A finite-difference time-domain beam-propagation method (TD-BPM) is proposed, in which the fourth-order accuracy is achieved in both time and space. With the aid of a (2, 2) Pade approximant in the time axis, a time step can be chosen to be ten times as large as that in a (1, 1) Pade approximant corresponding to the Crank-Nicholson scheme. Using the formulation with the boundary condition of a dielectric interface, the present method allows to simulate the TM mode propagation as well as the TE mode with the fourth-order accuracy. To validate the method, the reflected power from a waveguide facet is evaluated for the TE and TM modes. The results agree well with those obtained by the spectral method.
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