## Complex modes and artificial magnetism in three-dimensional periodic arrays of titanium dioxide microspheres at millimeter waves |

JOSA B, Vol. 29, Issue 7, pp. 1697-1706 (2012)

http://dx.doi.org/10.1364/JOSAB.29.001697

Enhanced HTML Acrobat PDF (1123 KB)

### Abstract

We characterize the modes with real and complex wavenumbers for both longitudinal
and transverse polarization states (with respect to the mode traveling
direction) in three dimensional (3D) periodic arrays of titanium dioxide
(

© 2012 Optical Society of America

**OCIS Codes**

(160.1245) Materials : Artificially engineered materials

(260.2065) Physical optics : Effective medium theory

(160.3918) Materials : Metamaterials

**ToC Category:**

Materials

**History**

Original Manuscript: November 22, 2011

Revised Manuscript: February 14, 2012

Manuscript Accepted: April 3, 2012

Published: June 20, 2012

**Citation**

Salvatore Campione, Sylvain Lannebère, Ashod Aradian, Matteo Albani, and Filippo Capolino, "Complex modes and artificial magnetism in three-dimensional periodic arrays of titanium dioxide microspheres at millimeter waves," J. Opt. Soc. Am. B **29**, 1697-1706 (2012)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-29-7-1697

Sort: Year | Journal | Reset

### References

- J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
- T. J. Yen, W. Padilla, N. Fang, D. Vier, D. Smith, J. Pendry, D. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494 (2004). [CrossRef]
- M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Single-slit split-ring resonators at optical frequencies: limits of size scaling,” Opt. Lett. 31, 1259–1261 (2006). [CrossRef]
- S. Zhang, W. Fan, K. J. Malloy, S. R. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13, 4922–4930 (2005). [CrossRef]
- H. K. Yuan, U. K. Chettiar, W. S. Cai, A. V. Kildishev, A. Boltasseva, V. P. Drachev, and V. M. Shalaev, “A negative permeability material at red light,” Opt. Express 15, 1076–1083 (2007). [CrossRef]
- W. Cai, U. K. Chettiar, H. K. Yuan, V. C. De Silva, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Metamagnetics with rainbow colors,” Opt. Express 15, 3333–3341 (2007). [CrossRef]
- G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: particle resonances, phenomena and properties,” Metamaterials 3, 10–27 (2009).
- A. Vallecchi, F. Capolino, and A. G. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microw. Wireless Compon. Lett. 19, 269–271 (2009). [CrossRef]
- A. Vallecchi and F. Capolino, “Tightly coupled tripole conductor pairs as constituents for a planar 2D-isotropic negative refractive index metamaterial,” Opt. Express 17, 15216–15227 (2009). [CrossRef]
- A. Vallecchi and F. Capolino, “Metamaterials based on pairs of tightly coupled scatterers,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 19.1.
- A. Vallecchi, S. Campione, and F. Capolino, “Symmetric and antisymmetric resonances in a pair of metal-dielectric nanoshells: tunability and closed-form formulas,” J. Nanophoton. 4, 041577 (2010). [CrossRef]
- S. Campione, A. Vallecchi, and F. Capolino, “Closed form formulas and tunability of resonances in pairs of gold-dielectric nanoshells,” Proc. SPIE 7757, 775738 (2010). [CrossRef]
- V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005). [CrossRef]
- C. L. Holloway, E. F. Kuester, J. Baker-Jarvis, and P. Kabos, “A double negative (DNG) composite medium composed of magnetodielectric spherical particles embedded in a matrix,” IEEE Trans. Antennas Propag. 51, 2596–2603 (2003). [CrossRef]
- C. L. Holloway, M. A. Mohamed, E. F. Kuester, and A. Dienstfrey, “Reflection and transmission properties of a metafilm: with an application to a controllable surface composed of resonant particles,” IEEE Trans. Electromagn. Compat. 47, 853–865 (2005). [CrossRef]
- J. Liu and N. Bowler, “Analysis of double-negative (DNG) bandwidth for a metamaterial composed of magnetodielectric spheres embedded in a matrix,” IEEE Antennas Wireless Propagat. Lett. 10, 399–402 (2011). [CrossRef]
- I. Vendik, O. Vendik, and M. Odit, “Isotropic artificial media with simultaneously negative permittivity and permeability,” Microw. Opt. Technol. Lett. 48, 2553–2556 (2006). [CrossRef]
- I. B. Vendik, M. A. Odit, and D. S. Kozlov, “3D isotropic metamaterial based on a regular array of resonant dielectric spherical inclusions,” Metamaterials 3, 140–147 (2009).
- V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys. Condens. Matter 17, 3717 (2005). [CrossRef]
- T. G. Mackay and A. Lakhtakia, “Correlation length and negative phase velocity in isotropic dielectric-magnetic materials,” J. Appl. Phys. 100, 063533–063535 (2006). [CrossRef]
- L. Jylha, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102–043107 (2006). [CrossRef]
