Approximate analysis of planar photonic bandgap waveguides: a simple semi-analytical method

A semi-analytical approximate method, Vopt, is applied to a planar photonic bandgap (PBG) waveguide and a coupler configuration. The variational process of the Vopt method presents simple effective index analysis of the complex two dimensional (2-D) structures. The Vopt method expresses the refractive index profile of the 2-D structure as two 1-D refractive index profiles and obtains the optimized indices for the two structures iteratively. The Vopt method separates the planar PBG waveguide into an effective multilayer waveguide confining optical field in the lateral direction and a 1-D Bragg reflector that gives characteristic reflection/transmission spectra. The results obtained by the Vopt method show good agreement with the numerical results of the finite difference time domain analysis. The present analysis is helpful in understanding the optical properties of such complex waveguides and can be used as starting approximation for optimizing the structures for various applications.     

Effective index approximations of photonic crystal slabs: a 2-to-1-D assessment

The optical properties of slab-like photonic crystals are often discussed on the basis of effective index (EI) approximations, where a 2-D effective refractive index profile replaces the actual 3-D structure. Our aim is to assess this approximation by analogous steps that reduce finite 2-D waveguide Bragg-gratings (to be seen as sections through 3-D PC slabs and membranes) to 1-D problems, which are tractable by common transfer matrix methods. Application of the EI method is disputable in particular in cases where locally no guided modes are supported, as in the holes of a PC membrane. A variational procedure permits to derive suitable effective permittivities even in these cases. Depending on the structural properties, these values can well turn out to be lower than one, or even be negative. Both the “standard” and the variational procedures are compared with reference data, generated by a rigorous 2-D Helmholtz solver, for a series of example structures.     

半解析对偶棱边元及其在波导不连续性问题中的应用

给出电磁波导的对偶变量变分原理,并采用对偶棱边元对波导的横截面进行半解析离散. 将波导中沿纵向均匀的区段视为子结构,运用基于Riccati方程的精细积分算法求出其出口刚度阵,然后与不均匀区段的常规有限元网格拼装即可对波导不连续性问题进行求解. 半解析对偶棱边元的采用可以在最大程度上对有限元网格进行缩减,并且能够在不增加计算量的前提下任意增加子结构的长度,从而可以将截断求解区域的人工边界设置在距离不均匀区段充分远的地方,极大地减少了近似边界条件所带来的误差. 数值算例证明这种方法具有很高的精度与效率. 关键词： 波导的不连续性 半解析辛分析 对偶棱边元 精细积分     

一种简单精准的渐变折射率分布光波导分析方法

渐变折射率分布的光波导分析对光波导器件的设计和研究至关重要, 近年来已提出了多种分析方法, 然而在简便性或准确性上都存在着不足. 为此, 提出了一种分析渐变折射率分布光波导的方法, 能够结合现有的Wentzel-Kramers-Brillouin近似法和离散化的波动方程, 构建模场分布, 再结合变分运算方程和修正的模式本征方程, 计算出较为精确的有效折射率. 与其他分析方法相比, 该方法较为简单, 而且有一定的精度.     

Fabrication of ultralow-loss Si/SiO(2) waveguides by roughness reduction

We demonstrate 0.8-dB/cm transmission loss for a single-mode, strip Si/SiO(2) waveguide with submicrometer cross-sectional dimensions. We compare the conventional waveguide-fabrication method with two smoothing technologies that we have developed, oxidation smoothing and anisotropic etching. We observe significant reduction of sidewall roughness with our smoothing technologies, which directly results in reduced scattering losses. The rapid increase in the scattering losses as the waveguide dimension is miniaturized, as seen in conventionally fabricated waveguides, is effectively suppressed in the waveguides made with our smoothing technologies. In the oxidation smoothing case, the loss is reduced from 32 dB/cm for the conventional fabrication method to 0.8 dB/cm for the single-mode waveguide width of 0.5 microm . This is to our knowledge the smallest reported loss for a high-index-difference system such as a Si/SiO(2) strip waveguide.     

Variational analysis of propagation characteristics in thermally diffused expanded core fibers

We present a scalar variational method for the analysis of light-propagation characteristics in thermally diffused expanded core (TEC) fibers. The method leads to simple closed-form expressions regarding the mode field diameter, numerical aperture, waveguide dispersion as well as coupling losses produced by radial, longitudinal and angular misalignments. The dependence of coupling losses on the ‘taper ratio’ and normalized frequency is investigated and previous predictions that TEC fibers transmit light more effectively in free space over the order of millimeters, is confirmed. The coupling losses between small core diameter step-index fibers typically used in most erbium-doped fiber amplifiers and TEC-fibers is also considered.     

