25 September 2007 Fast numerical algorithm for ultrashort THz pulse diffraction
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A numerical method, based on the fast Fourier transform, is proposed that efficiently calculates the 2D (x,y) diffraction pattern formed when an ultrashort pulse of light is incident upon an aperture. Since ultrashort pulses are becoming increasingly important in modern optics from THz generation and spectroscopy to confocal microscopy, a fast numerical technique for calculating typical diffraction patterns is of significant interest. Pulses are not monochromatic but rather have a finite spectral distribution about some central frequency. Under paraxial conditions, the spatial diffraction pattern due to an individual spectral component may be calculated using the Fresnel transform. This is performed for each spectral component giving a spatio-spectral distribution. The diffracted spatio-temporal pulse can then be calculated by performing an inverse Fourier transform (with respect to the temporal frequency) on this spatio-spectral distribution. Numerical implementation raises two questions: (a) for a given distance and temporal frequency what is the minimum number of samples needed to efficiently calculate the corresponding Fresnel diffraction pattern and (b) for a given temporal pulse profile how many spectral components are required to accurately describe the diffraction of the pulse? By examining the distribution of the pulses energy in phase space using Wigner diagrams we identify a simple set of rules for determining these optimal sampling conditions. Then, using these rules we examine the diffraction patterns from both a square and circular aperture. A discussion of the results and potential THz applications follows.
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Damien P. Kelly, Damien P. Kelly, Bryan M. Hennelly, Bryan M. Hennelly, Alexander Grün, Alexander Grün, Juraj Darmo, Juraj Darmo, Karl Unterrainer, Karl Unterrainer, } "Fast numerical algorithm for ultrashort THz pulse diffraction", Proc. SPIE 6697, Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, 66970Q (25 September 2007); doi: 10.1117/12.735531; https://doi.org/10.1117/12.735531

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