Fast interpolation method for field evaluation in a periodic unit cell

In this paper, we present a fast interpolation method (FIM) to compute fields in a unit cell of general periodic problems with periodicities smaller or on the order of the wavelength. The important properties of FIM are that (i) its computational time scales linearly as cN with a very small constant c, (ii) it can handle many periodic problem types for which periodic Green´s function (PGF) are available (i.e. it is kernel independent), (iii) it requires only O(1) PGF evaluations, which can be accomplished with any existing method, and (iv) it can be incorporated into existing integral equation (IE) solvers.