聚合物Y分支脊形波导的单模条件

有机聚合物光波导近年来成为研究的热点,它为实现下一代的光电集成回路提供了另外一种选择。它所具有的一系列优点如下:(1)与传统的材料相比,有机聚合物光波导容易在各种衬底上制作,其制作成本也得以降低,并且使得与有源器件如激光器、调制器、探测器的单片集成成为可能;(2)有机聚合物波导材料的折射率可以进行调整以满足耦合损耗和弯曲损耗的折中选择;(3)此外,有机聚合物的热光系数比SiO₂大一个数量级,而其导热系数却比SiO₂和Si小得多。有机聚合物Y分支是强度调制器和光开关等器件的重要组成。光波导器件在和单模光纤一起使用时要求其实现单模传输,这样可以减少耦合损耗。利用变分有效折射率法计算了聚合物Y分支脊形波导的光场分布。变分有效折射率法是变分法(VM)和有效折射率法(EIM)的结合,它结合了两种方法各自的优点,能够很精确地模拟光场分布情况。利用变分有效折射率法验证了满足单模传输的脊形波导结构参数:芯层厚度为1.5μm,脊高为0.2μm,脊宽为5μm。     

聚合物波导M-Z调制器TM模的泰勒级数展开法研究

根据聚合物脊型波导的结构特点,利用有效折射率法求出其横向折射率分布,将三维传播转化为二维传播,并从标量波动方程出发,在傍轴近似的情况下,采用Crank-Nicholson差分格式,得到了泰勒级数展开法基本计算格式,并对算法进行了适当优化;通过对Mach-Zehnder光波导TM模的模拟,分析了各种参数对损耗的影响。结果表明：泰勒级数展开法具有精度高、稳定性好、算法简单、易于编程等优点,是一种比较理想的光波导数值分析方法,可为聚合物电光调制器的设计制作提供理论参考。     

Lu, Gd codoped KY(WO(4))(2):Yb epitaxial layers: towards integrated optics based on KY(WO(4))(2)

Codoping KY(WO(4))(2):Yb layers with optically inert Lu and Gd ions allows a large increase of the refractive index contrast with respect to KY(WO(4))(2) substrates. This paves the way for the realization of integrated optical circuits based on this very promising material. First riblike waveguide structures have been fabricated and propagation losses below 1 dB/cm have been evaluated. A Y-junction with a splitting ratio close to 1:1 and additional losses of 1.4 dB has also been demonstrated.     

聚合物脊形光波导的变分有效折射率法分析

聚合物脊形光波导是聚合物集成光电子器件的重要构成单元.利用有效折射率法计算聚合物脊形光波导的横向折射率分布及有效折射率,将各区域中的光场分布近似用分段函数表达.基于导模满足的标量波动方程,利用变分法确定变分参量,以求得准确的横向光场分布.对聚合物脊形多模光波导基模和高阶模的色散特性与横向场分布进行分析,研究了波导结构参数对色散特性的影响,计算出TM基模和高阶模的光场分布,得出了聚合物脊形光波导的单模传输条件.研究表明,该方法计算量小、精度高,对聚合物光电子器件中脊形光波导的理论分析与设计优化提供了简单高效的方法.     

Mode matching analysis of the dielectric waveguide 3-D discontinuity problem

In this paper, the dielectric waveguide 3-D discontinuity problem is investigated by the method which combines the multimode network theory with the rigorous mode matching procedure both in the transverse cross section and in the longitudinal direction. Good agreement has been found between the numerical results and the experimental data in the literature, and the effectiveness and accuracy of the present method are justified. Some numerical results are given to establish useful guidelines for the design of dielectric waveguide components in the millimeter and optical wave integrated circuits.     

基于光子晶体波导定向耦合的光子晶体分/合频器

在完整二维光子晶体中引入线缺陷后,就形成了光子晶体波导。将时域有限差分法(FDTD)和平面波法作为光子晶体理论研究的工具。研究结果表明,光子晶体波导之间的耦合遵循普通介质波导耦合的一般规律,有定向耦合的功能;将两个具有不同耦合长度的光子晶体波导定向耦合器顺序集成在一起,可以组成一个三波长的光子晶体分/合频器。     

Analysis of multiple reflections in hybrid photonic crystal multimode interference coupler

In this paper the analysis of multiple reflections in photonic crystal (PhC) multimode interference (MMI) couplers using eigen-mode expansion method is presented. The analysis is conducted on a hybrid PhC structure which consisted of 1-D PhC multimode waveguide sandwiched between 2-D PhC input/output waveguides. In PhC multimode waveguide, where the mechanism of wave confinement is not due to total internal reflection but due to photonic bandgap properties, the reflectivity at 2-D PhC facet wall would be very large for all the guided modes in the waveguide when ever the image formed due to MMI effect does not coincides with the output access waveguide.     

