrically perturbed sine-square map

We discuss the emergence and destruction of complex, critical and completely chaotic attractors in a nonlinear system when subjected to a small parametric perturbation in trigonometric, hyperbolic or noise function forms. For this purpose, a hybrid optical bistable system, which is a nonlinear physical system, has been chosen for investigation. We show that the emergence of new attractors is responsible for transients in many trajectories obeying power-law decay. The effect of perturbation on certain critical bifurcations such as period-2, onset of chaos, chaotic attractor with less complexity etc., has been studied and characterized using certain statistical features. Further, the effect of Gaussian noise with other types of perturbation has also been studied.     

A novel method of high resolution imaging through random perturbation wave front

A novel method is proposed for eliminating the effect of the traditional optical aberration on high resolution imaging by random perturbation wave front and digital image processing. A random phase mask, whose phase spectrum fluctuation is accordant with Kolmogorov distribution, is positioned near the aperture stop of optical system, making the optical aberration image become random perturbation image, that is, the intermediate image. The blind deconvolution algorithm based on maximum-likelihood estimation technique is used to restore the intermediate image acquired by a digital detector. The effects of optical aberrations and the noise on the restoration image are explored. To demonstrate the validity of the method proposed, the computer simulation and laboratory experiments are carried out for the imaging of the optical system with primary aberration. The results have shown that the present method is well suited for effectively improving the imaging quality of the optical system with certain aberration, thus making the optical system resolution close to or reach the diffraction-limit of the optical system.     

Effective simulation method for parametric signal-noise interaction in transmission fibers

We propose a new method for effective numerical simulation of transmission system performance and study of correlated noise evolution along an optical fiber with nonlinear parametric interaction between the amplified spontaneous emission (ASE) and the modulated optical signal. The method is based on an evaluation of the noise covariance matrix by using full nonlinear Schr?dinger equation (NLSE) and an analytical model for the optical receiver. Using extensive brute-force Monte Carlo simulation as a verification tool, we test the accuracy of the method and illustrate the analytical receiver model limitations in the case of moderate as well as substantial growth of non-Gaussian optical noise along the optical fiber transmission link.     

三光子吸收效应与误码率

本文用噪音微扰场讨论了三光子吸收效应对光纤放大器的增益噪音和误码率的影响.由此得到三光子吸收效应能抑制该类噪音和减小误码率而有利于光孤子通信的结论.     

激光陀螺中的光学抖动及其对锁区的影响分析

为了提高激光陀螺的性能,提出利用光学抖动改善陀螺锁区的方法.研究了环形光路中背向散射对锁区的影响,理想状态下可以消除陀螺的零阶锁区.在微扰条件下对光学抖动下陀螺腔内的光路变化进行了分析计算,得到了使陀螺锁区达到最佳改善的理论光学抖动量并进行了实验研究.实验结果表明:光学抖动可以起到类似机械抖动加噪的效果,改善陀螺的零偏稳定性.     

Soliton squeezing in a highly transmissive nonlinear optical loop mirror

A perturbation approach is used to study the quantum noise of optical solitons in an asymmetric fiber Sagnac interferometer (a highly transmissive nonlinear optical loop mirror). Analytical expressions for the three second-order quadrature correlators are derived and used to predict the amount of detectable amplitude squeezing along with the optimum power-splitting ratio of the Sagnac interferometer. We find that it is the number-phase correlation owing to the Kerr nonlinearity that is primarily responsible for the observable noise reduction. The group-velocity dispersion affecting the field in the nonsoliton arm of the fiber interferometer is shown to limit the minimum achievable Fano factor.     

Suppression of noise in a noisy optical trap

We have experimentally explored and clarified the concept of noise suppression in intrinsically noisy systems by adding noise at the input using a microscopic bead held in a moving and intensity-modulated optical trap. By coupling the stiffness of the optical trap to its position, we have explicitly constructed an experimental model system in which added fluctuations in the trap position result in reduced variance of the observed bead position as compared to a stationary trap. This reduction in variance and the spectral properties of the observed output noise agree with theoretical predictions. Our experiment demonstrates that the essential aspect of noise reduction in such a system is that the added fluctuations drive the system into states with a reduced intensity of intrinsic noise sufficiently often.     

多程放大器输出焦斑相对于靶的漂移

 对激光光路中光学元件矩阵分别施加“随机微扰”,用光线追踪程序计算光学元件几何参数失调对放大器漂的移影响。并给出漂移量的统计计算结果。     

Optical solitons in resonant and nonresonant nonlinear media in the presence of perturbations

We studied the optical solitons in nonlinear resonant and nonresonant media in the presence of perturbations, assuming that the transient effects are stimulated by the light scanning beam. We treated a slight deviation from the exact necessary condition for the soliton existence (2betanu=1), as a small perturbation for the integrable system, studying its influence upon the soliton propagation conditions. The approximation is constructed by the help of an algebraic version of the soliton perturbation theory using a Riemann boundary problem in connection with the inverse scattering method. We have obtained the soliton equation and we have solved it in the presence of a small perturbation in the adiabatic approximation. In this case we have demonstrated that for a Lorentz profile line the amplitude of the soliton remains unchanged, the only effect of the perturbation results in a phase shift.     

Biased transportations in a spatially asymmetric system at the nano-scale under thermal noise

Under the theory of ratchet effect for mesoand macro-scale systems, the additional perturbation with a long time correlation and the breaking of spatial inversion symmetry are two main ingredients to bring unidirected transportations. With the help of a simple model system, we show that a spatially asymmetric system of the nano-scale length may induce biased transportations under thermal noise.     

