New method for nonparaxial beam propagation.

A new method for solving the wave equation is presented that is nonparaxial and can be applied to wide-angle beam propagation. It shows very good stability characteristics in the sense that relatively larger step sizes can be taken. An implementation by use of the collocation method is presented in which only simple matrix multiplications are involved and no numerical matrix diagonalization or inversion is needed. The method is hence faster and is also highly accurate.

[1]  C. Vassallo.  Limitations of the wide-angle beam propagation method in nonuniform systems , 1996 .

[2]  J. Yamauchi,et al.  Improved multistep method for wide-angle beam propagation , 1996, IEEE Photonics Technology Letters.

[3]  Robert Scarmozzino,et al.  Investigation of the Pade approximant-based wide-angle beam propagation method for accurate modeling of waveguiding circuits , 1996 .

[4]  A. Sharma.  Collocation Method for Wave Propagation through Optical Waveguiding Structures , 1995 .

[5]  Anurag Sharma,et al.  Propagation of beams through optical waveguiding structures: comparison of the beam-propagation method and the collocation method , 1993 .

[6]  I. Betty,et al.  The application of complex Pade approximants to reflection at optical waveguide facets , 2000, IEEE Photonics Technology Letters.

[7]  D Yevick,et al.  Forward wide-angle light propagation in semiconductor rib waveguides. , 1990, Optics letters.

[8]  R. P. Ratowsky,et al.  Accurate solution of the Helmholtz equation by Lanczos orthogonalization for media with loss or gain. , 1992, Optics letters.

[9]  C.L. Xu,et al.  A wide-angle vector beam propagation method , 1992, IEEE Photonics Technology Letters.

[10]  Ya Yan Lu,et al.  A new iterative bidirectional beam propagation method , 2002, IEEE Photonics Technology Letters.

[11]  N. Dagli,et al.  A wide angle propagation technique using an explicit finite difference scheme , 1994, IEEE Photonics Technology Letters.

[12]  Jun Shibayama,et al.  Efficient nonuniform schemes for paraxial and wide-angle finite-difference beam propagation methods , 1999 .

[13]  S Banerjee,et al.  Method for propagation of total fields or beams through optical waveguides. , 1989, Optics letters.

[14]  Michael J. Steel,et al.  Complex propagators for evanescent waves in bidirectional beam propagation method , 2000 .

[15]  C. Law,et al.  Discrete Bessel-based Arnoldi method for nonparaxial wave propagation , 2002, IEEE Photonics Technology Letters.

[16]  Masanori Koshiba,et al.  A wide-angle beam propagation method based on a finite element scheme , 1997 .

[17]  Reinhard Maerz,et al.  Results of benchmark tests for different numerical BPM algorithms , 1994, Integrated Optoelectronics.

[18]  G. R. Hadley,et al.  Multistep method for wide-angle beam propagation. , 1992, Optics letters.