全矢量有限元模型及其在光波导中的应用

为了研究光波导和光子晶体光纤的模式特性和传输特性,从矢量波动方程出发,推导出了各向异性介质中场微分方程复数泛函表达式,利用棱边/节点混合元离散了该泛函,加入了各向异性介质匹配层边界条件,得到关于传播常量的广义特征值方程.以矩形波导为例,对各向异性介质匹配层边界条件的吸收特性进行了研究,得到了基模以及几个高阶模的场分布、色散曲线和损耗曲线.结果表明该方法可靠有效.对正六边形晶格光子晶体光纤进行了分析.数据表明：光纤有效折射率随空气孔直径或波长的增大而减小,但与空气孔圈数无关;光纤限制损耗(confinement loss)随波长增大近似成指数增大,而增加空气孔直径或者空气孔圈数则可使之显著降低.     

Full-vector mode solver for bending waveguides based on the finite-difference frequency-domain method in cylindrical coordinate systems

A full-vector mode solver for bending waveguides is described based on the finite-difference frequency-domain method in a local cylindrical coordinate system in which the formulas are directly derived from Maxwell's equations with the help of Yee's mesh. The perfectly matched layer absorbing boundary conditions are incorporated into the present approach in order to effectively demonstrate the leaky nature of bending waveguides. A typical bending rib waveguide is considered as a numerical example to show the effectiveness of the established method.     

Simple high-order Galerkin finite element scheme for the investigation of both guided and leaky modes in anisotropic planar waveguides

A simple high-order Galerkin finite element scheme is formulated to compute both the guided and leaky modes of anisotropic planar waveguides with a diagonal permittivity tensor. Transparent boundary conditions derived from the Sommerfield radiation conditions are used to model the fields at the computational boundaries that allow the radiation into the high index cladding/substrate and decay into the low index cladding/substrate, hence work for both guided and leaky modes. Richardson's extrapolation is employed to achieve high-order accuracy by only using simple first-order-polynomial basis functions. Schemes up to sixth-order of accuracy in the effective index are demonstrated. The resulted non-linear sparse matrix eigenvalue equation is solved using an iterative procedure. The ability of the scheme to compute leaky and guided modes of various structures with isotropic and anisotropic materials, step and graded index profiles is demonstrated; including its applications to investigate the properties of ARROW structures.     

硅基脊型波导器件过渡区损耗及偏振效应

在绝缘层上的硅材料上制作了四种具有不同输入输出结构的星形耦合器并进行了测试,对脊形波导与平板波导相互过渡时过渡区的损耗问题进行了研究和讨论,计算得到在所使用的材料参量下利用锥形结构可以得到1dB左右的最小损耗,这一损耗是由于脊型波导与平板波导间的模式失配造成的。以文献中的实验数据为出发点,分析了脊形波导的偏振问题,并通过对脊型波导器件层厚度、脊高、脊宽进行优化设计,得到了不同偏振模式的有效折射率差仅为10^-5量级的单模脊型波导结构,这样的偏振效应在器件设计中可以忽略。     

梯形截面脊波导的特性分析

提出了用有效折射率法结合转移矩阵理论对梯形截面脊波导进行数值分析的新方法。对梯形截面脊波导中模式传播常数和模式间耦合系数的分析表明,梯形截面脊波导与稍宽的矩形截面脊波导行为相同。这一结论有利于简化梯形截面脊波导的设计,提高实际器件的精度。     

Anti-resonant reflecting photonic crystal waveguide (ARRPCW): modeling and design

In this paper, we apply an antiresonant reflecting layer concept in photonic crystal based waveguides. We have proposed a thin core ARRPCW with linear waveguide carved in it and hence calculated the transmission spectra for various length of waveguide and have shown that the longer waveguides in ARRPCW yields transmission with significantly high quality factor. Comparison of the transmission characteristics of normal conventional planar ARROW-B waveguides & ARRPCW has also been reported. The 2D FDTD numerical modeling reveals improved transmission for various lengths of planar ARROW and ARRPCW with low losses in long waveguides. Transmittance and quality factor are also calculated to confirm superior performance of the proposed design of ARROW based photonic crystal waveguide.     

