Reflection Properties of Dual-Mode Filters Consisting of a Circular Array of Microring Resonators

A circular array consisting of an odd number of microring resonators is a dual-mode reflection filter. Based on the photonic energy band of a coupled microring resonator string and the resonant condition of the circular array, reflection characteristics of the circular array filter are discussed in detail. The parameters that influence the reflection characteristics and their effect mechanisms are demonstrated. The critical coupling phenomenon and its condition are revealed. We also show that the existence of loss in the rings can suppress split peaks and subsequently flatten the reflection spectrum to the whole pass band. Our work illuminates the application potential of a circular array of an odd number of microring resonators as an integrated photonics reflection filter.     

基于微环谐振器阵列与马赫-曾德尔干涉仪的反射型滤波器性能分析

理论分析了一种将微环谐振器阵列与马赫-曾德尔干涉仪(MZI)相结合实现的反射型滤波器结构。将此结构类比为两类四端口网络级联模型,利用传输矩阵法推导出其通用函数形式,并给出单环及三环结构下的能量反射系数具体公式。通过传输函数矩阵模拟计算了取不同耦合系数值情况下的反射谱形变化,给出了原因分析及讨论。并模拟了引入传输损耗对三环结构谐振峰反射率的影响。数值结果表明:适当选取直波导与微型环以及微型环间耦合系数幅值时,此结构能够作为反射型滤波器件应用于密集波分复用(DWDM)系统,也可实现激光器反射镜面的功能;由于传输损耗增加而引起的谐振峰反射率下降程度依赖于所选取的耦合系数值。     

Performance Investigation of Photonic Crystal-Based Microring Resonator for Optical Signal Processing

Abstract

A detailed theoretical analysis is presented to characterize wave propagation at 1,550 nm inside a glass (SiO₂) microring resonator implemented using photonic crystal technology. A photonic crystal reflection is used at each microring resonator corner to enhance the bending efficiency. The characteristics of both photonic crystal beam splitter and microring resonator bending losses are analyzed and investigated using both effective refractive index and finite difference time domain methods. Analytical expressions are also derived to describe the field enhancement inside the microring resonator, the transfer function of the microring resonator, and the main parameters characterizing the resonator such as resonator band width and quality factor. The analysis is also extended to characterize a drop filter implemented using photonic crystal-based microring resonator. The results indicate clearly that the effective refractive index method can give accurate results if one starts the calculations with finite difference time domain-estimated beam splitter parameters. Further, bending efficiency as high as 99% can be obtained using a ten-post layer photonic crystal mirror at each microring resonator corner.     

Optical stack filters using parallel fuzzy logic

Stack filters are more general and robust nonlinear filters than median filter, which possess threshold decomposition and stacking properties. Stack filters can be carried out one step using optical parallel fuzzy logic technique instead of three steps in threshold decomposition. All window, width 3 stack filters but two trivial stack filters are expressed in unified expression with coefficiencies to choose desired stack filter, so they are realized by an optical approach, window 3×3 separable stack filters can be realized by cascading the window width 3 stack filters. Window width 5 stack filters can be realized using the same method.     

一种热光可调谐级联微环滤波器的理论分析

根据Vernier效应可大幅度提高滤波器自由光谱范围和调谐范围,设计了一种热光可调谐级联微环滤波器. 利用传输矩阵方法和有限元方法从理论上计算了对于第一级微环半径为48 μm,第二级半径为50 μm的级联微环滤波器的自由光谱范围和调谐范围可以达到75.6 nm,而功耗仅为103.1 mW,这是目前为止我们 所知的基于微环谐振腔的硅基热光可调谐滤波器中最大的自由光谱范围和在如此低功耗下最大的调谐范围. 利用有限元方法,还计算了半径为50 μm微环的热光调谐响应时间,上升沿时间为3.5 μs,下降沿时间仅为0.8 μs.     

