Accuracy of Gaussian Approach for the Performance Evaluation of Direct-Detection Receiver with Partially Polarized Noise

Abstract

We investigate the accuracy of a Gaussian approach (GA) developed to estimate the performance of a direct-detection optical receiver with arbitrary optical and electrical filtering and in the presence of partially polarized noise due to polarization-dependent loss (PDL). The accuracy is assessed by comparison of the performance estimates obtained from the GA with the estimates obtained from a rigorous method (RM) based on the calculation of the moment-generating function of the current at the optical receiver output.

We show that the GA has a good accuracy when considering the variation of the optical filter bandwidth, extinction ratio, degree of polarization of the noise (DOP), and angle between signal and noise polarizations. However, it fails to predict the receiver sensitivity within 2 dB of the RM when DOP is greater than 0.7 and signal and noise polarizations are orthogonal in the Jones space.

Nevertheless, it is shown that the GA provides receiver sensitivity estimates with good accuracy in most cases of long-haul optical communication systems influenced by PDL, where the typical average DOP is below 0.15. Due to its simplicity, shorter computation time, and good accuracy, the GA is a good tool to assess the performance of such optical systems.     

被光阑衍射部分偏振高斯-谢尔模型光束的远场特性

从部分相干光的传输理论出发,采用光束相干-偏振矩阵方法研究了被光阑衍射部分偏振高斯-谢尔模型光束的远场特性,对远场偏振和光强特性作了详细的数值计算和物理分析。研究结果表明,光阑衍射部分偏振高斯-谢尔模型光束的远场特性与光阑截断参量、光的空间相干性和衍射角有关。并与自由空间的传输特性和以前的工作作了比较分析。     

部分相干部分偏振电磁束通过光阑透镜的传输

基于广义斯托克斯参量,推导出了部分相干部分偏振高斯谢尔模型(GSM)电磁柬通过光阑透镜后交叉谱密度矩阵、光强、偏振度、偏振椭圆的方位角及椭偏角的解析表达式,并用以研究菲涅耳数、自相关和互相关长度以及束腰宽度对焦移和偏振特性的影响.对主要数值计算结果做了物理解释.     

部分相干部分偏振电磁束通过光阑透镜的传输

基于广义斯托克斯参量,推导出了部分相干部分偏振高斯谢尔模型(GSM)电磁束通过光阑透镜后交叉谱密度矩阵、光强、偏振度、偏振椭圆的方位角及椭偏角的解析表达式,并用以研究菲涅耳数、自相关和互相关长度以及束腰宽度对焦移和偏振特性的影响。对主要数值计算结果做了物理解释。     

光阑对偏振高斯-谢尔模型光束偏振特性的影响（英文）

根据广义惠更斯-菲涅尔原理和Collins公式,基于复高斯函数展开法,推导出椭圆偏振的高斯-谢尔模型光束经过矩形光阑衍射后的交叉谱密度公式,结合斯托克斯矢量理论推导了椭圆偏振高斯-谢尔模型光束在接收平面的光强、偏振度、方位角和椭圆度的表达式,数值分析了光阑的孔径遮拦比对光强、偏振度及方位角和椭圆度的影响.结果表明,光阑的孔径遮拦比在近场区对经过光阑后椭圆偏振高斯-谢尔模型光束的光强和偏振特性有显著影响;随着传输距离的增大,光强和偏振特性受孔径遮拦比的影响减小,光强和偏振特性变化平稳.     

Propagation properties of partially polarized Gaussian Schell-model beams through an axis-unsymmetric paraxial ABCD system

By using the beam coherence-polarization (BCP) matrix approach, analytical propagation equations of partially polarized Gaussian Schell-model (PGSM) beams through an axis-unsymmetric paraxial optical ABCD system are derived, which enable us to study the propagation-induced polarization changes and irradiance distributions at any propagation distance of PGSM beams through axis-unsymmetric systems within the framework of the paraxial approximation. Detailed numerical results for a PGSM beam passing through a bifocal lens are presented to illustrate the propagation properties of PGSM beams. A comparison with the previous work is also made.     

The aperture effect on the propagation of partially polarized Gaussian Schell-model beams

Based on the beam coherence-polarization (BCP) matrix approach and propagation law of partially coherent beams, the propagation of partially polarized Gaussian Schell-model (PGSM) beams through an aperture is studied. Numerical calculation results are given to illustrate the propagation-induced polarization changes and irradiance distribution of PGSM beams for the apertured case.     

