Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

[1]  Beam propagation method using a [(p- 1)/ p] Padé approximant of the propagator. , 2002, Optics letters.

[2]  D. Yevick,et al.  The application of complex Pade approximants to vector field propagation , 2000, IEEE Photonics Technology Letters.

[3]  Luca Vincetti,et al.  Finite-element full-vectorial propagation analysis for three-dimensional z-varying optical waveguides , 1998 .

[4]  E. E. Kriezis,et al.  A three-dimensional full vectorial beam propagation method for z-dependent structures , 1997 .

[5]  Antonio-Daniele Capobianco,et al.  Noniterative vectorial beam propagation method with a smoothing digital filter , 1996 .

[6]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[7]  Propagation of nonparaxial beams with a modified Arnoldi method. , 2001, Optics letters.

[8]  Hugo Hoekstra,et al.  On beam propagation methods for modelling in integrated optics , 1997 .

[9]  Junji Yamauchi,et al.  Full-vectorial beam-propagation method based on the McKee-Mitchell scheme with improved finite-difference formulas , 1998 .

[10]  R. P. Ratowsky,et al.  Accurate numerical solution of the Helmholtz equation by iterative Lanczos reduction. , 1991, Optics letters.

[11]  G. R. Hadley,et al.  Wide-angle beam propagation using Pade approximant operators. , 1992, Optics letters.

[12]  Wei-Ping Huang,et al.  Simulation of three-dimensional optical waveguides by a full-vector beam propagation method , 1993 .

[13]  J R Taylor,et al.  Copropagating and counterpropagating pumps in second-order- pumped discrete fiber Raman amplifiers. , 2002, Optics letters.

[14]  M. Feit,et al.  Light propagation in graded-index optical fibers. , 1978, Applied optics.

[15]  W. Bardyszewski,et al.  Stability issues in vector electric field propagation , 1995, IEEE Photonics Technology Letters.

[16]  D. Yevick,et al.  A guide to electric field propagation techniques for guided-wave optics , 1994 .

[17]  R. Scarmozzino,et al.  Numerical techniques for modeling guided-wave photonic devices , 2000, IEEE Journal of Selected Topics in Quantum Electronics.

[18]  Hung-Chun Chang,et al.  Three-dimensional noniterative full-vectorial beam propagation method based on the alternating direction implicit method , 1999 .