Improved Dirichlet-to-Neumann map method for scattering by circular cylinders on a lattice

Abstract

A simple model for two-dimensional photonic crystal devices consists of a finite number of possibly different circular cylinders centered on lattice points of a square or triangular lattice and surrounded by a homogeneous or layered background medium. The Dirichlet-to-Neumann (DtN) map method is a special method for analyzing the scattering of an incident wave by such a structure. It is more efficient than existing numerical or semianalytic methods, such as the finite element method and the multipole method, since it takes advantage of the underlying lattice structure and the simple geometry of the unit cells. The DtN map of a unit cell is a relation between a wave field component and its normal derivative on the cell boundary, and it can be used to avoid further computation inside the unit cell. In this paper, an improved DtN map method is developed by constructing special DtN maps for boundary and corner unit cells using the method of fictitious sources.

Efficient Near-Field Analysis of the Electromagnetic Scattering Based on the Dirichlet-to-Neumann Map

“…An extension to the multiple scattering problems is also provided in [20]. The treatment of periodic structures, as those arising from arrays of conductors or Photonic Crystals, can be found in [21][22][23][24], based on the use of a semi-analytical DtN. A DtN-related approach can also be found in modeling atomic and molecular physics [25].…”

Modeling of a structural coloration of a photonic-crystal fiber

“…At present, various methods have been proposed of calculation of optical fields scattered by systems of parallel cylinders that possess [4][5][6][7][8][9] or, in a more general case, do not possess [10][11][12] circular symmetry. These methods can be applied in situations when cylinders either are surrounded by an infinite homogeneous medium [4,7,[10][11][12], or are embedded into a semi-infinite substrate [9], or are located inside of a plane-parallel layer with a finite thickness [5,6,8]. However, they are inefficient in solving this problem, since they are incapable of taking into account the reflection of light from a closed outer boundary of the PCF.…”