Multipole Perfectly Matched Layer for Finite-Difference Time-Domain electromagnetic modelling

A new multipole perfectly matched layer (PML) formulation is presented. Based on the stretched-coordinate approach the formulation, that utilises a recursive integration concept in its development, introduces a PML stretching function that is created as the sum of any given number of complex- frequency shifted (CFS) constituent poles. Complete formulae for up to a 3-pole formulation, to facilitate its implementation in finite-difference time-domain (FDTD) codes, are developed. The performance of this new multipole formulation compares favourably with existing higher order PMLs that instead utilise stretching functions that are developed as the product of elemen- tary CFS constituent poles. It is argued that the optimisation of the new multipole PML could be more straightforward when compared to that of a higher order PML due to the absence of extra terms generated by the process of multiplication used in the development of the overall PML stretching function in higher order PMLs. The new multipole PML is found to perform very well when compared to standard CFS-PMLs requiring equivalent computational resources.