## Effective-medium description of disordered photonic alloys

JOSA B, Vol. 23, Issue 7, pp. 1414-1419 (2006)

http://dx.doi.org/10.1364/JOSAB.23.001414

Enhanced HTML Acrobat PDF (96 KB)

### Abstract

We calculate the effective electric permittivity of photonic crystals of spherical particles with substitutional disorder. The effective permittivity is obtained by using a coherent-potential approximation scheme for photonic crystals in the context of multiple-scattering theory. The method is applied to the case of dielectric spheres in air as well as to inverted structures, i.e., air spheres in a dielectric medium. The results are compared against the standard Maxwell–Garnett effective-medium theory and its variations.

© 2006 Optical Society of America

**OCIS Codes**

(290.3770) Scattering : Long-wave scattering

(290.4210) Scattering : Multiple scattering

**ToC Category:**

Scattering

**History**

Original Manuscript: December 2, 2005

Manuscript Accepted: January 29, 2006

**Citation**

Vassilios Yannopapas, "Effective-medium description of disordered photonic alloys," J. Opt. Soc. Am. B **23**, 1414-1419 (2006)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-23-7-1414

Sort: Year | Journal | Reset

### References

- V. V. Jikov, S. M. Kozlov, and O. A. Oleinik, Homogenization of Differential Operators and Integral Functionals (Springer, 1994). [CrossRef]
- G. W. Milton, The Theory of Composites (Cambridge U. Press, 2002). [CrossRef]
- D. Felbacq and G. Bouchittè, "Homogenization of a set of parallel fibres," Waves Random Media 7, 245-256 (1997). [CrossRef]
- A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 60, 6118-6127 (1999). [CrossRef]
- A. A. Asatryan, P. A. Robinson, L. C. Botten, R. C. McPhedran, N. A. Nicorovici, and C. M. de Sterke, "Effects of geometric and refractive index disorder on wave propagation in two-dimensional photonic crystals," Phys. Rev. E 62, 5711-5720 (2000). [CrossRef]
- F. Zolla and S. Guenneau, "Duality relation for the Maxwell system," Phys. Rev. E 67, 026610 (2003). [CrossRef]
- D. Felbacq and G. Bouchittè, "Negative refraction in periodic and random photonic crystals," New J. Phys. 7, 159 (2005). [CrossRef]
- P. Mallet, C. A. Guérin, and A. Sentenac, "Maxwell-Garnett mixing rule in the presence of multiple scattering: derivation and accuracy," Phys. Rev. B 72, 014205 (2005). [CrossRef]
- B. T. Holland, C. F. Blanford, and A. Stein, "Synthesis of macroporous minerals with highly ordered three-dimensional arrays of spheroidal voids," Science 281, 538-540 (1998). [CrossRef] [PubMed]
- Yu. A. Vlasov, B. Xiang-Zheng, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001). [CrossRef] [PubMed]
- Yu. A. Vlasov, V. N. Astratov, A. V. Baryshev, A. A. Kaplyanskii, O. Z. Karimov, and M. F. Limonov, "Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals," Phys. Rev. E 61, 5784-5793 (2000). [CrossRef]
- Z.-Y. Li and Z.-Q. Zhang, "Fragility of photonic band gaps in inverse-opal photonic crystals," Phys. Rev. B 62, 1516-1519 (2000). [CrossRef]
- R. Biswas, M. M. Sigalas, G. Subramania, C. M. Soukoulis, and K.-M. Ho, "Photonic band gaps of porous solids," Phys. Rev. B 61, 4549-4553 (2000). [CrossRef]
- V. Yannopapas, N. Stefanou, and A. Modinos, "Effect of stacking faults on the optical properties of inverted opals," Phys. Rev. Lett. 86, 4811-4814 (2001). [CrossRef] [PubMed]
- V. N. Astratov, A. M. Adawi, S. Fricker, M. S. Skolnick, D. M. Whittaker, and P. N. Pusey, "Interplay of order and disorder in the optical properties of opal photonic crystals," Phys. Rev. B 66, 165215 (2002). [CrossRef]
