Improving the Beam Propagation Method for TM Polarization

The beam propagation method (BPM) has been widely used in numerical simulations of optical waveguides that vary slowly in the propagation direction. However, when BPM is used over a large propagation distance, a significant amplitude error in the coefficient of the leading propagating mode can be observed. Energy conserving corrections and the single scatter approximation have been used to improve the accuracy of the BPM.

[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]  C. Vassallo,et al.  Difficulty with vectorial BPM , 1997 .

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

[5]  Michael D. Collins,et al.  An energy‐conserving parabolic equation for elastic media , 1993 .

[6]  J. Yamauchi,et al.  Norm-conserving finite-difference beam-propagation method for TM wave analysis in step-index optical waveguides , 2000, Journal of Lightwave Technology.

[7]  L. Poladian,et al.  Unification of TE and TM beam propagation algorithms , 1998, IEEE Photonics Technology Letters.

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

[9]  H. Bremmer,et al.  The W.K.B. approximation as the first term of a geometric-optical series , 1951 .

[10]  Ya Yan Lu,et al.  A complex coefficient rational approximation of 1+x , 1998 .

[11]  Oleg A. Godin,et al.  Reciprocity and energy conservation within the parabolic approximation , 1999 .

[12]  A Bidirectional Beam Propagation Method for Periodic Waveguides , 2001 .

[13]  Ya Yan Lu,et al.  A single scatter improvement for beam propagation methods , 2002, IEEE Photonics Technology Letters.

[14]  M. D. Collins.  A split‐step Padé solution for the parabolic equation method , 1993 .

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

[16]  Gijsbertus J.M. Krijnen,et al.  A comparison between different propagative schemes for the simulation of tapered step index slab waveguides , 1996 .

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

[18]  Gary H. Brooke,et al.  Rational square-root approximations for parabolic equation algorithms , 1997 .

[19]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .