In this paper we calculate Green's function of a single point source in a one-dimensional infinite periodic lossless medium. The method is based on Broadband Green's Functions with Low Wavenumber Extractions (BBGFL) that express the Green's functions in terms of band solutions that are wavenumber independent. The converegnce of the band expansions are accelerated by a low wavenumber extraction with the wavenumber chosen at the mid-bandgap. The choice of mid-bandgap means that the extracted low wavenumber Green's function can be calculated with very few number of layers. The broadband Green's functions are illustrated for stopband, passband and close to the bandedge. For the case of passband and close to band edge, a modal method is used with first order and second order pole extractions respectively. The modal terms are extracted and integrated analytically. The calculated solutions of single point source Green's functions are compared with the scattering solutions of multilayers using as many as 200,000 layers for the case of passband and near bandedge. The BBGFL computed solutions are in good agreement with those of scattering solutions for stopband, passband, and close to the bandedge.
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