- J. P. Hoogenboom, A. K. van Langen-Suurling, H. Romijn, and A. van Blaaderen, "Hard-sphere crystals with hcp and non-close-packed structure grown by colloidal epitaxy," Phys. Rev. Lett. 90, 138301 (2003). [CrossRef] [PubMed]
- V. Yannopapas, N. Stefanou, and A. Modinos, "Anderson localization of light in inverted opals," Phys. Rev. B 68, 193205 (2003). [CrossRef]
- Z. L. Wang, C. T. Chan, W. Y. Zhang, Z. Chen, N. B. Ming, and P. Sheng, "Optical properties of inverted opal photonic band gap crystals with stacking disorder," Phys. Rev. E 67, 016612 (2003). [CrossRef]
- N. Stefanou, V. Karathanos, and A. Modinos, "Scattering of electromagnetic waves by periodic structures," J. Phys. Condens. Matter 4, 7389-7400 (1992). [CrossRef]
- N. Stefanou, V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: frequency bands and transmission coefficients," Comput. Phys. Commun. 113, 49-77 (1998). [CrossRef]
- N. Stefanou, V. Yannopapas, and A. Modinos, "MULTEM 2: a new version of the program for transmission and band-structure calculations of photonic crystals," Comput. Phys. Commun. 132, 189-196 (2000). [CrossRef]
- N. Stefanou and A. Modinos, "Scattering of electromagnetic waves by a disordered two-dimensional array of spheres," J. Phys. Condens. Matter 5, 8859-8868 (1993). [CrossRef]
- A. Modinos, V. Yannopapas, and N. Stefanou, "Scattering of electromagnetic waves by nearly periodic structures," Phys. Rev. B 61, 8099-8107 (2000). [CrossRef]
- P. Soven, "Coherent-potential model of substitutional disordered alloys," Phys. Rev. 156, 809-813 (1967). [CrossRef]
- B. L. Györffy and G. M. Stocks, Electrons in Disordered Metals and at Metallic Surfaces, P.Phariseau, B.L.Györffy, and L.Scheire, eds. (Plenum, 1979), p. 89.
- A. Gonis, Green Functions for Ordered and Disordered Systems (North-Holland, 1992).
- L. Tsang, J. A. Kong, and R. T. Shin, Theory of Microwave Remote Sensing (Wiley, 1985).
- J. D. Jackson, Classical Electrodynamics (Wiley, 1975).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- A. Moroz, "Inward and ouward integral equations and the KKR method for photons," J. Phys. Condens. Matter 6, 171-182 (1994). [CrossRef]
- A. Moroz, "Density-of-states calculations and multiple-scattering theory for photons," Phys. Rev. B 51, 2068-2081 (1995). [CrossRef]
- F. S. Ham and B. Segall, "Energy bands in periodic lattices—Green's function method," Phys. Rev. 124, 1786-1796 (1961). [CrossRef]
- K. Kambe, "A multiple-scattering theory of LEED intensities," Surf. Sci. 20, 213-219 (1970). [CrossRef]
- J. L. Beeby, "The diffraction of low-energy electrons by crystals," J. Phys. C 1, 82-87 (1968). [CrossRef]
- K. Busch and S. John, "Photonic band gap formation in certain self-organizing systems," Phys. Rev. E 58, 3896-3908 (1998). [CrossRef]
- A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J. Mondia, G. A. Ozin, O. Toader, and H. M. van Driel, "Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres," Nature 405, 437-440 (2000). [CrossRef] [PubMed]
- A. Liebsch and B. J. Persson, "Optical properties of small metallic particles in a continuous dielectric medium," J. Phys. C 16, 5375-5391 (1983). [CrossRef]
- W. T. Doyle, "Optical properties of a suspension of metal spheres," Phys. Rev. B 39, 9852-9858 (1989). [CrossRef]
- R. Ruppin, "Evaluation of extended Maxwell-Garnett theories," Opt. Commun. 182, 273-279 (2000). [CrossRef]
- B. U. Felderhof and R. B. Jones, "Effective dielectric constant of dilute suspensions of spheres," Phys. Rev. B 39, 5669-5677 (1989). [CrossRef]
- L. G. Grechko, V. N. Pustovit, and K. W. Whites, "Dielectric function of aggregates of small metallic particles embedded in host insulating matrix," Appl. Phys. Lett. 76, 1854-1856 (2000). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.