A (1,1) Padé-operator-based fourth-order accurate finite-difference beam-propagation method is described for the analysis of the transverse-magnetic (TM) wave, with an emphasis on power conservation. As an application, a polarization splitter with a multilayer filter is analyzed. Reflectivities of more than 98% for the transverse-electric wave and transmissivities of more than 94% for the TM wave are obtained over a wide wavelength range of 1.1-1.65 m.Index Terms-Beam-propagation method (BPM), finitedifference time-domain (FDTD) method, multilayer filter, optical waveguide, polarization splitter.