The method of broadband Green's functions with low wavenumber extractions (BBGFL) is used to calculate Green's function for inhomogeneous waveguides filled with different dielectrics and with irregular boundaries. To construct the BBGFL modal solutions, we derive governing equations of the linear eigen-matrix problem and orthonormalization condition. In BBGFL, the Green's function is represented in modal expansions with convergence accelerated by higher order low wavenumber extractions. To obtain a linear eigenvalue problem for the modes, we use two BBGFLs of rectangular waveguides with two dielectric wavenumbers. The orthonormalized mode functions are used to construct the Green's function. Current wavenumber derivatives and Green's function wavenumber derivatives are computed by a single low wavenumber MoM impedance matrix. The wavenumber derivatives are used to accelerate the convergence of modal summations to 6th order. Numerical results are illustrated and compared with the direct MoM method of using free space Green's function. Results show accuracies and computation efficiencies for broadband simulations of Green's functions.
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