Analysis of a 1×32 polymer microring resonant wavelength de-multi/multiplexer assistant with interleave filter

A new 1×32 wavelength de-multi/multiplexer utilizing the microring resonator and interleave filter is proposed in this paper. A novel formula of transfer functions is presented, the parameters of microring are optimized, and the transmission characteristics of the system are analyzed. The channel spacing of the presented device is 0.4 nm. The analytical result shows that the crosstalk between adjacent channels can be reduced greatly and the filter response of the device can be improved by using the interleave filter. A bandwidth (3 dB) of 0.21 nm, an insertion loss less than 1.1 dB, and crosstalk below −32 dB were obtained for the optimized device. A method for compensating the manufacturing tolerances is discussed.     

Backscattering in silicon microring resonators: a quantitative analysis

Silicon microring resonators very often exhibit resonance splitting due to backscattering. This effect is hard to quantitatively and predicatively model. This paper presents a behavioral circuit model for microrings that quantitatively explains the wide variations in resonance splitting observed in experiments. The model is based on an in‐depth analysis of the contributions to backscattering by both the waveguides and couplers. Backscattering transforms unidirectional microrings into bidirectional circuits by coupling the clockwise and counterclockwise circulating modes. In high‐Q microrings, visible resonance splitting will be induced, but, due to the stochastic nature of backscattering, this splitting is different for each resonance. Our model, based on temporal coupled mode theory, and the associated fitting method, are both accurate and robust, and can also explain asymmetrically split resonances. The cause of asymmetric resonance splitting is identified as the backcoupling in the couplers. This is experimentally confirmed and its dependency on gap and coupling length is further analyzed. Moreover, the wide variation in resonance splitting of one spectrum is analyzed and successfully explained by our circuit model that incorporates most linear parasitic effects in the microring. This analysis uncovers multi‐cavity interference within the microring as an important source of this variation.

     

Experimental investigation on submicron rib waveguide microring/racetrack resonators in silicon-on-insulator

In experiment, characteristics of silicon microring/racetrack resonators in submicron rib waveguides have been systematically investigated. It is demonstrated that only a transverse-electric mode is guided for a ratio of slab height to rib height h/H = 0.5. Thus, these microring/racetrack resonators can only function for quasi-transverse-electric mode, while they get rid of transverse-magnetic polarization. Electron beam lithography and inductively coupled plasma etching were employed and improved to reduce sidewall roughness for low propagation loss and high performance resonators. Then, the effects of waveguide dimensions, coupling region design, waveguide roughness, and oxide cladding for the resonators have been considered and analyzed.     

Angular and power characteristics of noncollinear acousto-optic tunable filters

The angular and the power characteristics of noncollinear acousto-optic tunable filters are investigated both experimentally and theoretically. The dependencies of the acoustic wave frequency, the bandpass width and the diffraction efficiency of the filter are studied as functions of the angle of incidence of the optical wave and of the acoustic signal power density. These dependencies are illustrated and tested on the basis of a realized such a filter based on tellurium dioxide (TeO₂). A good agreement of theory and experiment is demonstrated, which indicates that the approach used can be effective in designing such devices.     

含有光纤光栅的萨尼亚克环的透射特性分析

详细分析了由光纤光栅和萨尼亚克（Sagnac)环构成的透射滤波器的特性,给出了在均匀光纤光栅的情况下,该滤波器透过率的解析公式,结果表明该滤波器的透射光谱是余弦函数调制后的光纤光栅反射光谱,当光纤光栅是“强”耦合时,该滤波器可以构成多通带滤波器,而当纤光栅为“弱”耦合时,该滤波器可以构成单通带滤波器,这些滤波器可应用于现代光纤通信系统中。     

Microdisk resonator filters made of dielectric-loaded plasmonic waveguides

Microdisk resonator filters, an alternative to microring resonator filters, are studied by means of vectorial three dimensional finite element method simulations. Their performance characteristics are highlighted for different microdisk radii, and compared with those of the respective, footprint-wise, microring filters. We show that microdisk filters are advantageous, as the resonator involved exhibits smaller radiation losses. Extinction ratios as high as 30 dB are possible by properly tuning the gap separating the waveguide from the microdisk in each case. Transmission dips due to higher-radial-order modes that drastically change the transmission picture appear only for very large microdisk radii.     

