Efficient evaluation of Sommerfeld integrals for the optical simulation of many scattering particles in planarly layered media

A strategy for the efficient numerical evaluation of Sommerfeld integrals in the context of electromagnetic scattering at particles embedded in a plane parallel layer system is presented. The scheme relies on a lookup table approach in combination with an asymptotic approximation of the Bessel function in order to enable the use of fast Fourier transformation (FFT). The accuracy of the algorithm is enhanced by means of singularity extraction and a novel technique to treat the integrand at small arguments. For short particle distances, this method is accomplished by a slower but more robust direct integration along a deflected contour. As an example we investigate enhanced light extraction from an organic light emitting diode (OLED) by optical scattering particles. The calculations are discussed with respect to accuracy and computing time. By means of the present strategy, an accurate evaluation of the scattered field for several thousand wavelength scale particles can be achieved within a few hours on a conventional workstation computer. © 2016 Optical Society of America

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