The finite-difference vector beam propagation method: analysis and assessment

The newly developed finite-difference vector beam propagation method (FD-VBPM) is analyzed and assessed for application to two-dimensional waveguide structures. The general formulations for the FD-VBPM are derived from the vector wave equations for the electric fields. The stability criteria, the numerical dissipation, and the dispersion of the finite-difference schemes are analyzed by applying the von Neumann method. Important issues regarding the implementation, such as the choice of reference refractive index, the application of numerical boundary conditions, and the use of numerical solution schemes, are discussed. The FD-VBPM is assessed by calculating the attenuation coefficients and the percentage errors of the propagation constants of the TE and TM modes of a step-index slab waveguide. Several salient features of the FD-VBPM are illustrated. >

[1]  J. M. Arnold,et al.  Beam propagation method and geometrical optics , 1988 .

[2]  J V Moloney,et al.  Beam-propagation method analysis of a nonlinear directional coupler. , 1986, Optics letters.

[3]  Paul Lagasse,et al.  Loss calculation and design of arbitrarily curved integrated-optic waveguides , 1983 .

[4]  N. Dagli,et al.  Explicit finite difference beam propagation method: application to semiconductor rib waveguide Y-junction analysis , 1990 .

[5]  Youngchul Chung,et al.  An assessment of finite difference beam propagation method , 1990 .

[6]  B. Hermansson,et al.  Efficient beam propagation techniques , 1990 .

[7]  Paul Lagasse,et al.  Beam-propagation method: analysis and assessment , 1981 .

[8]  L. Thylen,et al.  A beam propagation method analysis of active and passive waveguide crossings , 1985, Journal of Lightwave Technology.

[9]  David Yevick,et al.  New formulations of the matrix beam propagation method: application to rib waveguides , 1989 .

[10]  Lars Thylén,et al.  Analysis of gratings by the beam-propagation method , 1982 .

[11]  B. Hermansson,et al.  The unitarity of split-operator finite difference and finite-element methods: Applications to longitudinally varying semiconductor rib waveguides , 1990 .

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

[13]  G. R. Hadley,et al.  Transparent boundary condition for beam propagation. , 1991, Optics letters.

[14]  Paul Lagasse,et al.  Application of propagating beam methods to electromagnetic and acoustic wave propagation problems: A review , 1987 .

[15]  R. Osgood,et al.  Comparison of finite-difference and Fourier-transform solutions of the parabolic wave equation with emphasis on integrated-optics applications , 1991 .

[16]  M. Feit,et al.  Computation of mode properties in optical fiber waveguides by a propagating beam method. , 1980, Applied optics.

[17]  C.L. Xu,et al.  A finite-difference vector beam propagation method for three-dimensional waveguide structures , 1992, IEEE Photonics Technology Letters.

[18]  P. Danielsen,et al.  Two-dimensional propagating beam analysis of an electrooptic waveguide modulator , 1984 .

[19]  Wei-Ping Huang,et al.  A vector beam propagation method for guided-wave optics , 1991 .