We apply the method of the Broadband Green's Functions with Low wavenumber extraction (BBGFL) to calculate band diagrams in periodic structures. We consider 2D impenetrable objects placed in a 2D periodic lattice. The low wavenumber extraction is applied to the 2D periodic Green's function for the lattice which is used to formulate the surface integral equation. The low wavenumber extraction accelerates the convergence of the Floquet modes expansion. Using the BBGFL to the surface integral equation and the Method of Moments gives a linear eigenvalue equation that gives the broadband (multi-band) solutions for a given point in the first Brillouin zone. The method only requires the calculation of the periodic Green's function at a single low wavenumber. Numerical results are illustrated to show the computational efficiency and accuracy of the method. Because of the acceleration of convergence, an eigenvalue problem with dimensions 49 plane wave Floquet modes are sufficient to give the multi-band solutions that are in excellent agreement with results of the Korringa Kohn Rostoker (KKR) method. The multiband solutions for the band problem and the complementary band problem are also discussed.
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