Free-space propagation of extreme NA polarized beams using the vector plane wave spectrum method and multi-gigabyte FFTsV

Abstract

Certain lasers can have initial waists only a wavelength or less in size. Therefore, collection optics with extreme numerical apertures (NA) approaching unity are required. Although the design of these macro-optics using geometrical ray-tracing is trivial, determining the exact vectorial field entering them is not. The theory and implementation of Fourier, or plane wave spectrum (PWS), based methods is presented for not only the far-field, but also the near and intermediate. A real-world example is given for which at one point a 12 gigabyte two-dimensional fast Fourier transform (FFT) is required and unexpected polarization effects are observed.