A program for calculating photonic band structures and Greenʹs functions using a non-orthogonal FDTD method Original Research Article

We present a program which will calculate either the photonic band structure or the causal Greenʹs function for photons incident on a complex dielectric structure. The method we use is a variant on the finite difference time domain (FDTD) method familiar to the electric engineering community, also known as the order(N) method. However, we employ a new transparent formalism which simplifies the stability analysis and identification of conserved quantities, as well as allowing the use of non-orthogonal coordinate systems without the usual computational overheads. Both the electric and magnetic fields are placed onto a discrete lattice by approximating the spacial and temporal derivatives with finite differences. This results in discrete versions of Maxwellʹs equations which can be used to integrate the fields forwards in time. The time required for a calculation using this method scales linearly with the number of real space points used in the discretisation so the technique is ideally suited to handling systems with large and complicated unit cells.