Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides

The generalized Douglas scheme is applied to the time-domain finite difference beam propagation methods (TD-BPMs) in rectangular and cylindrical coordinates. High accuracy and efficiency are demonstrated through the analysis of optical pulse propagation in slab and circularly symmetric waveguides. As an example of a reflection problem, the TD-BPM in cylindrical coordinates is applied to the analysis of a fiber Bragg grating with a sinusoidal index change. Effectiveness of the present scheme is discussed in comparison with the conventional TD-BPM and the finite-difference time-domain method.