部分相干光学成像系统的光学传递函数和像质评价准则

根据光学成像理论，建立了部分相干成像光学系统的光学传递函数。该函数与非相干成像光学系统传递函数相同，因而部分相干成像和非相干成像两者的光学系统波面像差公差标准也是相同的。这一点解释了显微镜光学系统的光学设计惯用法则：镜头像差公差标准的选择，并不因为采用成像照明方式的不同而有所差异。     

Propagation Characteristics of a Partially Coherent Gaussian Schell-model Array Vortex Beam in the Joint Turbulence Effect of a Jet Engine and Atmosphere

This work investigates the joint effects of jet engine exhaust-induced turbulence and atmospheric turbulence on the propagation of a partially coherent Gaussian Schell-model Array (GSMA) vortex beam. Using the two-process propagation method, analytical formulae are derived for the cross-spectral density, spectral density, degree of coherence, and beam width of the considered beam. The results show that the considered beam takes different shapes; when the spatial coherence is large, the spectral density of the GSMA vortex beam takes an elliptical shape, whereas when the spatial coherence is smaller, the spectral density remains a Gaussian shape. The evolution profile of the degree of coherence weakens gradually when the propagation distance, topological charge, and turbulence strength increase. Moreover, the profile of the degree of coherence takes the Gaussian profile when the propagation distance is longer or turbulence atmospheric is stronger. Furthermore, the results reveal that the corresponding beam spreads faster with a larger propagation distance, lower spatial coherence, and high-strength turbulence. This study also concludes from the results that the beam is affected more when its propagation is near the jet engine exhaust, which means that this latter has a significant impact.     

利用4400系统构造具有光学多道分析功能的信号处理系统

基于4400系统,通过引入光电二极管列阵作为传感器,构造了具有光学多道分析功能的信号处理系统。利用该系统对实际的激光空间分布进行了描绘,给出了高斯场分布的相应参数。通过进一步观测p偏振光在K9玻璃上下表面反射光强比(γ)的角度调制曲线,获得了玻璃表面层的光学参数。实验结果表明,该系统测量精度高,可应用在激光时间信号及空间场分布的表征与测量领域。     

Focal shift and focal switch of partially polarized Gaussian Schell-model beams passing through a system with the aperture and spherically aberrated lens separated

Based on the beam coherent-polarization (BCP) matrix approach and propagation law of partially coherent beams, the focal shift and focal switch of partially polarized Gaussian Schell-model (PGSM) beams passing through a system with the aperture and spherically aberrated lens separated is studied in detail. Our main attention is focused on the effect of spherical aberration and partial coherence on the focal shift and focal switch of PGSM beams. It is shown that for polarizer-free case there is no focal switch of PGSM beams, the focal shift of PGSM beams is closely related with spherical aberration coefficient C₄, auto-coherence length σ_a, truncation parameter δ and relative position s/f between the aperture and lens in general, and is independent of the cross-coherence length σ_c. After inserting a polarizer the focal switch can take place. Numerical calculation results are given to illustrate how the spherical aberration and partial coherence affect the focal shift and focal switch of PGSM beams.     

Characteristics of the Phase Noise Correlation of Injection Locked Lasers for RF Signal Generation and Transmission

Theoretical and experimental results on phase noise characteristics of an optical radio-frequency generation and transmission system using heterodyne photo-detection and side band injection locking is reported. Optical phase noise correlation of the lasers is achieved by noise transfer from a modulated master laser. Our investigation takes into account phase noise enhancement in optical comb generation, injection dynamic, path delay, and fiber dispersion. Theoretical expressions are derived from an adiabatic approximation and compared with experimental measures.     

一种测量光具组基准点的实验方法

提出了一种新的测量光具组基准点的实验方法。基于光具组焦点的定义，利用平行光法先确定其焦点位置，并利用牛顿公式法测定光具组的焦距，进一步确定光具组主点（与节点）的位置。     

Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture

By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems.     

