title: Vertical mode expansion method for numerical modeling of biperiodic structures.
abstract: 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 this paper, two VMEM variants are presented for biperiodic structures with cylindrical objects of circular or general cross sections. Cylindrical wave expansions and boundary integral equations are used to handle the 2D Helmholtz equations that appear in the vertical mode expansion process. A number of techniques are introduced to overcome some difficulties associated with the periodicity. The method is relatively simple to implement and highly competitive in terms of efficiency and accuracy.
authors.forename: Hualiang
authors.initials: H
authors.lastname: Shi
authors.forename: Xun
authors.initials: X
authors.lastname: Lu
authors.forename: Ya Yan
authors.initials: YY
authors.lastname: Lu