Analytical study of crosstalk propagation in all-optical networks using perturbation theory

The performance of current optical networks is inherently limited by the speed of electronic components and, in particular, by electronic switches. A new generation of optical networks, referred to as all-optical networks, overcomes this limitation by switching data entirely optically using all-optical crossconnects (OXCs). However, all-optical networks are prone to phenomena that are unknown to current optical networks with electrical regeneration: OXCs are subject to optical leaks, called crosstalk, resulting in unwanted components being added to transmitted signals, and this crosstalk is transmitted over very long paths without any signal regeneration. In this paper, we consider the interplay between fiber nonlinearity and crosstalk signals over long distances as the source of performance degradation, measured in terms of Q factor. We present an analytical crosstalk model for all-optical networks and give expressions for the performance degradation resulting from the joint propagation of a signal [using a continuous-wave (CW) assumption and perturbation theory] and crosstalk in large networks. Analytical calculations required by this model are shown to be much less computationally intensive than simulations. Simulations are carried out to validate our analytical model and good agreement is found between the analytical model and simulations for wide ranges of parameters.     

中长波双色碲镉汞红外探测器器件模拟与分析

利用Crosslight公司的APSYS软件模拟准平面结构中长波双色碲镉汞红外探测器的不同结构的光谱串音。研究表明中波层厚度增加将抑制中波对长波的光谱串音,同时将小幅增大长波对中波的光谱串音;阻挡层组分越大,阻挡层与中波层的导带带阶越大,光生载流子跃迁过带阶势垒的几率减少,使得光谱串音减小;阻挡层厚度越大量子隧穿效应减弱,导致光谱串音减小。通过优化器件结构可使中波对长波的光谱串音以及长波对中波的光谱串音都控制在2.5 %以下。     

Estimation of gravity wave momentum flux with spectroscopic imaging

Atmospheric gravity waves play a significant role in the dynamics and thermal balance of the upper atmosphere. In this paper, we present a novel technique for automated and robust calculation of momentum flux of high-frequency quasi-monochromatic wave components from spectroscopic imaging and horizontal radar wind measurements. Our approach uses the two-dimensional (2-D) cross periodogram of two consecutive Doppler-shifted time-differenced (TD) images to identify wave components and estimate intrinsic wave parameters. Besides estimating the average perturbation of dominant waves in the whole field of view, this technique applies 2-D short-space Fourier transform to the TD images to identify localized wave events. With the wave parameters acquired, the momentum flux carried by all vertically propagating wave components is calculated using an analytical model relating the measured intensity perturbation to the wave amplitude. This model is tested by comparing wave perturbation amplitudes inferred from spectroscopic images with those from sodium lidar temperature measurements. The proposed technique enables characterization of the variations in the direction and strength of gravity waves with high temporal resolution for each clear data-taking night. The nightly results provide statistical information for investigating seasonal and geographical variations in momentum flux of gravity waves.     

Computations of scattering cross sections for composite surfaces and the specification of the wavenumber where spectral splitting occurs

The scattering cross sections for composite random rough surfaces are evaluated using the full wave approach. They are compared with earlier solutions based on a combination of perturbation theory which accounts for Bragg scattering, and physical optics which accounts for specular point theory. The full wave solutions which account for both Bragg scattering and specular point scattering in a self-consistent manner are expressed as a weighted sum of two cross sections. The first is associated with a filtered surface, consisting of the larger scale spectral components, and the second is associated with the surface consisting of the smaller scale spectral components. The specification of the surface wavenumber that separates the surface with the larger spectral components from the surface with the smaller spectral components is dealt with in detail. Since the full wave approach is not restricted by the limitations of perturbation theory, it is possible to examine the sensitivity of the computed values for the backscatter cross sections to large variations in the value of the wavenumber where spectral splitting is assumed to occur.     

Increased Nonlinear Crosstalk in Analog Wavelength-Division-Multiplexed Links Due to the Chromatic Dispersion of Optical Filters

The effect of the chromatic dispersion of an interference filter on the nonlinear crosstalk in a wavelength-division-multiplexed microwave photonic system is investigated. For a simple two-channel pump–probe system with 200-GHz channel spacing, a crosstalk variation of greater than 30 dB is observed as the wavelength of the probe is varied across the flat-top region of the filter. The crosstalk is correlated with the dispersion of the filter and a variation of less than 7% of the filter width is observed to increase the crosstalk by 10 dB. An analytical model for calculating the crosstalk is presented.     