A Novel Approach for the Evaluation of Band Gap Energy in Semiconductors

On the basis of absorption nature of semiconductors, we present a novel and simple method to determine the band gap energies of semiconductors directly from their absorption spectra at any temperatures, without any fitting processes and restrictions of sample thickness. The key point of the approach is the different dependence of the absorption coefficient derivative on the photon energy at different absorption regions in semiconductors. We first demonstrate and verify the approach by detailed temperature-dependent absorption measurements, combined with photoluminescence measurements and empirical band gap equations for the direct band gap of uniform InAs films, and then extend successfully to the indirect band gap of elemental Ge and to the ternary HgCdTe alloys with composition gradient. Furthermore, we have also shown that our approach can not only evaluate the average band gap energy for ternary semiconductor alloys, but also estimate their composition uniformity to monitor the material quality.     

Approximate analytical representation of Wigner distribution function for Gaussian beams passing through ABCD optical systems with hard aperture

Based on the treatment that a rectangular function can be expanded as an approximate sum of complex Gaussian functions with finite numbers, the analytical expression of the Wigner distribution function for a Gaussian beam passing through a paraxial ABCD optical system with hard-edged aperture is obtained. By numerical simulation, it is shown that the effect of the aperture on the Wigner distribution function is prominent. By comparing the analytical results with the numerical integral results, it is shown that this method of expanding hard-edged aperture into Gaussian functions with finite numbers is proper and ascendant. This method could be extended to study the Wigner distribution functions of other light beams passing through a paraxial ABCD optical system with hard-edged aperture.     

平衡接收直接检测DPSK接收机噪声统计特性分析

以带光前置放大器且采用MZI相干和直接检测方式的DPSK接收机为分析模型,从考虑线性附加噪声和非线性相位噪声入手,对噪声统计特性进行了数学分析,并推导出了概率密度函数和BER公式。结果表明:数值计算结果与已发表论文的试验结果较为吻合;非线性相位噪声会对系统性能造成严重影响;高斯近似法不能很好的分析此模型。     

The Effects of Polarization and Non-Linearity on the Performance of WDM System with Optical Cross-Connects

The performance of a wavelength division multiplexing (WDM) system with optical cross-connects (OXCs) and in the presence of polarization and nonlinear effects was analyzed. We determined the effect of PMD and PDL; nonlinearity such as XPM, SPM, and FWM; and CD on the system performance. We found that the system outage probability is highest at DGD threshold for the respective maximum eye closure (EC). We showed that the allowable DGD depends on the time slot for one bit T, which is the inverse of the network bit rate. Wider T is more immune to large PMD with the EC still maintained at the same level since DGD/T is unchanged. Our analysis also indicated that as DGD increases, BER increases. The BER also increases with increase in PDL and further increases with the presence of XPM, SPM, FWM, and CD.     

基于镜像焦面检测对准标记的套刻性能原位测量技术

套刻性能是现代高精度步进扫描投影光刻机的重要性能指标之一。提出了一种基于镜像焦面检测对准标记(简称“镜像焦面检测对准标记”)的光刻机套刻性能原位测量技术。该技术通过对曝光在硅片上的镜像焦面检测对准标记图形进行光学对准,利用标记图形对准位置与理想位置偏差实现套刻性能的原位检测。实验结果表明该技术在进行套刻误差的精确测量的同时还可以全面、定量地计算影响光刻机单机套刻误差的场内参量及场间参量。与目前套刻性能原位测量技术相比,该技术有效地避免了测量精度对轴向像质限制的依赖,简化了光刻机整机性能检测的过程。     

Assessment of the coherent potential approximation for the absorption spectra of a one-dimensional Frenkel exciton system with a Gaussian distribution of fluctuations in the optical transition frequency

We investigate the accuracy of the coherent potential approximation (CPA) for the optical absorption spectra of a one-dimensional Frenkel exciton system with nearest-neighbor interactions and a Gaussian distribution of fluctuations in the optical transition frequency (diagonal Gaussian disorder). Our earlier studies have established that the CPA gives highly accurate results for the integral of the density of states of this system. In this paper we compare the CPA results for the normalized optical absorption with the finite-array calculations of Schreiber and Toyozawa and Schreiber for the same model. It is found that the CPA results for the absorption are in good agreement with their findings. It is pointed out that an expansion of the density of states in terms of the eigenstates of the ideal (no disorder) array contains a term proportional to the normalized absorption. Since the density of states is accurately approximated by the CPA, the presence of this term explains the success of the CPA in reproducing the absorption spectra. Our findings support the use of the Gaussian disorder model to interpret the absorption spectra of one and quasi-one dimensional exciton systems.