Modeling of coupling loss in ultra-compact SOI microring resonators

Ultra-compact microring resonators, made of high index contrast (HIC)-silicon on insulator (SOI) materials, have become key optical devices in integrated photonics systems. Both computer simulations and actual experiments have showed that coupling loss was a significant contributor to the total losses in ultra-compact microring resonators. In this paper, a computable model derived from step approximation method was present to theoretically determine the coupling loss. Excellent matching results between the model and literatures were achieved. The proposed model can be applied to evaluate the coupling loss for microring resonators with various geometries and guide the design of low loss optical devices based on ultra-compact microring resonators.     

Group delay and dispersion analysis of compound high order microring resonator all-pass filter

In this paper, we propose a novel compound high order microring resonator all-pass filter employing two cascaded microrings and an assistant microring. It improves the dispersion compensation ability and provides a wide bandwidth. The group delay range is effectively extended, which provides flexibility in choosing the geometrical parameters of the microring for technical convenience and bend loss improvement. The careful design of coupling coefficients can optimize the group delay response. This device is able to provide dispersion compensation to systems such as the high speed dense wavelength division multiplexer (DWDM) optical fiber links.     

薄膜截止滤光片的消偏振设计

薄膜截止滤光片在倾斜入射时不可避免地会产生s和p二个偏振分量的分离,因而在许多应用,特别是光通讯的应用中成为一个棘手的难题。提出了一种新的设计方法,对最常用的45°入射角,实现了长波通和短波通两种截止滤光片的完全消偏振, 在透射率为50%处,其偏振分离分别为0.3 nm和0.1 nm。基本的设计方法是采用宽带法布里珀罗薄膜干涉滤光片中心波长两侧的干涉带作为长波通或短波通截止滤光片的初始膜系,然后经过适当的优化以提高透射带的透射率。宽带干涉滤光片的间隔层常由半波长厚度的高、低折射率混合膜层组成,如2H2L2H或2L2H2L。由于这种设计的截止区和透射带带宽常嫌不足,故提出了展宽截止区和透射带的方法。对一个典型的短波通截止滤光片,在波长1550 nm,截止区和透射带宽均达到了200 nm。这种设计方法不仅简单、性能优良,而且膜厚控制容差较大,故易于制造。     

一种通道数可变的光纤光栅梳状滤波器

利用级联长周期光纤光栅与具有宽带反射功能的啁啾光纤光栅,构成了一种反射型的光纤光栅梳状滤波器.由于光在输出前经过两次干涉滤波作用,所以该梳状滤波器的消光比与透射输出型(即反射前)相比,增加了一倍.而且,通过调节啁啾光纤光栅的反射带宽,可以改变滤波器输出信道的数目.实验中利用弹性梁弯曲的方法,获得了两个可调的光纤光栅梳状滤波器,其信道数可分别在1～5和3～9之间的奇数间调谐(如果改变啁啾光纤光栅的初始中心波长,也可以获得偶数信道间的调谐).     

Optimization and analysis of series-coupled microring resonator arrays

In terms of the coupled mode theory and transfer matrix technique, novel formulas of the amplitude coupling ratios and transfer functions are presented for a series-coupled microring resonator (MRR) array. By using these formulas, parameters are optimized, and transmission characteristics including the transmission spectrum and the insertion loss are analyzed for a SiN/SiO₂ series-coupled MRR array on Si substrate. The box-like spectral response is successfully obtained owing to the proper selection of the amplitude coupling ratio between the channel and the ring, and that between adjacent rings, as well as the number of series-coupled rings.     

