Perfectly matched layers as nonlinear coordinate transforms: A generalized formalization

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

Volumn 22, Issue 9, 2005, Pages 1844-1849

  Hugonin, Jean Paul ^a   Lalanne, Philippe ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; CONVERGENCE OF NUMERICAL METHODS; DEGREES OF FREEDOM (MECHANICS); FOURIER TRANSFORMS; LIGHT ABSORPTION; MAXWELL EQUATIONS; MODAL ANALYSIS; NONLINEAR EQUATIONS; OPTICAL WAVEGUIDES;

CARTESIAN COORDINATES; CONVERGENCE RATE; FOURIER-MODAL METHODS; NONLINEAR COORDINATE TRANSFORMS; PERFECTLY MATCHED LAYERS (PML);

DIFFRACTION;

EID: 25444451623     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.22.001844     Document Type: Article

References (21)

1. J. P. Bérenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
2. Z. Sacks, D. Kingsland, R. Lee, and J. Lee, "A perfectly matched anisotropic absorber for use as an absorbers boundary conditions," IEEE Trans. Antennas Propag. 43, 1460-1463 (1995).
3. W. C. Chew and W. H. Weedon, "A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates," Microwave Opt. Technol. Lett. 7, 599-604 (1994).
4. J. M. Elson and P. Tran, "R-matrix propagator with perfectly matched layers for the study of integral optical components," J. Opt. Soc. Am. A 16, 2983-2989 (1999).
5. P. Bienstman and R. Baets, "Advanced boundary conditions for eigenmode expansion models," Opt. Quantum Electron. 34, 523-540 (2002).
6. E. Silberstein, Ph. Lalanne, J. P. Hugonin, and Q. Cao, "On the use of grating theory in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001).
7. Q. Cao, Ph. Lalanne, and J. P. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguide," J. Opt. Soc. Am. A 19, 335-338 (2002).
8. J. C. Chen and K. Li, "Quartic perfectly matched layers for dielectric waveguides and gratings," Microwave Opt. Technol. Lett. 10, 319-323 (1995).
9. E. A. Marengo, C. M. Rappaport, and E. L. Miller, "Optimum PML ABC conductivity profile in FDTD," IEEE Trans. Magn. 35, 1506-1509 (1999).
10. E. Bahar, "Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrary varying thickness-generalized field transforms," J. Math. Phys. 14, 1024-1029 (1972).
11. D. Maystre, "General study of grating anomalies from electromagnetic surface modes," in Electromagnetic Surface modes, A. D. Boardman, ed. (Wiley, 1982), Chap. 17.
12. K. Knop, "Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves," J. Opt. Soc. Am. 68, 1206-1210 (1978).
13. T. K. Gaylord and M. G. Moharam, "Analysis and application of optical diffraction by gratings," Proc. IEEE 73, 894-936 (1985).
14. F. Montiel and M. Nevibre, "Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity through the R-matrix propagation algorithm," J. Opt. Soc. Am. A 11, 3241-3250 (1994).
15. Ph. Lalanne and E. Silberstein, "Fourier-modal method applied to waveguide computational problems," Opt. Lett. 25, 1092-1094 (2000).
16. J. Tervo, M. Kuittinen, P. Vahimaa, J. Turunen, T. Aalto, P. Heimala, and M. Leppihalme, "Efficient Bragg waveguide-grating analysis by quasi-rigorous approach based on Redheffer's star product," Opt. Commun. 198, 265-272 (2001).
17. 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).
18. P. Lalanne, J. P. Hugonin, and J. M. Gérard, "Electromagnetic study of the Q of pillar microcavities in the small limit diameter," Appl. Phys. Lett. 84, 4726-4728 (2004).
19. C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in photonic crystal microcavities," Opt. Express 13, 245-255 (2005).
20. C. Sauvan, P. Lalanne, J. C. Rodier, J. P. Hugonin, and A. Talneau, "Accurate modeling of line-defect photonic crystal waveguides," IEEE Photonics Technol. Lett. 15, 1243-1245 (2003).
21. J. P. Hugonin, P. Lalanne, I. Del Villar, and I. R. Matias, "Fourier modal methods for modeling optical dielectric waveguides," Opt. Quantum Electron. 37, 107-119 (2005).