We adapted a fast Fourier transform-based Beam Propagation Method (FFT-BPM) to
investigate waveguide discontinuities in plasmonic waveguides. The adaptation of the FFT-BPM to
treat transverse magnetic (TM) fields requires the circumvention of two major difficulties: the mixed
derivatives of the magnetic field and waveguide refractive index profile in the TM wave equation and
the step-like index change at the transverse metal-dielectric boundary of the plasmonic guide and the
transverse boundaries of the dielectric waveguide as well. An equivalent-index method is adopted to
transform TM fields to transverse electric (TE) ones, thus enabling the benefit of the full power and
simplicity of the FFT-BPM. Moreover, an appropriate smoothing function is used to approximate
the step-like refractive index profile in the transverse direction. At the junction plane, we used an
accurate combined spatial-spectral reflection operator to calculate the reflected field. To validate
our proposed scheme, we investigated the modal propagation in a silicon waveguide terminated
by air (like a laser facet in two cases: with and without a coating layer). Then we considered a
subwavelength plasmonic waveguide (metal-insulator-metal MIM) butt-coupled with a dielectric
waveguide, where the power transmission efficiency has been calculated and compared with other
numerical methods. The comparison reveals good agreement.