On beam propagation methods for modelling in integrated optics

In this paper the main features of the Fourier transform and finite difference beam propagation methods are summarized. Limitations and improvements, related to the paraxial approximation, finite differencing and tilted structures are discussed.

[1]  J. B. Davies,et al.  Finite element/finite difference propagation algorithm for integrated optical device , 1989 .

[2]  Fow-Sen Choa,et al.  Slow-wave finite-difference beam propagation method , 1995 .

[3]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[4]  David Yevick,et al.  Split-step finite difference analysis of rib waveguides , 1989 .

[5]  Sai T. Chu,et al.  A finite-difference time-domain method for the design and analysis of guided-wave optical structures , 1989 .

[6]  D. Yevick,et al.  Split-operator electric field reflection techniques , 1991, IEEE Photonics Technology Letters.

[7]  S. Jungling,et al.  A study and optimization of eigenmode calculations using the imaginary-distance beam-propagation method , 1994 .

[8]  S. Wales,et al.  Factorization and path integration of the Helmholtz equation: Numerical algorithms , 1987 .

[9]  H. M. Masoudi,et al.  Parallel beam propagation method for the analysis of second harmonic generation , 1995, IEEE Photonics Technology Letters.

[10]  Gijsbertus J.M. Krijnen,et al.  Numerical solution method of nonlinear guided modes with a finite difference complex axis beam propagation method , 1995 .

[11]  C. Vassallo.  Wide-angle BPM and power conservation , 1995 .

[12]  H. Unger,et al.  Analysis of vectorial mode fields in optical waveguides by a new finite difference method , 1994 .

[13]  Gijsbertus J.M. Krijnen,et al.  New formulation of the beam propagation method based on the slowly varying envelope approximation , 1993 .

[14]  Gijsbertus J.M. Krijnen,et al.  On the accuracy of the finite difference method for applications in beam propagating techniques , 1992 .

[15]  J. Yamauchi,et al.  Modified finite-difference beam propagation method based on the generalized Douglas scheme for variable coefficients , 1995, IEEE Photonics Technology Letters.

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

[17]  J. R. Morris,et al.  Time-dependent propagation of high energy laser beams through the atmosphere , 1976 .

[18]  A. V. Popov,et al.  Implementation of transparent boundaries for numerical solution of the Schrödinger equation , 1991 .

[19]  Roberto Sorrentino,et al.  An FD-BPM with adaptive mesh for longitudinally varying optical structures , 1995 .

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

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

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

[23]  Hugo E. Hernandez-Figueroa,et al.  Simple nonparaxial beam-propagation method for integrated optics , 1994 .

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

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

[26]  J. C. Chen,et al.  Computation of higher-order waveguide modes by imaginary-distance beam propagation method , 1994 .

[27]  R. M. de Ridder,et al.  Efficient interface conditions for the semi-vectorial finite-difference beam propagation method , 1995 .

[28]  Lars Thylén,et al.  The beam propagation method: an analysis of its applicability , 1983 .

[29]  K. Petermann,et al.  A novel beam propagation method for large refractive index steps and large propagation distance , 1991, IEEE Photonics Technology Letters.

[30]  H.-P. Nolting,et al.  Results of benchmark tests for different numerical BPM algorithms , 1995 .

[31]  Wei-Ping Huang,et al.  The finite-difference vector beam propagation method: analysis and assessment , 1992 .

[32]  G. Sztefka,et al.  Bidirectional eigenmode propagation for large refractive index steps , 1993, IEEE Photonics Technology Letters.

[33]  Akira Hasegawa,et al.  Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion , 1973 .

[34]  Frank Schmidt,et al.  An adaptive approach to the numerical solution of Fresnel's wave equation , 1993 .

[35]  R. Ridder,et al.  Modal fields calculation using the finite difference beam propagation method , 1994 .

[36]  The bidirectional mode expansion method for two-dimensional waveguides: the TM case , 1995 .

[37]  Allen Taflove,et al.  Theory and application of radiation boundary operators , 1988 .

[38]  J. Arnold,et al.  Beam-propagation method ray equation. , 1988, Optics letters.

[39]  S. Chu,et al.  A scalar finite-difference time-domain approach to guided-wave optics , 1991, IEEE Photonics Technology Letters.

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

[41]  Gijsbertus J.M. Krijnen,et al.  Efficient interface conditions for the finite difference beam propagation method , 1992 .

[42]  Dirk Schulz,et al.  Three-dimensional finite difference beam propagation algorithms for photonic devices , 1992 .

[43]  Piero Ravetto,et al.  Finite difference methods for the analysis of integrated optical waveguides , 1990 .

[44]  C. Vassallo,et al.  Highly efficient absorbing boundary conditions for the beam propagation method , 1996 .

[45]  Z. Kam,et al.  Absorption and Scattering of Light by Small Particles , 1998 .