Recurrence phase shift in Fermi-Pasta-Ulam nonlinear dynamics

We show that the dynamics of Fermi-Pasta-Ulam recurrence is associated with a nonlinear phase shift between initial and final states that are otherwise identical, after a full growth-return cycle. The properties of this phase shift are studied for the particular case of the self-focussing nonlinear Schrödinger equation, and we describe the magnitude of the phase shift in terms of the system parameters. This phase shift, accumulated during the nonlinear recurrence cycle, is a previously-unremarked feature of the Fermi-Pasta-Ulam problem, and we anticipate its wide significance as an essential feature of related dynamics in other systems.     

Beyond the absorption-limited nonlinear phase shift with microring resonators

We show that the nonlinear phase shift produced by a ring resonator constructed from a given nonlinear optical material can be greater than the phase shift produced by a single pass through an infinite length of the same material when linear and nonlinear absorption are taken into consideration. The figure of merit (defined by the phase shift times the throughput) also improves for the ring resonator over that of the native nonlinear absorbing material. We finally show that these benefits of using the ring resonator as a nonlinear phase-shifting element can enhance the switching characteristics of a Mach-Zehnder interferometer.     

High-order nonlinear phase shift caused by cascaded third-order processes

We show, for the first time to our knowledge, that the fundamental beam that participates in the process of third-harmonic generation experiences an additional high-order nonlinear phase shift. The magnitude of the shift is proportional to the square of the pump intensity and the length of the sample and depends on the deviation from the exact phase-matched condition. This phase shift arises from cascaded third-order processes. Its value can exceed the value of the phase shift that originates from inherent fifth-order susceptibility of the nonlinear medium. Its sign is controllable by the sign of the phase mismatch of the third-harmonic generation process.     

大非线性相移下光学非线性Z扫描特性的研究

采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析,通过对数值算法的优化,将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较,发现在大非线性相移的情况下,Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加,Z扫描曲线峰的变化要明显快于谷的变化,而且在谷明显存在的情况下,峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证,实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义,避免在大非线性相移下对Z扫描结果产生错误的分析.     

非线性相移对Z-scan曲线对称性的影响

 基于由光束传输的ABCD矩阵得出的Z-scan透过率的解析结果,分析了Z-scan实验曲线随非线性相移的变化规律。发现随着相移的增加,折射非线性相移比吸收非线性相移对Z-scan曲线对称性的影响更大。对于具有强饱和吸收和弱自聚焦特性的非线性介质,其Z-scan曲线随非线性折射相移的变小将失去典型的类色散特点。对于1μm厚的ZnCdSe-ZnSe多量子阱,扫描光源采用532 nm的基模高斯光束,采用透过率表达式来拟合所得的实验数据,在吸收非线性相移为0.9与耦合因子为-10条件下,推算出三阶非线性吸收系数为2×10^-3 cm/W,三阶非线性折射系数为 8.0×10^-8 cm²/W,这与J.Ma等人的结果吻合。最后对曲线特征参数随非线性相移变化进行了数值计算,得到的曲线所对应的非线性相移与曲线谷位置的乘积近似为一常量,值为0.166。     

Phase-matched third-harmonic generation by nonlinear phase shift in a hollow fiber

14 W/cm² are introduced into a 1.8-cm hollow fiber in room air. From the observation of the third-harmonic beam quality and spectra, it is clarified that the harmonics are pumped at the leading edge of the fundamental pulse. The model calculation accounting for the nonlinear refractive index change of air shows a quantitative agreement with the experimental results. Received: 19 September 1997/Revised version: 2 December 1997     

大非线性相移下光学非线性Z扫描特性的研究

采用高斯分解法(GD)对大非线性相移下的Z扫描特性进行了分析，通过对数值算法的优化，将GD推广到对脉冲入射激光下大非线性相移下的Z扫描理论分析.对不同条件下大非线性相移Z扫描曲线峰谷结构的比较，发现在大非线性相移的情况下，Z扫描曲线的峰和谷随透过光阑或入射光强变化表现出某些新的特性.随着透过光阑孔径的增加，Z扫描曲线峰的变化要明显快于谷的变化，而且在谷明显存在的情况下，峰很快消失.采用皮秒脉冲激光下的纯二硫化碳实验对理论结果加以验证，实验结果和理论分析相一致.我们的分析结果对大非线性相移下Z扫描测量有一定的指导性意义，避免在大非线性相移下对Z扫描结果产生错误的分析. 关键词： 大非线性相移 高斯分解法 Z扫描     

New features of a single-mode nonlinear Stark shift in the presence of phase damping

The influence of the nonlinear Stark shift, for the multi-quanta JCM in the presence of phase damping is studied. In particular the temporal evolution of the atomic inversion, the linear entropy and the entropy squeezing are investigated. The linear entropy is used as an indicator of the degree of entanglement between the atom and the field. The results indicate the sensitivity of these aspects to changes either in the decay parameter or the Stark shift parameter.     

Electro-optic modulation on nonlinear phase shift and fundamental transmission in quasi-phase-matched second-harmonic generation

Nonlinear phase shift and transmission experienced by a beam at the fundamental frequency during electro-optic modulated quasi-phase-matched second-harmonic generation are studied. Numerical results indicate that the nonlinear phase shift of fundamental wave shows a difference of π, while fundamental transmission is controllable only by applying a DC electric field along z-axis. The above effect can be implemented on high-contrast optical switching devices such as Mach-Zehnder push-pull device. The relationships between the characteristic (peak and dip) electric fields and the initial pump intensity are also discussed.     

Optimized all-optical amplitude reshaping by exploiting nonlinear phase shift in fiber for degenerated FWM

We describe a novel performance optimization method for all-optical amplitude reshaping via degenerated four-wave mixing(FWM) in highly nonlinear optical fiber.The proposed optimization method is achieved by judiciously configuring the FWM operational condition and exploiting the nonlinear phase shift induced by self-and cross-phase modulations to properly influence the FWM conversion efficiency.Through the proposed scheme,fully functional and prevailing reshaping performance,including significant amplitude jitter suppression and extinction ratio improvement,is obtained within a single FWM stage.Results of the present theoretical calculation and numerical simulation verify the feasibility and advantages of the proposed scheme.     

Measurement of the nonlinear phase shift induced by cascaded interactions in a periodically poled lithium niobate waveguide

We report on the measurement of nonlinear phase shift phiNL induced by a strong pump at wavelength lamda p on a weak signal at lamda s through a cascade of two second-order interactions in a periodically poled lithium-niobate waveguide. The experiment is performed by use of an interferometric scheme especially designed to be insensitive to slow mechanical and thermal drift effects. The observed behavior of phiNL as a function of pump power and of wavelength difference lamda p - lamda s, is in good agreement with the theoretical predictions.     

Variation of wave action: Modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation

Strongly nonlinear dispersive waves described by a general Klein—Gordon equation with slowly varying coefficients and a dissipative perturbation are analyzed using the method of multiple scales. We use the exact equation of wave action. The spatial and temporal slow modulations of the phase shift are shown to be governed by a new equation, which results from linearization of the wave action, its flux, and its dissipation due to perturbations of the slow parameters: frequency and wave number (vector). This result extends to nonlinear partial differential equations, the quite recent work by the authors on nonlinear oscillations governed by ordinary differential equations.     

Physical origin of the Gouy phase shift

We show explicitly that the well-known Gouy phase shift of any focused beam originates from transverse spatial confinement, which, through the uncertainty principle, introduces a spread in the transverse momenta and hence a shift in the expectation value of the axial propagation constant. A general expression is given for the Gouy phase shift in terms of expectation values of the squares of the transverse momenta. Our result also explains the phase shift in front of the Kirchhoff diffraction integral.     

