Wide-angle, finite-difference beam propagation in oblique coordinate system.
The one-way wave equation in the oblique coordinate system in terms of the square root operator is derived. This equation forms the basis for the development of efficient algorithms using the beam propagation method for the design and optimization of integrated optical devices. In an illustrative example, using the derived one-way wave equation, Anada's very-wide-angle algorithm is generalized to the oblique coordinate system. Since in the oblique coordinate system the direction of propagation can be selected freely to follow the path of the optical beam and to minimize the stair-casing errors, the algorithm is expected to show superior performance, which is confirmed by the results obtained.