We introduce and develop a new explicit vector beam propagation method, based on the iterated Crank–Nicolson scheme, which is an established numerical method in the area of computational relativity. The proposed approach results in a fast and robust method, characterized by simplicity, efficiency, and versatility. It is free of limitations inherent in implicit beam propagation methods, which are associated with poor convergence or uneconomical use of memory in the solution of large sparse linear systems, and thus it can tackle problems of considerable size and complexity. The advantages offered by this approach are demonstrated by analyzing a multimode interference coupler and a twin-core photonic crystal fiber. A possible wide-angle generalization is also provided.
© 2009 Optical Society of America
Original Manuscript: May 22, 2009
Revised Manuscript: August 19, 2009
Manuscript Accepted: August 21, 2009
Published: September 16, 2009
Traianos V. Yioultsis, Giannis D. Ziogos, and Emmanouil E. Kriezis, "Explicit finite-difference vector beam propagation method based on the iterated Crank-Nicolson scheme," J. Opt. Soc. Am. A 26, 2183-2191 (2009)