Reference phase shift determination in phase shifting interferometry

The phase shifting technique has recently seen application to many types of interferometers, including holographic, speckle and moiré systems for strain analysis. In these applications, close control of the phase shifts may be impossible due to the effect of mechanical vibrations, and this presents difficulties when extracting the phase information, since the reference phase shifts are generally assumed to be known. In this work, several approaches to the problem of determining the reference phase shifts in a perturbing environment are critically evaluated using computer simulations. The analyses provide a general relationship between precision and reference phase shift errors and demonstrate the performance of each method as certain idealised fringe pattern error parameters are varied. A practical example confirms the predictions of the numerical simulations and demonstrates the feasibility of using reference phase shift estimates to improve data reduction procedures.     

Weighted nonlinear phase shift with group velocity dispersion to assess the nonlinear penalty in C+L band long-haul fiber optical amplified transmission link

To assess the penalty due to nonlinear effect in C L band long-haul optical amplified transmission link,a new parameter of modified nonlinear phase shift (φD) is proposed,which is the accumulated nonlinear phase shift weighted by a normalized group velocity dispersion (GVD).Based on the numerical simulation result of broadband long-haul hybrid Raman/erbium-doped fiber amplified transmission line,it is validated that φD is more reasonable and suitable than the previous proposed nonlinear phase shift (φNL) for broadband applications.     

Temperature dependence of phase shift in ferrite phase shifters

Reciprocal ferrite phase shifters exhibit a pronounced dependence of phase shift upon temperature. In a sample of magnesium-copper-chromium ferrite it is shown that the temperature dependence of the phase shift is basically determined by the temperature dependence of the microwave magnetic permeability.In conclusion the authors wish to thank G. I. Yudin for making the measurements of phase shift and its dependence on the field for various temperatures.     

Generalized eikonal treatment of the Gouy phase shift

We use a generalized refractive index that includes diffraction effects to show that the Gouy phase shift can be seen as an intensity averaged optical path difference between the generalized eikonal and the geometrical eikonal. This approach generalizes previous treatments to include the effects of phase distortion and confirms the role of transverse spatial confinement in the Gouy shift.     

Blind phase shift extraction and wavefront retrieval by two-frame phase-shifting interferometry with an unknown phase shift

An iterative algorithm to extract the arbitrary unknown phase shift in two-frame phase-shifting interferometry and then reconstruct the complex object wave is proposed. In combination with the least square principle and some calculation formulae we developed, this algorithm allows us to find the value of unknown phase shift by using only two interferograms without additional knowledge or measurement. Computer simulations have shown that this algorithm works well for both the smooth and diffusing objects to a very high accuracy over a wide range of the phase shift from 0.4 to 2.5 rad.     

Carrier squeezing interferometry: suppressing phase errors from the inaccurate phase shift

The carrier squeezing interferometry algorithm is proposed to retrieve the phase from interferograms with phase shift errors. A linear carrier is introduced in the interferograms, and the image data is rearranged by the squeezing interferometry technology. In the spectrum of the rearranged image, the error lobe and the phase lobe are separated so the error-free phase can be retrieved by filtering. The simulated interferograms with phase shift errors are computed, and the precisions are better than 8.4×10(-4)λ. Its validation is verified by experiments, where a mean precision of 0.0040λ is obtained.     

Rapid extraction of the phase shift of the cold-atom interferometer via phase demodulation

Generally, the phase of the cold-atom interferometer is extracted from the atomic interference fringe, which can be obtained by scanning the chirp rate of the Raman lasers at a given interrogation time T. If mapping the phase shift for each T with a series of measurements, the extraction time is limited by the protocol of each T measurement, and therefore increases dramatically when doing fine mapping with a small step of T. Here we present a new method for rapid extraction of the phase shift via phase demodulation. By using this method, the systematic shifts can be mapped though the whole interference area. This method enables quick diagnostics of the potential cause of the phase shift in specific time. We demonstrate experimentally that this method is effective for the evaluation of the systematic errors of the cold atomic gravimeter. The systematic phase error induced by the quadratic Zeeman effect in the free-falling region is extracted by this method. The measured results correspond well with the theoretic prediction and also agree with the results obtained by the fringe fitting method for each T.