Abstract
We study the long-wavelength limit for an arbitrary photonic crystal (PC) of 2D periodicity. Light propagation is not restricted to the plane of periodicity. We proved that 2D PC’s are uni-axial or bi-axial and derived compact, explicit formulas for the effective (“principal”) dielectric constants; these are plotted for silicon - air composites. This could facilitate the custom design of optical components for diverse spectral regions and applications. Our method of “homogenization” is not limited to optical properties, but is also valid for electrostatics, magnetostatics, DC conductivity, thermal conductivity, etc. Thus our results are applicable to the Physics of Inhomogeneous Media where exact, compact formulas are scarce. Our numerical method yields results with very high accuracy, even for very large dielectric contrasts and filling fractions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
Joannopoulos, J., Meade, R. and Winn, J., Photonic Crystals (Princeton Press, Princeton, NJ, 1995).
Hui, P.M. and Johnson, F., Solid State Phys. 49, 151 (1995).
Joannopoulos, J., Villeneuve, P.R. and Fan, S., Nature 386, 143 (1997).
Krauss, T.F. De la Rue, R.M. and Brand, S., Nature 383, 699 (1996).
Foresi, J.S. et al., Nature 390, 143 (1997).
Datta, S., Chan, C.T., Ho, K.M. and Soukoulis C.M., Phys. Rev. B 48, 14936 (1993).
Leung, K.M. and Lin, Y.F., Phys. Rev. Lett. 65, 2646 (1990).
Haus, J.W., Sözüer, H.S. and Inguva, R., J. Mod. Optics 39, 1991 (1992).
Zabel, I.H.H. & Stroud, D., Phys. Rev. B 48, 5004 (1993).
McPhedran, R.C. Nicorovici, N.A. and Botten, L.C., J. Electrom. Waves Appl. 11, 981 (1997); Phys. Rev. Lett., 75, 1507 (1995).
Krokhin, A.A., Arriaga, J. and Halevi, P., Physica A 241, 52 (1997).
Bora, M. and Wolf, E. Principles of Optics (Pergamon Press, Oxford, 1975), chap. 14.
Bergman, D.J. and Stroud, D., Solid State Phys. 46, 197 (1992).
P. Halevi, A. A. Krokhin, and J. Arriaga, Phys. Rev. Lett. 82, 719 (1999).
Nevard, J. and Keller, J.B., J. Math. Phys. 26, 2761 (1985).
Landau L.D. and E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, Oxford, 1984).
Hashin, Z. and Shtrikman, S., J. Appl. Phys. 33, 3125 (1962).
Lin, S.Y., Hietala, V.M., Wang, L. and Jones, E.D., Optics Lett. 21, 1771, (1996).
Karathanos, V., Stefanou, N. and Modinos, A., J. Mod. Optics 42, 619 (1995).
Bergman, D.J. and Dunn, K.J., Phys. Rev. B 45, 13262 (1992). It is possible to prove that Eqs. (2.5), (2.23) and (2.26) of this paper lead to our Eq. (2) (D. Bergman, private communication).
Milton, G.W., McPhedran, R.C. and McKenzie, D.R., Appl. Phys. 25, 23 (1981).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Kluwer Academic Publishers
About this paper
Cite this paper
Halevi, P., Krokhin, A.A., Arriaga, J. (2001). Photonic Crystal Optics and Homogenization of 2D Periodic Composites. In: IUTAM Symposium on Mechanical and Electromagnetic Waves in Structured Media. Solid Mechanics and Its Applications, vol 91. Springer, Dordrecht. https://doi.org/10.1007/0-306-46955-3_17
Download citation
DOI: https://doi.org/10.1007/0-306-46955-3_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-7038-3
Online ISBN: 978-0-306-46955-8
eBook Packages: Springer Book Archive