Vertical mode expansion method for numerical modeling of biperiodic structures

Due to the existing nanofabrication techniques, many periodic photonic structures consist of different parts where the material properties depend only on one spatial variable. The vertical mode expansion method (VMEM) is a special computational method for analyzing the scattering of light by structures with this geometric feature. It provides two-dimensional (2D) formulations for the original three-dimensional problem. In th is paper, twoVMEM variants are presented for biperiodic structures with cylindrical objects of circular or ge neral cross sections.Cylindrical wave expansions and boundary integral equations are used to handle the 2D Helmhol tz equationsthat appear in the vertical mode expansion process. A number of techniques are introduced to ove rcome some difficulties associated with the periodicity. The method is relatively simple to implement and highly competitive in terms of efficiency and accuracy.