硅衬底上锗硅合金光波导设计及工艺的优化考虑

报道用射频加热化学气相沉积法制备Ｓｉ／ＧｅＳｉ／Ｓｉ大断面单模脊形光波导中设计和工艺的进一步完善，ＧｅＳｉ合金层中Ｇｅ的含量Ｘ要满足脊形光波导是单模，光波导的数值，孔径接近单模光纤值，脊高小于临界厚度值等，计算表明兼顾上述三项要求应取ｘ＝１～３％，脊的高与宽受大断面及单模的制约。Ｓｉ的晶体结构使脊的二个腐蚀侧壁是斜坡，为此起始脊宽取５～６μｍ为宜；腐蚀液，抛光液的选取人保证脊则壁及波导面端的优良镜     

Leaky modes of channel waveguides with uniaxial anisotropy

An exact numerical method for analyzing the propagation properties of leaky modes of inhomogeneous channel optical waveguides with a complex uniaxial diagonal permittivity tensor is developed. The method is based on solving the system of integro-differential equations formulated with respect to transversal components of the magnetic field and the longitudinal component of the electric field. Some results of investigation of leaky modes of diffused channel waveguides in LiNbO₃ and LiTaO₃ crystals are given.     

Characteristic equations for different ARROW structures

Based on radiation modes and phase relations in different ARROW structures, the characteristic equations are presented that can avoid root searching in the complex plane and find the effective index, loss and field profile easily. This simple model gives an accurate intuitive picture for low loss leaky modes and it can be used to design and optimize the low loss ARROW devices of practical interest.     

用平面映射边界条件的伽辽金法分析耦合脊形光波导

用平面射映边界条件的伽辽金法分析耦合脊形光波导的结果表明，耦合脊形光波导的耦合能力随脊高增加而减小，随波导间距增加呈指数衰减。给出了耦合脊形光波导所承载的偶、奇模电场分布，其结果与采用其它方法得出的结果吻合得较好，可以优化波导光电子器件的结构参数。另外，平面映射边界条件避免了非物理反射，待求矩阵小，计算效率高。     

Numerical algorithm for waveguide and leaky modes determination in multilayer optical waveguides

A new algorithm for waveguide and leaky modes spectrum calculation in multilayer planar waveguides is proposed. The method is of high computational efficiency due to the preliminary search for propagation constants approximation. Numerical efficiency of this algorithm is demonstrated for several waveguide structures. Waveguide and leaky modes propagation constants calculated for these structures using proposed method are in good agreement with previously published results.     

一种分析三维楔脊形光波导与光纤耦合的方法

和直波导的不同在于，三维楔脊形波导中的光场都是不稳定的.分别对波导-光纤耦合、光纤-波导耦合两种情况，将三维楔脊形波导等效为多段短的直波导，利用束传播法同时对三维楔脊形波导内不稳定的入射、反射场，及它们在传播方向上的偏导进行处理，再用自由空间辐射模法计算透射率和反射率.以SOI楔脊形波导和光纤的耦合为例，验证了该方法的可行性. 关键词： 自由空间辐射模法 束传播法 耦合 透射 楔脊形光波导 绝缘体上硅(SOI)     

Waveguide cores containing silicon nanocrystals as active spectral filters for silicon-based photonics

Layers of densely packed luminescent Si nanocrystals embedded in fused silica act as wavelength-specific planar waveguides that filter the wide-band spontaneous emission. The waveguides’ light output consists of two spectrally narrow (∼10 nm), orthogonally polarized, and spatially directed bands. This effect is shown to result from leaky modes of the lossy waveguides. The results have general applicability to lossy, asymmetric waveguides and show the way to produce spectrally narrow emission without the use of optical cavities. PACS 78.67.Bf; 42.79.Gn; 81.07.Bc     

Analysis of ARROWs with thin cores

The paper provides theoretical analysis of planar antiresonant reflecting optical waveguides (ARROWs) with thin cores. It is shown that the appropriate choice of the cladding system parameters enables fabrication of thin-core ARROWs with all desired properties, such as low-loss single-mode operation and high refractive-index sensitivity of ARROW mode attenuation.     

