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借助于Marcatili原理,将二维分布的空间四波导分解为波导横截面上两个垂直的五层平板波导的组合,提出适于用分离变量处理的解析模型。利用微扰方法对模型与实际结构的偏差进行了一级修正,给出了传播常量的一级和二级近似表达式、静态模场分布、耦合系数以及传输特性公式,并比较了此方法与有限差分直解波动方程和光束传输两种数值方法的计算结果,探讨了该模型的适用性和优点,并检验了其精确性。应用该理论设计了包含光纤到户交换机常用的1.31μm,1.49μm,1.55μm波长的四波长粗波分复用器件,其插入损耗为0.68 dB,通过进一步优化分离的输出端口和波导结构可以获得更好的性能。
With the help of Marcatili principle, the four-dimensional waveguide with two-dimensional distribution is decomposed into a combination of two vertical five-layer slab waveguides in the cross-section of the waveguide. An analytical model suitable for processing with discrete variables is proposed. First-order and second-order approximate expressions of propagation constants, static mode field distribution, coupling coefficient and transmission characteristic formula are given by using the perturbation method to correct the deviation between the model and the actual structure. Finite difference direct solution wave equation and beam transmission two numerical methods of calculation results, discusses the applicability and advantages of the model, and test the accuracy. The theory is applied to design a four-wavelength coarse wavelength division multiplexing device with the wavelength of 1.31μm, 1.49μm and 1.55μm, which is commonly used in FTTH switches. Its insertion loss is 0.68 dB, which can be obtained by further optimizing the separated output port and waveguide structure Better performance.