All-frequency effective medium theory of a photonic crystal

doi:10.1364/OE.11.001590

Optics Express

Editor: Michael Duncan
Vol. 11, Iss. 13 — Jun. 30, 2003
pp: 1590–1595

All-frequency effective medium theory of a photonic crystal

Geesche Boedecker and Carsten Henkel »View Author Affiliations

Optics Express, Vol. 11, Issue 13, pp. 1590-1595 (2003)
http://dx.doi.org/10.1364/OE.11.001590

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Abstract
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Abstract

We consider light propagation in a finite photonic crystal. The transmission and reflection from a one-dimensional system are described in an effective medium theory, which reproduces exactly the results of transfer matrix calculations.We derive simple formulas for the reflection from a semi-infinite crystal, the local density of states in absorbing crystals, and discuss defect modes and negative refraction.

[Optical Society of America ]

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(260.2110) Physical optics : Electromagnetic optics
(290.4210) Scattering : Multiple scattering

ToC Category:
Research Papers

History
Original Manuscript: May 28, 2003
Revised Manuscript: June 23, 2003
Published: June 30, 2003

Citation
Geesche Boedecker and Carsten Henkel, "All-frequency effective medium theory of a photonic crystal," Opt. Express 11, 1590-1595 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-13-1590

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References

E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley & Sons, New York, 1998).
M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).
D. W. L. Sprung, H. Wu, and J. Martorell, �??Scattering by a finite periodic potential,�?? Am. J. Phys. 61, 1118 (1993). [CrossRef]
K. Sakoda, K. Ohtaka, and T. Ueta, �??Low-threshold laser oscillation due to group-velocity anomaly peculiar to two-and three-dimensional photonic crystals,�?? Opt. Express 4, 481 (1999), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481</a>. [CrossRef] [PubMed]
D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, �??Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,�?? J. Appl. Phys. 92, 4194 (2002). [CrossRef]
P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, �??Fundamental quantum optics in structured reservoirs,�?? Rep. Prog. Phys. 63, 455 (2000). [CrossRef]
J. M. Bendickson, J. P. Dowling, and M. Scalora, �??Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,�?? Phys. Rev. E 53, 4107 (1996). [CrossRef]
A. Moroz, �??Minima and maxima of the local density of states for one-dimensional periodic systems,�?? Europhys. Lett. 46, 419 (1999). [CrossRef]
M. Wubs and A. Lagendijk, �??Local optical density of states in finite crystals of plane scatterers,�?? Phys. Rev. E 65, 046612 (2002). [CrossRef]
A. Tip, A. Moroz, and J. M. Combes, �??Band structure of absorptive photonic crystals,�?? J. Phys. A: Math. Gen. 33, 6223 (2000). [CrossRef]
J. B. Pendry, �??Photonic band structures,�?? J. Mod. Optics 41, 209 (1994). [CrossRef]
S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, �??Refraction at media with negative refractive index,�?? Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]

Am. J. Phys.

D. W. L. Sprung, H. Wu, and J. Martorell, �??Scattering by a finite periodic potential,�?? Am. J. Phys. 61, 1118 (1993). [CrossRef]

Europhys. Lett.

A. Moroz, �??Minima and maxima of the local density of states for one-dimensional periodic systems,�?? Europhys. Lett. 46, 419 (1999). [CrossRef]

J. Appl. Phys.

D. Y. Jeong, Y. H. Ye, and Q. M. Zhang, �??Effective optical properties associated with wave propagation in photonic crystals of finite length along the propagation direction,�?? J. Appl. Phys. 92, 4194 (2002). [CrossRef]

J. Mod. Optics

J. B. Pendry, �??Photonic band structures,�?? J. Mod. Optics 41, 209 (1994). [CrossRef]

J. Phys. A: Math. Gen.

A. Tip, A. Moroz, and J. M. Combes, �??Band structure of absorptive photonic crystals,�?? J. Phys. A: Math. Gen. 33, 6223 (2000). [CrossRef]

Opt. Express

K. Sakoda, K. Ohtaka, and T. Ueta, �??Low-threshold laser oscillation due to group-velocity anomaly peculiar to two-and three-dimensional photonic crystals,�?? Opt. Express 4, 481 (1999), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-12-481</a>. [CrossRef] [PubMed]

Phys. Rev. E

M. Wubs and A. Lagendijk, �??Local optical density of states in finite crystals of plane scatterers,�?? Phys. Rev. E 65, 046612 (2002). [CrossRef]
J. M. Bendickson, J. P. Dowling, and M. Scalora, �??Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,�?? Phys. Rev. E 53, 4107 (1996). [CrossRef]

Phys. Rev. Lett.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, �??Refraction at media with negative refractive index,�?? Phys. Rev. Lett. 90, 107402 (2003). [CrossRef] [PubMed]

Rep. Prog. Phys.

P. Lambropoulos, G. M. Nikolopoulos, T. R. Nielsen, and S. Bay, �??Fundamental quantum optics in structured reservoirs,�?? Rep. Prog. Phys. 63, 455 (2000). [CrossRef]

Other

E. Merzbacher, Quantum Mechanics, 3rd ed. (Wiley & Sons, New York, 1998).
M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, 1999).

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