Effective noise in thresholded intensity distribution: influence on centroid statistics

It is usual to preprocess data before reduction, but it is not so common to study how this operation affects the final results. Determination of the centroid is a relevant task for many optical measurement devices, and the centroid is very often calculated over thresholded data. The influence of preprocessing thresholding algorithms on the statistical properties of intensity data affected by additive Gaussian noise is described as a different effective additive signal perturbation. Theoretical, simulated, and experimental analyses of the model of the effective noise were performed, and good agreement among the analyses was obtained. Direct extension of the analyses from the influence of preprocessing to centroid determination is also presented.     

Optical transfer functions of Kerr nonlinear cavities and interferometers

We present the optical transfer functions for third-order nonlinear cavities that involve an optical carrier frequency and its modulation sideband fields. Our approach is based on linearized transformations and provides a convenient tool to calculate squeezed light sources as well as complex interferometer topologies, containing subsystems that involve intensity dependent phase shifts, i.e., optical Kerr media. As the result we present the noise spectral density of a Michelson interferometer with Kerr nonlinear arm cavities and resonant sideband extraction and find that quantum noise can be squeezed by arbitrary amounts even outside the cavity linewidth. Such a system might apply for future gravitational wave detectors or simply for a continuous wave source of squeezed states.     

The Mean First-Passage Time of the System Driven by Internal and External Noise Simultaneously

We derive an equation of motion of mean firat-passage time (MFPT) for the nonlinear system driven by the external and internal noise simultaneously. An approximate formula of MFPT is obtained by the perturbation technique. We find the coupling effect of the internal and the external noise for the MFPT. Using the steepest descending method we obtain the MFPT for a specific model.     

光纤陀螺的噪声及其实验分析

通过对FOG-110-I全光纤陀螺仪样机的研制,分析了光纤陀螺的噪声源,并对信号光背向反馈进入激光器引起的强度噪声和由光纤PZT位相调制器引起的幅度调制对光纤陀螺系统的影响作了重点分析。最后,给出了FOG-110-I全光纤陀螺样机的测试结果和实验分析。     

Excess-noise suppression in a fibre-optic balanced heterodyne detection system

We have investigated balanced heterodyne detection in applications where laser intensity fluctuations are the dominant noise source, as, for example, in laser Doppler velocimetry with a He-Ne laser. The suppression of excess noise in comparison with a single receiver detection system is analysed theoretically. In our heterodyne experiment we have compared two different fibre-optic Mach-Zehnder interferometers, both with single-mode polarization-preserving fibres, one in integrated form using a directional coupler, the other one with a dielectric beam-splitter as the optical mixing element. With the former we have verified the theoretical results; with the latter we have demonstrated that with a good balance the fundamental short noise detection limit can be reached.     

Perturbation of Super-Sech Solitons in Dispersion-Managed Optical Fibers

The dynamics of super-sech solitons in dispersion-managed optical fibers is obtained in this paper. The dynamical system of soliton parameters is obtained for such pulses for dispersion-managed fibers, in presence of various perturbation terms. The perturbation terms studied are Hamiltonian, as well as non-Hamiltonian along with non-local types.     

Synchronization of noise-perturbed optical systems with multiple time delays

In this paper, complete synchronization and generalized synchronization between two unidirectionally coupled optical systems with multiple time delays and noise perturbation are investigated. Sufficient conditions for both complete synchronization and generalized synchronization are rigorously established. Numerical simulations fully support the theoretical results. The effect of parameter mismatch on the quality of synchronization is also explored.     

Trace Formulas for Stochastic Evolution Operators: Weak Noise Perturbation Theory

Periodic orbit theory is all effective tool for the analysis of classical and quantum chaotic systems. In this paper we extend this approach to stochastic systems, in particular to mappings with additive noise. The theory is cast in the standard field-theoretic formalism and weak noise perturbation theory written in terms of Feynman diagrams. The result is a stochastic analog of the next-to-leading ? corrections to the Gutzwiller trace formula, with long-time averages calculated from periodic orbits of the deterministic system. The perturbative corrections are computed analytically and tested numerically on a simple 1-dimensional system.     

窄带傅里叶变换光谱仪中平稳高斯噪声的理论分析

在本文所研究的空间调制型傅里叶变换光谱仪中, 在窄的光谱带宽内进行探测可以有效提高光谱的分辨率. 为了研究光源辐射噪声对系统的影响, 本文将辐射噪声归纳为一种高斯窄带的平稳随机过程, 利用线性系统分析方法, 根据统计学原理推导了辐射噪声作为随机变量通过干涉系统前后的输入信噪比与输出信噪比. 然后, 对于一个具有窄带矩形光谱的系统进行了计算仿真, 得出了信噪比增益随着光程差在不同自相关度和互相关度取值时的变化情况. 仿真结果表明, 不同光程差下的信噪比增益在相关度空间是一单调的平滑曲面, 增益极值始终沿着相关度圆的半径和周线移动, 并且经过一个光程差又回到初始的位置. 根据对信噪比增益的分析, 可以将噪声的相关度取值控制在某一范围之内, 并作为系统光源设计与测试的依据.     

Shot noise in a double-quantum-dot Aharonov-Bohm interferometer under the perturbation of ac fields

We have investigated the shot noise spectral density in the parallel double-quantum-dot (DQD) interferometer threaded with an Aharonov-Bohm (AB) flux under the perturbation of ac fields. The derivations are based on the nonequilibrium Green’s function (NGF) technique in the Coulomb blockade regime. The AB flux and the perturbation of ac fields together provide a photon-assisted AB interferometer for controlling the shot noise efficiently. The signature of the shot noise reflects the intrinsic microstructure of the DQD system, which plays important roles for the enhancement and suppression of shot noise. The versatile resonant structures of shot noise, Fano factor have been revealed to exhibit the sub-Poissonian and super-Poissonian types of shot noise by adjusting the gate voltages sequentially.