Yan Yi, Liu Pai, Zhang Xiaopeng, Luo Yangjun
Opt Express. 2021 Aug 2;29(16):24861-24883. doi: 10.1364/OE.430079.
Photonic crystals can be adopted to control light propagation due to their superior band gap feature. It is well known the band gap feature of photonic crystals depends significantly on the topological design of the lattices, which is rather challenging due to the highly nonlinear objective function and multiple local minima feature of such design problems. To this end, this paper proposed a new band-gap topology optimization framework for photonic crystals considering different electromagnetic wave polarization modes. Based on the material-field series-expansion (MFSE) model and the dielectric permittivity interpolation scheme, the lattice topologies are represented by using a small number of design variables. Then, a sequential Kriging-based optimization algorithm, which shows strong global search capability and requires no sensitivity information, is employed to solve the band gap design problem as a series of sub-optimization problems with adaptive-adjusting design spaces. Numerical examples demonstrated the effectiveness of the proposed gradient-free method to maximize the band gap for transverse magnetic field (TM), transverse electric field (TE), and complete modes. Compared with previously reported designs, the present results exhibit less dependency on the guess of the initial design, larger band gaps and some interesting topology configurations.
由于光子晶体具有优异的带隙特性，因此可用于控制光传播。众所周知，光子晶体的带隙特性很大程度上取决于晶格的拓扑设计，由于此类设计问题具有高度非线性目标函数和多个局部极小值特性，这一设计颇具挑战性。为此，本文提出了一种考虑不同电磁波极化模式的光子晶体带隙拓扑优化新框架。基于材料场级数展开（MFSE）模型和介电常数插值方案，利用少量设计变量来表示晶格拓扑。然后，采用一种基于序列克里金的优化算法，该算法具有强大的全局搜索能力且无需灵敏度信息，将带隙设计问题作为一系列具有自适应调整设计空间的子优化问题来求解。数值算例证明了所提出的无梯度方法对于最大化横向磁场（TM）、横向电场（TE）和全模式的带隙的有效性。与先前报道的设计相比，目前的结果对初始设计猜测的依赖性更小，带隙更大，并且具有一些有趣的拓扑结构。