硅光波导的束传播法设计及制备

报道用束传播法模拟设计、指导硅大断面单模脊形光波导的制备工艺，应用傅里叶变换法计算了硅光波导中导模的传播常数，对实际研制成功的ＳＩＭＯＸ及Ｓｉ／ＧｅｘＳｉ１－ｘ／Ｓｉ单模脊形光波导，比较了其性能差异并给予理论解释。     

Dispersion parameters and nonlinear optical properties of silicon nitride rib waveguides

Silicon nitride rib waveguides are numerically studied by use of a full-vectorial mode solver program based on finite difference method. Dispersion parameters, up to the third-order, are computed for waveguides of heights 0.8 μm, 0.9 μm, and 1 μm. Like silicon-on-insulator waveguides, silicon nitride rib waveguides allow us to tailor dispersion parameters at telecom wavelengths. Deeply-etched silicon nitride rib waveguides of height up to 1.5 μm are investigated for correct geometries to achieve polarization independence. The computations lead to a minimum etch depth which can be written as linear function of the waveguide height. Etch-depth and waveguide height dependencies of the nonlinear refractive index coefficient of the silicon nitride are studied. It is shown that third-order optical nonlinearities in silicon nitride rib waveguides can be enhanced by suitable choices of waveguide parameters.     

New method for calculating the spectra and radiation losses of leaky waves in multilayer optical waveguides

The efficiency of a new method for calculating the spectrum and attenuation coefficient of leaky electromagnetic modes is demonstrated with multilayer planar optical waveguides the guiding properties of which are determined by antiresonant reflection from the multilayer cladding (antiresonant reflecting optical waveguides) rather than by total internal reflection from the core-cladding interface as in standard optical waveguides. The new method applies to calculation of both electromagnetic modes in dielectric waveguides and electron quantum states in multibarrier semiconductor heterostructures. The characteristics of multilayer waveguides calculated by the new method are compared with published data obtained from a complex dispersion relation by the transfer matrix method. As an example, the wavelength dependence of the radiation losses for the first TE mode of a planar optical waveguide containing 52 pairs of layers is calculated.     

基于变量变换伽辽金法光波导半矢量分析

基于变量变换伽辽金法(VTGM),建立了半矢量分析光波导本征值问题的数理模型;获得了矩形光波导、脊形光波导的本征模的模场分布及归一化传播常数,计算结果和已发表的结果非常接近.半矢量VTGM采用平面映射边界条件,避免了边界截断,又能反映模场的偏振特性,是一种较为理想的光子器件分析方法.     

Compact wavelength-insensitive fabrication-tolerant silicon-on-insulator beam splitter

A star coupler-based beam splitter for rib waveguides is reported. A design method is presented and applied in the case of silicon-on-insulator rib waveguides. Experimental results are in good agreement with simulations. Excess loss lower than 1 dB is experimentally obtained for star coupler lengths from 0.5 to 1 μm. Output balance is better than 1 dB, which is the measurement accuracy, and broadband transmission is obtained over 90 nm.     

Modeling of Optical Waveguides and Devices by Combination of the Method of Lines and Finite Differences of Second Order Accuracy

Based on generalized transmission line equations a novel impedance/admittance transformation algorithm with finite differences is proposed and substantiated. The algorithm is of second order accuracy. It is combined with the Method of Lines. The algorithm is suitable for eigenmode calculations and for the analysis of optical waveguides and devices including anisotropic materials. The proposed algorithm is verified by numerical results for rib waveguide and azimuthally inhomogeneous fibres.