Application of Extended Taylor Series based Finite Difference Method in photonics

The Finite Difference Method (FDM) has numerous applications in the modelling and design of photonic devices. One of the main limitations to the accuracy and computational efficiency of FDM comes from the presence of discontinuities in the functions describing the unknown physical quantities, e.g. the normal component of the electric field vector field is discontinuous across a step change in the value of the refractive index. The presentation will focus on introducing the concept of the Extended Taylor Series and its application to an elegant and consistent derivation of the Finite Difference approximations to discontinuous functions. Selected illustrating examples will show the significance of the technique for the numerical modelling in photonics.