An Efficient Method for Band Structure Calculations in 2D Photonic Crystals

Journal of Computational Physics

Volumn 149, Issue 2, 1999, Pages 363-376

  Dobson, David C ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAND STRUCTURE; ITERATIVE METHODS; NUMERICAL METHODS; PHOTONIC CRYSTALS;

2-D PHOTONIC CRYSTALS; BAND STRUCTURE CALCULATION; DIELECTRIC PHOTONIC CRYSTALS; FINITE-ELEMENT DISCRETIZATION; ITERATION ALGORITHMS; SUBSPACE ITERATIONS;

CRYSTAL STRUCTURE;

EID: 0000060612     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.6157     Document Type: Article

References (16)

1. W. Axmann and P. Kuchment, A finite element method for computing spectra of photonic and acoustic band-gap materials. I. Scalar case, preprint, 1998.
2. C. M. Bowden, J. P. Dowling, and H. O. Everitt, editors, Development and applications of materials exhibiting photonic band gaps, J. Opt. Soc. Amer. B 10(2), (1993).
3. J. H. Bramble, A. V. Knyazev, and J. E. Pasciak, A subspace preconditioning algorithm for eigenvector/eigenvalue computation, Adv. Comput. Math. 6, 159 (1996).
4. P. G. Ciarlet, The Finite Element Method for Elliptic Problems (Elsevier North-Holland, Amsterdam, 1978).
5. S. J. Cox and D. C. Dobson, Maximizing band gaps in two-dimensional photonic crystals, SIAM J. Appl. Math., in press.
6. E. G. D'yakonov and M. Yu. Orekhov, Minimization of the computational labor in determining the first eigenvalues of differential operators, Math. Notes 27, 382 (1980).
7. J. M. Elson and P. Tran, Coupled-mode calculation with the R-matrix propagator for the dispersion of surface waves on a truncated photonic crystal, Phys. Rev. B 54(3), 1711 (1996).
8. A. Figotin and Y. A. Godin, The computation of spectra of some 2D photonic crystals, J. Comput. Phys. 136, 585 (1997).
9. A. Figotin and P. Kuchment, Band-gap structure of spectra of periodic dielectric and acoustic media. I. Scalar model, SIAM J. Appl. Math. 56, 68 (1996).
10. A. Figotin and P. Kuchment, Band-gap structure of spectra of periodic dielectric and acoustic media. II. Two-dimensional photonic crystals, SIAM J. Appl. Math. 56, 1561 (1996).
11. S. K. Godunov, V. V. Ogneva, and G. P. Prokopov, On the convergence of the modified steepest descent method in application to eigenvalue problems, Trans. Amer. Math. Soc. 2, 105 (1976).
12. J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 1993).
13. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton Univ. Press, Princeton, NJ, 1995).
14. P. Kuchment, Floquet Theory for Partial Differential Equations (Birkhäuser, Basel, 1993).
15. W. V. Petryshyn, On the eigenvalue problem Tu - λSu = 0 with unbounded and non-symmetric operators T and S, Philos. Trans. Roy. Soc. Math. Phys. Sci. 262, 413 (1968).
16. B. A. Samokish, The steepest descent method for an eigenvalue problem with semi-bounded operators, Izv. Vyssh. Uchebn. Zaved. Mat. 5, 105 (1958). [In Russian]