Fourier transforms of slowly converging functions exemplified by electromagnetic wave propagation in evanescent structures

Fourier-type integrals often balk at numerical evaluation with simple quadr ature algorithms. A suitable strategy to cope with slowly decaying oscillat ing integrands over unbounded integration intervals is to subdivide the int erval and extrapolate the sequence of partial sums. This paper, supported b y numerical examples, presents guidelines for the choice of the partition p oints. It will be shown that the first subdivision point must be selected w ith particular care in order to obtain reliable extrapolation results. As a practical example, we explore the propagation of an electromagnetic wavefr ont in a dispersive, evanescent medium, which should-despite recent specula tions on superluminal signal transmission-travel with exactly the speed of light. It appears that the partition extrapolation strategy correctly compu tes the behaviour of the wave, whereas other methods fail to give satisfyin g answers. What is particularly appealing about the proposed method is that it requires only moderate analysis of the integrand and can be composed fr om standard numerical algorithms.