Improved scalar analysis of integrated optical structures by the mapped galerkin method and arnoldi iteration

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 18, Issue 4, 2001, Pages 966-974

  Forastiere, Michele A ^a   Righini, Giancarlo C ^a  

^a IFAC CNR   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FREQUENCIES; INTEGRATED OPTICS; MATRIX ALGEBRA;

ARNOLDI ITERATION;

OPTICAL WAVEGUIDES;

EID: 0001417352     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.18.000966     Document Type: Article

References (11)

1. C. H. Henry and B. H. Verbeek, “Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis,” J. Lightwave Technol. 7, 308-313 (1989).
2. D. Marcuse, “Solution of the vector wave equation for general dielectric waveguides by the Galerkin method,” IEEE J. Quantum Electron. 28, 459-465 (1992).
3. R. G. Grimes, J. G. Lewis, and H. D. Simon, “A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems,” SIAM J. Matrix Anal. Appl. 15, 228-272 (1994).
4. M. A. Forastiere and G. C. Righini, “Scalar analysis of general dielectric waveguides by Fourier decomposition method and Lanczos reduction,” J. Lightwave Technol. 17, 362-368 (1999).
5. S. J. Hewlett and F. Ladouceur, “Fourier decomposition method applied to mapped infinite domains: Scalar analysis of dielectric waveguides down to modal cutoff,” J. Lightwave Technol. 13, 375-383 (1995).
6. R. W. Freund, M. H. Gutknecht, and N. M. Nachtigal, “An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices,” SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 14, 137-158 (1993).
7. W. Arnoldi, “The principle of minimized iterations in the solution of the matrix eigenvalue problem,” Q. Appl. Math. 9, 17-29 (1951).
8. S. F. Ashby, T. A. Manteuffel, and P. Saylor, “A taxonomy for conjugate gradient methods,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 27, 1542-1568 (1990).
9. R. B. Lehoucq and D. C. Sorensen, “Deflation techniques within an implicitly restarted iteration,” SIAM J. Matrix Anal. Appl. 17, 789-821 (1996).
10. G. R. Hadley and R. E. Smith, “Full-vector waveguide modeling using an iterative finite-difference method with transparent boundary conditions,” J. Lightwave Technol. 13, 465-499 (1999).
11. S. Pelli, M. Brenci, M. Fossi, G. C. Righini, C. Duverger, M. Montagna, R. Rolli, and M. Ferrari, “Optical and spectro-scopic characterization of Er/Yb-activated planar waveguides,” in Rare-Earth-Doped Materials and Devices IV, S. Jiang, ed., Proc. SPIE 3942, 139-145 (2000).