An Algorithm for Beam Propagation Method in Matrix Form

A new and efficient method for waveguide field calculation is proposed. In the proposed Fourier cosine beam propagation method, both dispersion and waveguide effects for each propagation interval are treated in a matrix form. Such a calculation method converts the conventional point-by-point analysis skill into a matrix-based one. By using the matrix method, the computing time required for calculating the field evolution is much less than that required by using the commonly used finite-difference beam propagation method. Two y-branches with, respectively, a rib-type and a channel-type cross sections are tested. The numerical results demonstrate the efficiency of the proposed method.