Crosstalk and switching characteristics in directional couplers

The normal mode approach is used to calculate the fundamental limits on crosstalk and switching characteristics in directional coupler switches of the stepped delta beta type. The normal modes are calculated numerically as well as analytically using a method for computing the eigenmodes of two coupled, identical waveguides with an antisymmetric index perturbation. The results of the two methods are compared to one another as well as to the results of coupled-mode theory. It is shown that the theoretical minimum for the crosstalk level is very low for the stepped delta beta structure. Nonzero crosstalk was found in some cases where coupled-mode theory predicts zero crosstalk. This is attributed to the improper handling of discontinuities in coupled-mode theory     

Perturbation Theory Generalized to Arbitrary (p,l) Modes in a Fabry-Perot Resonator (Letters)

The first-order perturbation calculation that was carried out to include the effects of the usually neglected delta/sup 2/psi / delta z/sup 2/ term in the wave equation for pure radial modes (l = 0) is generalized to the case of arbitrary p,l modes. The result, although requiring more algebra, is similar to that of the l= 0 case; the correction term is a monotonically increasing function of both p and l, and reduces to the original expression as l --> 0.     

光纤陀螺抑制过调制串扰的多态方波调制方法

光纤陀螺方波调制信号引起的调制串扰会导致陀螺输出信号的不稳定,恶化阈值、标度非线性等指标。过调制技术是采用增大调制相位来抑制噪声的一种方法,根据过调制串扰的相关解调原理和模型,推导出含过调制串扰的陀螺输出表达式,指出过调制相位是影响串扰量的重要因素。针对增大过调制相位引起串扰量增加的问题,提出一种抑制过调制串扰的多态方波调制方法,利用响应余弦函数的周期性和调制波形的重复性,产生统计上相关性很小的调制信号和解调信号,在一定的延迟时间下,调制信号及串扰信号与解调信号的相关结果为0,在相关解调过程中减小串扰量。仿真和实验结果表明,该调制方法对串扰信号的抑制作用相比方波过调制提高一个数量级,陀螺的零偏稳定性和阈值指标相比方波过调制改善约40%。     

柔软光纤传像束的传像特性

研究了柔软光纤传像束的传像特性.界面交扰是柔软光纤传像束最重要的传像特性之一.迄今为止,有关这些方面的研究尚未完善.描述了一种采用光学视频系统定量测量柔软光纤传像束交扰率的新技术,并通过对柔软光纤传像束的静态MTF的测量和目视法观察,分析对比了交扰率对传像束传像特性的影响,比较了多种传像束样品的测量结果.     

Analysis of Crosstalk Induced by Optical Cross-Connection in Multiwavelength Networks

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Optical Solitons with Power Law Nonlinearity and Hamiltonian Perturbations: An Exact Solution

This paper studies the optical solitons with power law nonlinearity in presence of Hamiltonian perturbation terms. The perturbation terms that are taken into account are inter-modal dispersion, third order dispersion, self-steepening term and nonlinear dispersion. An exact 1-soliton solution is obtained by the solitary wave ansatz. Both bright and dark optical soliton solutions are obtained. The domain restrictions have also been identified in the process.     

Asymptotic eigenvalues of vector wave equation for guided modes in graded-index fibre

Asymptotic eigenvalues of the vector wave equation?a system of coupled second-order differential equations?are calculated by the perturbation method in which we use the exact solutions of the scalar wave equation as the unperturbed term. We examine a graded-index fibre with a polynomial profile core and obtain the propagation constants of the vector modes in analytic form. The results coincide with those found by a sophisticated method.     

Radiation from Curved Dielectric Slabs and Fibers

The form taken by the radiation condition in the local coordinate system, pertinent to the determination by perturbation methods of the radiation from curved radiating structures, is not the same as it is at very great distances. Specifically, it may contain a term that appears as if it were an incoming or growing wave. A detailed analysis is made of the appropriate form of the condition in cylindrical and toroidal systems, and is applied to the calculation of radiation from curyed dielectric slabs and fibers.     

