阵列波导光栅是最有发展潜力的密集波分复用器件之一。它具有尺寸小、稳定性强、便于批量生产等优点。本论文主要研究阵列波导光栅的设计理论与方法，分析阵列波导光栅的光场传输特性，并探讨器件的加工工艺。本文提出并建立了阵列波导光栅的像差分析模型，丰富与发展了光栅的像差理论，并拓展了阵列波导光栅的结构设计。根据该理论，阵列波导光栅的星形耦合器结构和波导阵列分支都可以根据像差要求自由设计，从而生成各种结构形式的阵列波导光栅。其中一些非罗兰圆结构器件，由于像差很小，可以改善器件的串音、通道均匀性等性能。此外，还提出了迭代的像差计算方法，克服了传统像差理论有限次截断的局限性，利用本方法可以达到任意级次的像差计算精度。根据基尔霍夫衍射理论，利用曲线坐标，在小角度近似条件下，本文将罗兰圆星形耦合器的圆弧表面等价为傅立叶变换透镜的前后焦面，发展了阵列波导光栅的线性系统分析模型，并分析阵列波导光栅的传输特性。利用该模型，不仅获得了器件的基本特性方程，还证实了像差校正思路保证器件性能的正确性。此外，还研究建立了考虑像差因素的改进模型，可以获得更准确的模拟结果。本文提出径向传播柱坐标束传播方法，用于分析阵列波导光栅的星形耦合器。径向传播柱坐标束传播方法可以克服直角坐标束传播方法由于差分方向、设定光束传播方向与波导结构不一致带来的模型误差。径向传播柱坐标束传播方法包括标量、半矢量以及全矢量等三种形式。本文详细分析了束传播方法基本参数对结果的影响。此外，还讨论并模拟了波导设计的一些基本问题，包括模式求解、三维波导的二维等效以及弯曲波导的分析等。采用半矢量有限差分方法，获得二维分布的精确模场。寻求最优的一维模场分布逼近二维模场的投影，以获得与三维结构等效的二维结构，简化光场模拟。最后，本文讨论了阵列波导光栅的设计理论与方法在平面凹光栅研究方面的应用和拓展。在像差分析和标量衍射模拟时，可以认为平面凹光栅是阵列波导光栅的一个特例。去掉阵列波导光栅的波导阵列，将结构对叠就可以得到一个平面凹光栅。在光场矢量模拟方面，由于平面凹光栅是反射结构，分析阵列波导光栅的单向束传播方法不再适用。本文发展了相应的双向束传播方法。
Arrayed Waveguide Grating (AWG) is one of the most promising (de)multiplexers for Dense Wavelength Division Multiplexing (DWDM) system. AWG takes such advantages as small size, high stability and volume production. In this dissertation the theory and design of AWG are studied, the transmission characteristics are analyzed and the fabrication technology are also discussed.The aberration model for AWG is proposed and built, which enriches the aberration theory for grating and generalizes the geometry of AWG. In the proposed theory, the star couplers and arrayed waveguides of AWG are free parameters to produce various AWG structures according to aberration requirement. For some non-Rowland structures the crosstalk and channel uniformity of AWG can be improved because of their low aberration. Moreover, an iterative method for aberration coefficients is proposed to reduce the truncation error. With this method, the aberration can be evaluated up to any desired order.Based on the Kirchhoff diffraction theory, under the curved co-ordinates and small angle condition, the two arc surfaces of a Rowland-type star coupler are mapped to be the back and front focal planes of a Fourier transform lens. Straightforward, the linear system model of AWG is set up to analyze its transmission characteristics. With the model, not only some basic character equations of AWG are obtained, but the method to improve performance by aberration correction is proved. Furthermore, an improved model considering aberration is built for more accurate simulation.A radial Beam Propagation Method (BPM) in the cylindrical co-ordinate system is put forward to model the star couplers of AWG. The cylindrical BPM avoids the model error inherited in the rectangular BPM due to the discretion error and the departure of the assumed beam propagation direction from waveguide direction. There are scalar, semi-vector and full-vector cylindrical BPMs. The influence of the basic BPM parameters are analyzed in detail.In addition, some basic issues for modeling waveguides, including mode solver, 3D-to-2D equivalence, and bent analysis etc., are also discussed and simulated. The exact 2D mode distribution is obtained by utilizing the finite difference semi-vector method. Then the projected 1D field is approached by the mode of an optimized slab. Therefore, the question of 3D structure is approximated by a 2D one to reduce modeling complexity. Finally, the theory and design method of AWG are applied and generalized to model Planar Concave Grating (PCG). For aberration analysis and scalar diffraction simulation, PCG can be considered to be a simplified AWG without arrayed waveguides. However, In the case of vector simulation, the one-way BPM for AWG is no longer applicable. Thus a bi-directional cylindrical radial BPM is developed.
