Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media

Journal of Computational Physics

Volumn 216, Issue 1, 2006, Pages 391-402

  Borisov, Andrei G ^a   Shabanov, Sergei V ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Fabers polynomial approximation; Global propagation methods; Gratings; Maxwell's equation; Photonics; Time domain algorithms

Indexed keywords

APPROXIMATION ALGORITHMS; DISPERSION (WAVES); ELECTROMAGNETIC FIELDS; ELECTROMAGNETIC WAVES; GALERKIN METHODS; HAMILTONIANS; INITIAL VALUE PROBLEMS; MATHEMATICAL OPERATORS; NONLINEAR EQUATIONS; POLYNOMIAL APPROXIMATION; TIME DOMAIN ANALYSIS; WAVE FUNCTIONS; WAVE PACKETS;

FABER POLYNOMIAL APPROXIMATION; FABER POLYNOMIALS; FUNDAMENTAL SOLUTIONS; GLOBAL PROPAGATION; GLOBAL PROPAGATION METHOD; GRATING; PASSIVE MEDIA; PROPAGATION METHOD; TIME STEP; TIME-DOMAIN ALGORITHM;

MAXWELL EQUATIONS;

EID: 33646150205     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.12.011     Document Type: Article

References (44)

1. Taflove A., and Hagness S.C. Computational Electrodynamics - The Finite-difference Time-domain Method (2000), Artech House, Boston, MA
2. Tseng S.H., Greene J.H., Taflove A., Maitland D., Backman V., and Walsh J. Opt. Lett. 29 (2004) 1393
3. Mishchenko M.I., Videen G., Babenko V.A., Khlebtsov N.G., and Wriedt T. J. Quant. Spectrosc. Radiat. Transfer 88 (2004) 357 and references therein
4. Muinonen K. Waves Random Media 14 (2004) 365
5. Faber G. Math. Ann. 57 (1903) 398
6. Faber G., and Reine J. Angew. Math. 150 (1920) 79
7. Markushevich A.I. Theory of Functions of a Complex Variable (1977), Chelsea, New York
8. Smirnov V.L., and Lebedev N.A. Functions of a Complex Variable: Constructive Theory (1968), MIT, Cambridge
9. Huang Y., Zhu W., Kouri D.J., and Hoffman D.K. Chem. Phys. Lett. 206 (1993) 96
10. Chem. Phys. Lett. 213 (1993) 209E
11. Huang Y., Kouri D.J., and Hoffman D.K. J. Chem. Phys. 101 (1994) 10493
12. Pollard W.T., and Friesner R.A. J. Chem. Phys. 100 (1994) 5054
13. Huishinga W., Pesce L., Kosloff R., and Saalfrank P. J. Chem. Phys. 110 (1999) 5538
14. Tal-Ezer H., and Kosloff R. J. Chem. Phys. 81 (1984) 3967
15. For a review of different propagation schemes for the time-dependent Schrödinger equation see:. Leforestier C., Bisseling R.H., Cerjan C., Feit M.D., Friesner R., Guldberg A., Hammerich A., Jolicard G., Karrlein W., Meyer H.-D., Lipkin N., Roncero O., and Kosloff R. J. Comput. Phys. 94 (1991) 59 and references therein
16. In: Cerjan C. (Ed). Numerical Grid Methods and Their Application to Schrödinger's Equation. NATO ASI Series, Series C: Mathematical and Physical Sciences vol. 412 (1993), Kluwer Academic Publishers, London
17. De Raedt H., Michielsen K., Kole J.S., and Figge M.T. IEEE Trans. Antennas Propagat. 51 (2003) 3155
18. Phys. Rev. E 67 (2003) 056706
19. Borisov A.G., and Shabanov S.V. J. Comput. Phys. 209 (2005) 643
20. Boyd J.P. Chebyshev and Fourier Spectral Methods (1989), Springer-Verlag, New York
21. Kosloff D., and Kosloff R. J. Comput. Phys. 52 (1983) 35
22. Rung A., and Ribbing C.G. Phys. Rev. Lett. 92 (2004) 123901
23. Huang K.C., Bienstman P., Joannopoulos J.D., Nelson K.A., and Fan S. Phys. Rev. Lett. 90 (2003) 196402
24. S.V. Shabanov, Electromagnetic pulse propagation in passive media by path integral methods, a LANL e-preprint, 2003, Available from: .
25. Borisov A.G., and Shabanov S.V. J. Comput. Phys. 199 (2004) 742
26. Kövari T., and Pommerenke Ch. Math. Z. 99 (1967) 193
27. Trefethen L.N. SIAM J. Sci. Stat. Comput. 1 (1980) 82
28. Starke G., and Vagra R.S. Numer. Math. 64 (1993) 213
29. Spijker M.N. Appl. Numer. Math. 13 (1993) 241
30. Ellacott S.W. Math. Comput. 40 (1983) 575
31. Geddes K.O., and Mason J.C. SIAM J. Numer. Anal. 12 (1975) 111
32. Yablonovitch E. Phys. Rev. Lett. 58 (1987) 2059
33. Joannopoulos J.D., Meade R.D., and Winn J.N. Photonic Crystals (1995), Princeton University Press, Princeton, NJ
34. Lezec H.J., Degiron A., Devaux E., Linke R.A., Martin-Moreno L., Garcia-Vidal F.J., and Ebbesen T.W. Science 297 (2002) 820
35. Ebbesen T.W., Lezec H.J., Ghaemi H.F., Thio T., and Wolff P.A. Nature (London) 391 (1998) 667
36. Wood R.W. Phys. Rev. 48 (1935) 928
37. Magnusson R., and Wang S.S. Appl. Phys. Lett. 61 (1992) 1022
38. Peng S., and Morris G.M. Opt. Lett. 21 (1996) 549
39. Peter T., Bräuer R., and Bryngdahl O. Opt. Commun. 139 (1997) 177
40. Koshino K. Phys. Rev. B 67 (2003) 165213
41. Pilozzi L., D'Andrea A., and Del Sole R. Phys. Rev. B 54 (1996) 10763
42. Borisov A.G., García de Abajo F.J., and Shabanov S.V. Phys. Rev. B 71 (2005) 075408
43. Chen L.-S., Kuo C.-H., and Ye Z. Phys. Rev. E 69 (2004) 066612
44. Chow E., Lin S.Y., Johnson S.G., Villeneuve P.R., Joannopoulos J.D., Wendt J.R., Vawter G.A., Zubrzycki W., Hou H., and Alleman A. Nature 407 (2000) 983