One-dimensional coupled cavities photonic crystal filters with tapered Bragg mirrors

The performance of one-dimensional (1D) coupled cavities photonic crystal (PC) filters has been analyzed by finite-difference time-domain (FDTD) simulation. It is shown that the addition of tapered Bragg mirrors at each side of the cavities, to create near-Gaussian field profiles for the cavity modes, results in the prediction of near flat-top passband filters with high out-of-band rejection ratio and near unity transmission. The tapered structures suppress the vertical radiation loss to allow optimization of the number of mirror periods for the best filter response whilst guaranteeing high transmission. A critical coupling condition (k = 2L_out/L_in = 1) for flat-top responses in doubly coupled cavities filters is proposed in the tapered structures. An optimized filter for 100 GHz optical communication system are demonstrated with 1 dB bandwidth of 0.17 nm, roll-off of 0.6 dB/GHz, out-of-band signal rejection of 33 dB and transmission of 95%. Further improvement of roll-off and out-of-band rejection is demonstrated in a triply coupled cavities filter.     

Synthesis algorithm of a multi-channel lattice-form optical delay-line circuit

A novel synthesis algorithm for multi-channel (M?2) lattice form optical delay-line circuit is presented in this paper. This circuit offers multi-port FIR optical filter with delay time of N Δτ (Δτ: unit delay time). Synthesis algorithm is based on division of total transfer matrix into unit blocks. Developed method confirms that 1×M optical delay-line circuit offers same transmission characteristics as 1×M FIR digital filter. Band-pass flat group delay type filter is considered as an example in this paper. It is also confirmed that proposed delay-line circuit can realize 100% power transmittance.     

基于矢量衍射理论的相位型光瞳滤波器设计

根据矢量衍射理论,提出了一种设计纯相位型光瞳滤波器的新方法根据该方法所设计的滤波器主要应用于采用高数值孔径显微物镜的成像系统对点扩散函数中的指数因子进行二次近似处理后,可以得到超分辨参量与滤波器参量的近似关系式以三区相位型滤波器为例,讨论了该近似关系式的有效性给出一个设计实例,根据所要求的超分辨性能要求设计滤波器.模拟结果表明,该滤波器达到了设计要求,最后利用共焦系统点扩散函数的乘积特性,大大减弱了旁瓣的影响.     

Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter

Good performance with small ensemble filters applied to models with many state variables may require ‘localizing’ the impact of an observation to state variables that are ‘close’ to the observation. As a step in developing nearly generic ensemble filter assimilation systems, a method to estimate ‘localization’ functions is presented. Localization is viewed as a means to ameliorate sampling error when small ensembles are used to sample the statistical relation between an observation and a state variable. The impact of spurious sample correlations between an observation and model state variables is estimated using a ‘hierarchical ensemble filter’, where an ensemble of ensemble filters is used to detect sampling error. Hierarchical filters can adapt to a wide array of ensemble sizes and observational error characteristics with only limited heuristic tuning. Hierarchical filters can allow observations to efficiently impact state variables, even when the notion of ‘distance’ between the observation and the state variables cannot be easily defined. For instance, defining the distance between an observation of radar reflectivity from a particular radar and beam angle taken at 1133 GMT and a model temperature variable at 700 hPa 60 km north of the radar beam at 1200 GMT is challenging. The hierarchical filter estimates sampling error from a ‘group’ of ensembles and computes a factor between 0 and 1 to minimize sampling error. An a priori notion of distance is not required. Results are shown in both a low-order model and a simple atmospheric GCM. For low-order models, the hierarchical filter produces ‘localization’ functions that are very similar to those already described in the literature. When observations are more complex or taken at different times from the state specification (in ensemble smoothers for instance), the localization functions become increasingly distinct from those used previously. In the GCM, this complexity reaches a level that suggests that it would be difficult to define efficient localization functions a priori. There is a cost trade-off between running hierarchical filters or running a traditional filter with larger ensemble size. Hierarchical filters can be run for short training periods to develop localization statistics that can be used in a traditional ensemble filter to produce high quality assimilations at reasonable cost, even when the relation between observations and state variables is not well-known a priori. Additional research is needed to determine if it is ever cost-efficient to run hierarchical filters for large data assimilation problems instead of traditional filters with the corresponding total number of ensemble members.