A full vectorial generalized discontinuous Galerkin beam propagation method (GDG-BPM) for nonsmooth electromagnetic fields in waveguides

Journal of Computational Physics

Volumn 227, Issue 15, 2008, Pages 7178-7191

  Fan, Kai ^a   Cai, Wei ^a   Ji, Xia ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Beam propagation method; Dirac source; Discontinuous Galerkin method; Inhomogeneous optical waveguide; Schr dinger equation

Indexed keywords

CRACK PROPAGATION; ELECTROMAGNETIC FIELDS; GALERKIN METHODS; INTERFACES (MATERIALS); LIGHT PROPAGATION; NUMERICAL METHODS; OPTICAL FIBERS; OPTICAL WAVEGUIDES;

BEAM-PROPAGATION METHODS; DIRAC Δ SOURCE; DISCONTINOUS GALERKIN METHODS; DISCONTINUOUS GALERKIN; HELMHOLTZ'S EQUATIONS; INHOMOGENEOUS OPTICAL WAVEGUIDES; MATERIAL INTERFACES; NON-SMOOTH SOLUTIONS; PARAXIAL APPROXIMATIONS; SCHRÖDINGE EQUATION;

BEAM PROPAGATION METHOD;

EID: 45449095174     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.03.044     Document Type: Article

References (16)

1. Feit M.D., and Fleck Jr. J.A. Light propagation in graded-index optical fibers. Appl. Opt. 17 24 (1978) 3990-3998
2. Feit M.D., and Fleck Jr. J.A. Computation of mode properties in optical fiber waveguide by a propagating beam method. Appl. Opt. 19 7 (1980) 1154-1163
3. Fan K., Cai W., and Ji X. A generalized discontinuous Galerkin method (GDG) for Schrödinger equations with nonsmooth solutions. J. Comput. Phys. 227 (2008) 2387-2410
4. Tsuji Y., Koshiba M., and Takimoto N. Finite element beam propagation method for anisotropic optical waveguide. J. Lightwave Technol. 17 April (1999) 723-828
5. Thylen L., and Yevick D. Beam propagation method in anisotropic media. Appl. Opt. 21 August (1982) 2751-2754
6. Xu C.L., Huang W.P., Chrostowski J., and Chaudhuri S.K. A full-vectorial beam propagation method for anisotropic waveguide. J. Lightwave Technol. 12 November (1994) 1926-1931
7. Snyder A.W., and Love J. Optical Waveguide Theory. first ed. (1983), Springer
8. Gelfand I.M., and Vilenkin N.Y. Generalized Functions (1977), Academic Press
9. Baker G.A. Finite element methods for elliptic equations using nonconforming elements. Math. Comput. 31 (1977) 45-59
10. Wheeler M.F. An elliptic collocation finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152-161
11. Arnold D.N. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal. 19 (1982) 742-760
12. Arnold D., Brezzi F., Cockburn B., and Marini L.D. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39 5 (2002) 1749-1779
13. Funaro D., and Gottlieb D. A new method of imposing boundary conditions for hyperbolic equations. Math. Comput. 51 184 (1988) 599-613
14. Hesthaven J.S., and Gottlieb D. A stable penalty method for the compressible Navier-Stokes equations. I. Open boundary conditions. SIAM J. Sci. Comput. 17 3 (1996) 579-612
15. Cockburn B., and Shu C.-W. The local discontinuous Galerkin method for time-dependent convection-diffusion systems. SIAM J. Numer. Anal. 35 (1998) 2440-2463
16. Okamoto K. Fundamentals of Optical Waveguides (2006), Academic Press