volume | PIER Journals

Abstract

We present a hierarchical layer-multiple-scattering method of electromagnetic waves for the study of photonic structures consisting of many-scatterers per unit cell (clusters of scatterers) where the scatterers are in general non-spherical and/or anisotropic or inhomogeneous. Our approach is a two-stage process where we take into account all the multiple-scattering events involved: (a) among the scatterers of the cluster comprising the unit cell of the structure, and (b) among the clusters within the structure. As text cases, we model the optical properties of plasmonic metamaterials made from clusters of gold nanocubes.

1. Gonis, A. and W. H. Butler, Multiple Scattering in Solids, Springer, New York, 2000.
doi:10.1007/978-1-4612-1290-4

2. Wang, X., X.-G. Zhang, Q. Yu, and B. N. Harmon, "Multiple-scattering theory for electromagnetic waves," Phys. Rev. B, Vol. 47, No. 8, 4161-4167, 1993.
doi:10.1103/PhysRevB.47.4161

3. Moroz, A., "Density-of-states calculations and multiple-scattering theory for photons," Phys. Rev. B, Vol. 51, No. 4, 2068-2081, 1995.
doi:10.1103/PhysRevB.51.2068

4. Stefanou, N., V. Karathanos, and A. Modinos, "Scattering of electromagnetic waves by periodic structures," J. Phys.: Condens. Matter, Vol. 4, No. 36, 7389-7400, 1992.
doi:10.1088/0953-8984/4/36/013

5. Stefanou, N., V. Yannopapas, and A. Modinos, "Heterostructures of photonic crystals: Frequency bands and transmission coefficients," Comput. Phys. Commun., Vol. 113, No. 1, 49-77, 1998.
doi:10.1016/S0010-4655(98)00060-5

6. Stefanou, N., 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., Vol. 132, No. 1-2, 189-196, 2000.
doi:10.1016/S0010-4655(00)00131-4

7. Gantzounis, G. and N. Stefanou, "Layer-multiple-scattering method for photonic crystals of nonspherical particles," Phys. Rev. B, Vol. 73, No. 035115, 2006.

8. Gantzounis, G., N. Stefanou, and N. Papanikolaou, "Multiple-scattering calculations for layered phononic structures of nonspherical particles," Phys. Rev. B, Vol. 77, No. 214301, 2008.

9. Tserkezis, C., N. Papanikolaou, G. Gantzounis, and N. Stefanou, "Understanding artificial optical magnetism of periodic metal-dielectric-metal layered structures," Phys. Rev. B, Vol. 78, No. 165114, 2008.

10. Christofi, A., N. Stefanou, G. Gantzounis, and N. Papanikolaou, "Spiral-staircase photonic structures of metallic nanorods," Phys. Rev. B, Vol. 84, No. 125109, 2011.

11. Christofi, A. and N. Stefanou, "Nonreciprocal optical response of helical periodic structures of plasma spheres in a static magnetic field," Phys. Rev. B, Vol. 87, No. 115125, 2013.

12. Christofi, A. and N. Stefanou, "Nonreciprocal photonic surface states in periodic structures of magnetized plasma nanospheres," Phys. Rev. B, Vol. 88, No. 125133, 2013.

13. Christofi, A. and N. Stefanou, "Layer multiple scattering calculations for nonrecirpocal photonic structures," Int. J. Mod. Phys. B, Vol. 28, No. 1441012, 2014.

14. Muhlig, S., C. Rockstuhl, V. Yannopapas, T. Burgi, N. Shalkevich, and F. Lederer, "Optical properties of a fabricated self-assembled bottom-up bulk metamaterial," Opt. Express, Vol. 19, No. 10, 9607-9616, 2011.
doi:10.1364/OE.19.009607

15. Yannopapas, V. and A. Vanakaras, "Dirac point in the photon dispersion relation of a negative/zero/positive-index plasmonic metamaterial," Phys. Rev. B, Vol. 84, No. 045128, 2011.

16. Yannopapas, V. and A. Vanakaras, "Layer-multiple-scattering theory for metamaterials made from clusters of nanoparticles," Phys. Rev. B, Vol. 84, No. 085119, 2011.

17. Yannopapas, V., "Layer-multiple-scattering method for photonic structures of general scatterers based on a discrete-dipole approximation/T-matrix point-matching method," J. Opt. Soc. Am. B, Vol. 31, No. 3, 631-636, 2014.
doi:10.1364/JOSAB.31.000631

18. Jackson, J. D., Classical Electrodynamics, Wiley, New York, 1975.

19. Bohren, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particles, Wiley, New York, 1983.

20. Sainidou, R., N. Stefanou, and A. Modinos, "Green's function formalism for phononic crystals," Phys. Rev. B, Vol. 69, No. 064301, 2004.

21. Purcell, E. M. and C. R. Pennypacker, "Scattering and absorption of light by nonspherical dielectric grains," Astrophys. J., Vol. 186, 705-714, 1973.
doi:10.1086/152538

22. Draine, B. T. and P. J. Flatau, "Discrete-dipole approximation for scattering calculations," J. Opt. Soc. Am. A, Vol. 11, No. 4, 1491-1499, 1994.
doi:10.1364/JOSAA.11.001491

23. Yurkin, M. A. and A. G. Hoekstra, "The discrete dipole approximation: An overview and recent developments," J. Quant. Spec. Rad. Transfer, Vol. 106, No. 1-3, 558-589, 2007.
doi:10.1016/j.jqsrt.2007.01.034

24. Chaumet, P. C. and A. Rahmani, "Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers," Opt. Lett., Vol. 34, No. 7, 917-919, 2009.
doi:10.1364/OL.34.000917

25. Loke, V. L. Y., T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "T- matrix calculation via discrete dipole approximation, point matching and exploiting symmetry," J. Quantit. Spectrosc. Radiat. Transfer, Vol. 110, No. 14-16, 1460-1471, 2009.
doi:10.1016/j.jqsrt.2009.01.013

26. Loke, V. L. Y., T. A. Nieminen, S. J. Parkin, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "FDFD/T-matrix hybrid method," J. Quantit. Spectrosc. Radiat. Transfer, Vol. 106, No. 1-3, 274-284, 2007.
doi:10.1016/j.jqsrt.2007.01.040

27. Menzel, C., S. Muhlig, C. Rockstuhl, and F. Lederer, "Multipole analysis of meta-atoms," Metamaterials, Vol. 5, No. 2-3, 64-73, 2011.
doi:10.1016/j.metmat.2011.03.003

28. Yannopapas, V. and N. V. Vitanov, "Electromagnetic Greens tensor and local density of states calculations for collections of spherical scatterers," Phys. Rev. B, Vol. 75, No. 115124, 2007.

29. Johnson, R. B. and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B, Vol. 6, No. 12, 4370-4379, 1972.
doi:10.1103/PhysRevB.6.4370

30. Yu, N. and F. Capasso, "Flat optics with designer metasurfaces," Nat. Mater., Vol. 13, 139-150, 2014.
doi:10.1038/nmat3839

Dr. Vassilios Yannopapas