Seydou F, Ramahi Omar M, Duraiswami Ramani, Seppänen T
Opt Express. 2006 Nov 13;14(23):11362-71. doi: 10.1364/oe.14.011362.
We develop a numerical algorithm that computes the Green's function of Maxwell equation for a 2D finite-size photonic crystal, composed of rods of arbitrary shape. The method is based on the boundary integral equation, and a Nyström discretization is used for the numerical solution. To provide an exact solution that validates our code we derive multipole expansions for circular cylinders using our integral equation approach. The numerical method performs very well on the test case. We then apply it to crystals of arbitrary shape and discuss the convergence.
我们开发了一种数值算法，用于计算由任意形状的棒组成的二维有限尺寸光子晶体的麦克斯韦方程的格林函数。该方法基于边界积分方程，并使用Nyström离散化进行数值求解。为了提供一个验证我们代码的精确解，我们使用积分方程方法推导了圆柱体的多极展开。该数值方法在测试案例上表现良好。然后我们将其应用于任意形状的晶体并讨论收敛性。
