In this paper we develop a higher order extraction method to accelerate the convergence in the computation of broadband Green's function for an arbitrary shaped waveguide. This is applied to a homogeneous waveguide of arbitrary shape. The broadband Green's function is based on modal expansion in which the modal fields are frequency independent. The higher order extraction is obtained by using three low wavenumbers for extraction. It gives a modal expansion of Broadband Green's Function with Low Wavenumber Extraction (BBGFL) with 6th order convergence requiring much fewer evanescent modes for convergence. Numerical results are illustrated for homogeneous waveguides for both lossless and lossy dielectric cases. The accuracy of results are validated with direct method of moment (MoM) and HFSS. The BBGFL method is computationally efficient for broadband simulations.
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