Abstract
A formula for the effective permittivity for two-dimensional particles embedded in a host matrix is derived and a method for its numerical evaluation is described. The method is applied to specific cases of circular, square, rectangular and triangular particles. Shapes are assumed for the inclusion particles. Data for obtaining the effective permittivity is provided for a wide range of filling fractions, geometries and dielectric contrasts between the particles and the matrix under the assumption of the quasi-static approximation, that is, the wavelength of the electric field is assumed to be much larger than the particle size. Metallic particles with complex and frequency-dependent dielectric constants are treated, as well as no-loss dielectric inclusions. Calculations are validated by comparing the results of the reflectivity obtained for a composite layer using the transfer-matrix method, assuming the layer to be an effective medium, to those using the finite-element method and accounting for the heterogeneous material.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.D. Joannopoulos, R.D. Meade, J.N. Winn: Photonic Crystals – Molding the Flow of Light (Princeton University Press, Princeton, New Jersey 1995)
E. Yablonovitch: Phys. Rev. Lett. 58, 2059 (1987)
S. John: Phys. Rev. Lett. 58, 2486 (1987)
S.Y. Lin, V.M. Hietala, L. Wang, E.D. Jones: Opt. Lett. 21, 1771 (1996)
H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sako, S. Kawakami: Phys. Rev. B 58, R10 096 (1998)
T.C. Choy: Effective-Medium Theory – Principles and Applications (Oxford University Press, Oxford 1999)
J.C. Maxwell-Garnett: Philos. Trans. R. Soc. London Ser. A 203, 385 (1904)
K. Busch, C.M. Soukoulis: Phys. Rev. Lett. 75, 3442 (1995)
A. Priou: Dielectric Properties of Heterogeneous Materials (Elsevier, New York 1991)
S. Datta, C.T. Chan, K.M. Ho, C.M. Soukoulis: Phys. Rev. B 48, 14 936 (1993)
A.A. Krokhin, P. Halevi, J. Arriaga: Phys. Rev. B 65, 115 208 (2002)
H.F. Contopanagos, C.A. Kyriazidou, W.M. Merrill: J. Opt. Soc. Am. A 16, 1682 (1999)
A.D. Yaghjian: Proc. IEEE 68, 248 (1980)
A. Shivola, I.V. Lindell: J. Electromagnetic Waves Applic. 3, 37 (1989)
A. Shivola, I.V. Lindell: J. Electromagnetic Waves Applic. 4, 1 (1990)
J.D. Jackson: Classical Electrodynamics (Wiley, New York 1999)
F.J. Garcia-Vidal, J.M. Pitarke, J.B. Pendry: Phys. Rev. Lett. 78, 4289 (1997)
E.R. Brown: Appl. Phys. Lett. 67, 2138 (1995)
J.L. Volakis: Finite Element Method for Electromagnetics (IEEE Press, New York 1998)
P. Yeh, A. Yariv, C.S. Hong: J. Opt. Soc. Am. 67, 423 (1977)
E.D. Palik: Handbook of Optical Constants of Solids (Academic Press, San Diego 1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
78.20.-e; 78.20.Bh; 78.20.Ci; 78.66.Sq; 78.66.Vs
Rights and permissions
About this article
Cite this article
Maldovan, M., Bockstaller, M., Thomas , E. et al. Validation of the effective-medium approximation for the dielectric permittivity of oriented nanoparticle-filled materials: effective permittivity for dielectric nanoparticles in multilayer photonic composites. Appl. Phys. B 76, 877–884 (2003). https://doi.org/10.1007/s00340-003-1209-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00340-003-1209-4