Gap-edge Asymptotics of defect modes in 2D Photonic Crystals

doi:10.1364/OE.15.004753

Gap-edge Asymptotics of defect modes in 2D Photonic Crystals

K. B. Dossou, R. C. McPhedran, L. C. Botten, A. A. Asatryan, and C. M. de Sterke »View Author Affiliations

Optics Express, Vol. 15, Issue 8, pp. 4753-4762 (2007)
http://dx.doi.org/10.1364/OE.15.004753

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Abstract

We consider defect modes created in complete gaps of 2D photonic crystals by perturbing the dielectric constant in some region. We study their evolution from a band edge with increasing perturbation using an asymptotic method that approximates the Green function by its dominant component which is associated with the bulk mode at the band edge. From this, we derive a simple exponential law which links the frequency difference between the defect mode and the band edge to the relative change in the electric energy. We present numerical results which demonstrate the accuracy of the exponential law, for TE and TM polarizations, hexagonal and square arrays, and in each of the first and second band gaps.

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(050.1970) Diffraction and gratings : Diffractive optics
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Photonic Crystals

History
Original Manuscript: March 6, 2007
Revised Manuscript: March 30, 2007
Manuscript Accepted: March 30, 2007
Published: April 4, 2007

Citation
K. B. Dossou, R. C. McPhedran, L. C. Botten, A. A. Asatryan, and C. M. de Sterke, "Gap-edge Asymptotics of defect modes in 2D Photonic Crystals," Opt. Express 15, 4753-4762 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4753

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References

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, Princeton, 1995).
M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, "Anomalous dispersion relations by symmetry breaking in axially uniform waveguides," Phys. Rev. Lett. 92, 063903 (2004). [CrossRef] [PubMed]
A. Figotin and I. Vitebskiy, "Slow light in photonic crystals," Waves Random Complex Media 16, 293-382 (2006). [CrossRef]
E. N. Economou, Green’s functions in quantum physics, 2nd ed. (Springer-Verlag, Berlin, 1983).
R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, "Density of states functions for photonic crystals," Phys. Rev. E 69, 016609 (2004). [CrossRef]
S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. de Sterke, "Modeling of defect modes in photonic crystals using the fictitious source superposition method," Phys. Rev. E 71, 056606 (2005). [CrossRef]
L. C. Botten, K. B. Dossou, S. Wilcox, R. C. McPhedran, C. M. de Sterke, N. A. Nicorovici, and A. A. Asatryan, "Highly accurate modelling of generalized defect modes in photonic crystals using the FSS method," Int. J. Microwave and Optical Technol. 1, 133-145 (2006).
D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, "Two-dimensional treatment of the level shift and decay rate in photonic crystals," Phys. Rev. E 72, 046605 (2005). [CrossRef]
K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219, 120-143 (2006). [CrossRef]
W. Kohn and J. Luttinger, "Theory of donor states in silicon," Phys. Rev. 98, 915 - 922 (1955). [CrossRef]

Asatryan, A. A.
Botten, L. C.
Byrne, M. A.
de Sterke, C. M.
Dossou, K.
Dossou, K. B.
Figotin, A.
Fink, Y.
Fussell, D. P.
Ibanescu, M.
Joannopoulos, J. D.
Johnson, S. G.
Kohn, W.
Luo, C.
Luttinger, J.
McOrist, J.
McPhedran, R. C.
Nicorovici, N. A.
Poulton, C. G.
Roundy, D.
Vitebskiy, I.
Wilcox, S.

J. Comput. Phys.

K. Dossou, M. A. Byrne, and L. C. Botten, "Finite element computation of grating scattering matrices and application to photonic crystal band calculations," J. Comput. Phys. 219, 120-143 (2006). [CrossRef]

J. Microwave and Optical Technol.

L. C. Botten, K. B. Dossou, S. Wilcox, R. C. McPhedran, C. M. de Sterke, N. A. Nicorovici, and A. A. Asatryan, "Highly accurate modelling of generalized defect modes in photonic crystals using the FSS method," Int. J. Microwave and Optical Technol. 1, 133-145 (2006).

Phys. Rev.

W. Kohn and J. Luttinger, "Theory of donor states in silicon," Phys. Rev. 98, 915 - 922 (1955). [CrossRef]

Phys. Rev. E

D. P. Fussell, R. C. McPhedran, and C. M. de Sterke, "Two-dimensional treatment of the level shift and decay rate in photonic crystals," Phys. Rev. E 72, 046605 (2005). [CrossRef]
R. C. McPhedran, L. C. Botten, J. McOrist, A. A. Asatryan, C. M. de Sterke, and N. A. Nicorovici, "Density of states functions for photonic crystals," Phys. Rev. E 69, 016609 (2004). [CrossRef]
S. Wilcox, L. C. Botten, R. C. McPhedran, C. G. Poulton, and C. M. de Sterke, "Modeling of defect modes in photonic crystals using the fictitious source superposition method," Phys. Rev. E 71, 056606 (2005). [CrossRef]

Phys. Rev. Lett.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, "Anomalous dispersion relations by symmetry breaking in axially uniform waveguides," Phys. Rev. Lett. 92, 063903 (2004). [CrossRef] [PubMed]

Waves Random Complex Media

A. Figotin and I. Vitebskiy, "Slow light in photonic crystals," Waves Random Complex Media 16, 293-382 (2006). [CrossRef]

Other

E. N. Economou, Green’s functions in quantum physics, 2nd ed. (Springer-Verlag, Berlin, 1983).
J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic crystals: molding the flow of light (Princeton University Press, Princeton, 1995).

2006, Figotin, Waves Random Complex Media
2006, Botten, J. Microwave and Optical Technol.
2006, Dossou, J. Comput. Phys.
2005, Fussell, Phys. Rev. E
2005, Wilcox, Phys. Rev. E
2004, Ibanescu, Phys. Rev. Lett.
2004, McPhedran, Phys. Rev. E
1955, Kohn, Phys. Rev.

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