Multichannel signal processing for data communications in thepresence of crosstalk

Transceiver designs for multiple coupled channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. The authors propose a transmitter/receiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multi-input/multi-output channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adaptive FIR filters to cancel near- and far-end crosstalk, and to pre- and postprocess the input/output of the channel. Linear pre- and postprocessors that minimize mean squared error between the received and transmitted signal in the presence of both near- and far-end crosstalk are derived. The performance of an adaptive near-end crosstalk canceller using the stochastic gradient (least-mean-square) transversal algorithm is illustrated by numerical simulation. Plots of mean squared error versus time and eye diagrams are presented, assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented and illustrated explicitly for s simple model of two coupled channels     

Improved linear crosstalk tolerance in an un-amplified ring PON

There is increased interest in ring-based passive optical network (PON) architectures due to their local area network (LAN) capability among end users and inherent protection and restoration schemes. The ring architecture includes optical filters and switches with non-ideal channel isolation, leading to the generation of linear crosstalk, which can significantly degrade the system performance if it is not sufficiently suppressed. We use simulation to analyze the effects of linear crosstalk in an un-amplified TDM optical ring and show how we can improve the tolerance of the crosstalk in our architecture that employs optimized tap split ratios as a means of increasing the number of ONUs served. Our approach is based on simulation of the entire network using a combination of wavelength-domain and time-domain techniques. Typically, PON networks use two or three wavelengths that are separated by more than 50 nm to maintain the cost of components low and as such, it is logical that any crosstalk will be negligible. However, the subpar performance of such components motivated our study into the impact of crosstalk. We show that the tap ratio optimization which increases the number ONUs that can be served in the ring can also exacerbate the effects of linear interchannel crosstalk at the ONU’s downstream signal receivers. We also show that surplus power at the last ONU can be utilized to counter this degraded crosstalk performance by careful tap ratio selection, thereby improving the overall tolerance to linear crosstalk in the system.     

High Order Modes in a Spherical Fabry-Perot Resonator

The accuracy of the approximate solution to the wave equation in the "large aperture" case was investigated. The measured distribution of energy in the various transverse modes corresponded to the Laguerre-Gaussian solutions; resonant frequencies, however, deviated from those predicted by the approximate theory by as much as 2 percent for high radial mode numbers. Two first order perturbation calculations, including a neglected term in the wave equation and the nonsphericity of constant phase surfaces, yielded resonant frequencies in agreement with experiment.     

Electrooptic sampling of a packaged high-speed GaAs integratedcircuit

The authors describe the use of electrooptic sampling to characterize the performance of a packaged 1.7-GHz GaAs planar integrated decision circuit. To study the packaged device, it was necessary for the optical probe beam to impinge on the circuit from the front (active) side. This geometry enabled effective evaluation of the circuit, in spite of reduced spatial resolution and voltage sensitivity compared to a backside probing geometry. Using a gain-switched InGaAsP laser source, waveforms have been measured in the D flip-flop within the circuit and propagation delays of about 25 ps in the input buffers. Apparent crosstalk has been measured when the probe is positioned between adjacent active circuit lines and it is found that this crosstalk depends sensitively on the position of the probe beam     

Crosstalk in Balanced Interconnections Used for Differential Signal Transmission

This paper introduces a two-stage model for assessing crosstalk in balanced interconnections used for differential signal transmission, such as multipair cables. The first stage considers the interconnection as uniform and uses a change of variables based on the symmetries inherent to balancing, for the definition of a set of parameters to be measured. The second stage of the model takes into account the nonuniformity related to the fluctuations of the characteristics of the interconnection, using a first order perturbation expansion and a probabilistic approach. This model is compatible with published results on crosstalk in multipair cables.     

二维fBm分形分层介质粗糙面电磁波透射特征研究

该文运用微扰法研究了平面波入射分层介质粗糙面的电磁波透射问题,推导出不同极化状态的透射波散射系数公式。采用二维fBm分形粗糙面来模拟实际的分层介质粗糙面,结合其功率谱导出了平面波入射时的透射系数计算公式。通过数值计算得到了HH极化状态下二维fBm分形分层介质粗糙面透射系数随透射波的散射角变化的曲线,分形特征、基本特征、随频率变化的特征。结果表明分维、底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射波频率对透射系数的影响是非常复杂的。