A novel wavelength dispersive device with a dispersive element based on staircase-like straight and parallel arrayed waveguides

We propose a new type of arrayed waveguide grating (AWG) multiplexer/demultiplexer based on modified group refractive index. This device is composed by an array of straight and parallel waveguides of equal length and each waveguide consist of two sections with different width. The length of the two sections are changed from a waveguide to the adjacent one following a linear dependence resulting in a wavelength dispersive waveguide array. An example of the device design for silicon-on-insulator (SOI) platform is provided and numerical simulations have been carried out for various arrayed waveguide parameters. We demonstrate that the group index modification can be used for tailoring device dispersion properties, and that it can also result in new dispersion characteristics predicted numerically not observed in conventional AWGs. Additional advantages are that the demultiplexer does not necessarily require bending waveguide sections as in a conventional AWG (de)multiplexers, and thus yields highly compact devices with potentially very low insertion loss. Channel spacing of 1 nm have been predicted for sub-micron waveguides sizes. In this paper it is also proposed a novel wavefront converter based on waveguide array lens-like element with waveguides broadened sections. Numerical results for different input/output geometries are analized.     

A simple variational analysis of diffused channel waveguides

The variational analysis of Ti:LiNbO₃ strip waveguides is resolved into two related one-dimension problems, which provides a new iterative approach for the calculation of the mode parameters and the propagation constant. The analytical expressions of the local effective index profiles can be obtained from the variational analysis. The parameters of four trial solutions for the fundamental mode in a diffused-channel waveguide have been determined by using the present method. Comparison with results using the effective method shows that these four approximate expressions are accurate enough. It is also shown that this method converges very quickly and is suitable for both diffused channel waveguides and optical waveguides with rectangular cross-section.     

Sound propagation in two-dimensional waveguide with circular wavefront

Sound propagation through a waveguide is generally modeled by the Webster horn equation which assumes a planar pressure wavefront. However, most of the sources are non-planar in nature. In this work, a 1-D model is derived for sound propagation through a 2-D waveguide with circular wavefront. The model is derived from the 2-D Helmholtz equation using the weighted residual method. The model assumes a uniform pressure across the angular coordinate at a given radial distance. A 2-D finite element model is used to validate the results for different waveguide geometries and it shows good agreement.     

掩埋型离子交换玻璃光波导的变分分析

用变分法对离子交换法制备的掺铒光波导的传播特性进行了分析,推导出了适用于掩埋型离子交换玻璃沟道光波导中场分布传播常量的变分表达式,构建了场分布的厄米-高斯型试探解,在两种不同实验条件下,采用变分法确定了试探解中的待定参量,获得光波导中的场分布,利用传播常量的变分公式和已确定的场分布计算得到了传播常量和有效折射率。计算数据表明:导波区域的有效折射率稍稍地大于限制层的折射率,说明离子交换法制备的波导器件是弱波导;高的辅助退火电场强度和适当的退火时间下,所制备的光波导可以支持更多光模式的传输。该方法计算过程简洁、快速,计算结果与实验结果吻合。     

Reflection of a surface mode from a break in a dielectric waveguide

The problem of surface mode reflection from a break in a dielectric waveguide of arbitrary cross section is solved by a variational method. The dependences of the reflection coefficient on the size and cross-sectional shape of the waveguide are examined. Comparisons with results obtained by other methods, including the data calculated for the 2-D problem (a break in a dielectric plate), are presented. P. L. Kapitsa Institute of Physical Problems, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 1004–1018, August, 1997.     

An analysis of the folded waveguide: a compact waveguide launcherfor ICRF heating

Theoretical and experimental investigations of the folded waveguide launcher as proposed for use in the ion-cyclotron range of frequencies (ICRF) heating of tokamak plasmas are presented. Theoretical results include an analysis of the folded waveguide using Ritz's method to obtain various field quantities. The cutoff wavenumbers from this analysis are within 10% of those calculated using an unfolded equivalent rectangular waveguide model. Measurements of cavity resonances for a scale-model ICRF-folded waveguide with a cutoff frequency of 2.4 GHz also agree closely with those calculated using an unfolded equivalent model. An unfolded equivalent waveguide model is used to evaluate the properties of an inductive strip placed in the folded waveguide. Applying variational analyses provides upper and lower bounds to the reflection magnitude |S₁₁| that are in good agreement with measured values. Polarizing plates (which have been proposed to increase the on-axis directivity of the radiated power) are modeled using an unfolded equivalent waveguide. A variational analysis is used to determine an upper-bound value of |S₁₁| in air due to a polarizing plate inside a matched folded waveguide. Measured values are found to be within 3% of the calculated values, with |S₁₁|>0.95 for frequencies between 2.5 and 4.5 GHz     

聚合物电光调制器中M-Z波导TM模分析

M-Z光波导是聚合物电光调制器的重要结构单元。利用有效折射率法计算聚合物脊形波导的横向折射率分布，将三维光波场传播简化为二维传播。从导模满足的标量波动方程出发，结合透明边界条件，采用Crank-Nicholson差分格式，得出有限差分束传播法的基本计算格式。通过对M Z型波导结构中TM模的传播及损耗特性进行理论分析，系统地研究了脊宽、分支角等结构参数对损耗的影响。研究表明，有效折射率法与二维有限差分束传播法的结合可以较好地解决脊形M Z波导的设计问题。该方法具有精度高、计算量小及效率高等优点，为聚合物电光调制器的制备提供了理论依据。