- I. Vendik, O. G. Vendik, and M. Odit, “Isotropic double-negative materials,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 21.1.
- I. B. Vendik, O. G. Vendik, and M. S. Gashinova, “Artificial dielectric medium possessing simultaneously negative permittivity and magnetic permeability,” Tech. Phys. Lett. 32, 429–433 (2006). [CrossRef]
- I. Vendik, O. Vendik, I. Kolmakov, and M. Odit, “Modelling of isotropic double negative media for microwave applications,” Opto-Electron. Rev. 14, 179–186 (2006). [CrossRef]
- G. Nehmetallah, R. Aylo, and P. P. Banerjee, “Binary and core-shell nanoparticle dispersed liquid crystal cells for metamaterial applications,” J. Nanophoton. 5, 051603 (2011). [CrossRef]
- I. Vendik, M. Odit, and D. Kozlov, “All-dielectric metamaterials based on spherical and cubic inclusions,” in Selected Topics in Metamaterials and Photonic Crystals, A. Andreone, A. Cusano, A. Cutolo, and V. Galdi, eds. (World Scientific, 2011).
- I. Vendik, M. Odit, and D. Kozlov, “3D metamaterial based on a regular array of resonant dielectric inclusions,” Radioengineering 18, 111–116 (2009).
- R. A. Shore and A. D. Yaghjian, “Traveling waves on three-dimensional periodic arrays of two different alternating magnetodielectric spheres,” IEEE Trans. Antennas Propag. 57, 3077–3091 (2009). [CrossRef]
- E. F. Kuester, N. Memic, S. Shen, A. D. Scher, S. Kim, K. Kumley, and H. Loui, “A negative refractive index metamaterial based on a cubic array of layered nonmagnetic spherical particles,” Progr. Electromag. Res. B 33, 175–202 (2011).
- C.-W. Qiu and L. Gao, “Resonant light scattering by small coated nonmagnetic spheres: magnetic resonances, negative refraction, and prediction,” J. Opt. Soc. Am. B 25, 1728–1737 (2008). [CrossRef]
- A. Alu and N. Engheta, “Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles,” Phys. Rev. B 78, 085112 (2008). [CrossRef]
- C. R. Simovski and S. A. Tretyakov, “Model of isotropic resonant magnetism in the visible range based on core-shell clusters,” Phys. Rev. B 79, 045111 (2009). [CrossRef]
- A. Vallecchi, M. Albani, and F. Capolino, “Collective electric and magnetic plasmonic resonances in spherical nanoclusters,” Opt. Express 19, 2754–2772 (2011). [CrossRef]
- F. S. Ham and B. Segall, “Energy bands in periodic lattices-Green’s function method,” Phys. Rev. 124, 1786 (1961). [CrossRef]
- L. S. Benenson, “Dispersion equations of periodic structures,” Radio Eng. Electron. Phys. 16, 1280–1290 (1971).
- M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005). [CrossRef]
- R. A. Shore and A. D. Yaghjian, “Traveling waves on two- and three-dimensional periodic arrays of lossless scatterers,” Radio Sci. 42, RS6S21 (2007). [CrossRef]
- A. Alu, and N. Engheta, “Three-dimensional nanotransmission lines at optical frequencies: a recipe for broadband negative-refraction optical metamaterials,” Phys. Rev. B 75, 024304 (2007). [CrossRef]
- S. Steshenko and F. Capolino, “Single dipole approximation for modeling collection of nanoscatterers,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 8.1.
- R. A. Shore and A. D. Yaghjian, “Complex waves on 1D, 2D, and 3D periodic arrays of lossy and lossless magnetodielectric spheres” (Air Force Research Laboratory, 2010).
- S. Campione, S. Steshenko, M. Albani, and F. Capolino, “Complex modes and effective refractive index in 3D periodic arrays of plasmonic nanospheres,” Opt. Express 19, 26027–26043 (2011). [CrossRef]
- P. P. Ewald, “The calculation of optical and electrostatic grid potential,” Ann. Phys. 64, 253–287 (1921). [CrossRef]
- K. Berdel, J. G. Rivas, P. H. Bolivar, P. de Maagt, and H. Kurz, “Temperature dependence of the permittivity and loss tangent of high-permittivity materials at terahertz frequencies,” IEEE Trans. Microwave Theory Tech. 53, 1266–1271 (2005). [CrossRef]
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1965).
- J. D. Jackson, Classical Electrodynamics (Wiley, 1998).
- V. A. Markel, V. N. Pustovit, S. V. Karpov, A. V. Obuschenko, V. S. Gerasimov, and I. L. Isaev, “Electromagnetic density of states and absorption of radiation by aggregates of nanospheres with multipole interactions,” Phys. Rev. B 70, 054202 (2004). [CrossRef]
- D. W. Mackowski, “Calculation of total cross sections of multiple-sphere clusters,” J. Opt. Soc. Am. A 11, 2851–2861 (1994). [CrossRef]
- M. G. Silveirinha, “Generalized Lorentz–Lorenz formulas for microstructured materials,” Phys. Rev. B 76, 245117 (2007). [CrossRef]
- A. Alù, “First-principles homogenization theory for periodic metamaterials,” Phys. Rev. B 84, 075153 (2011). [CrossRef]
- E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, “Magnetoinductive waves in one, two, and three dimensions,” J. Appl. Phys. 92, 6252–6261 (2002). [CrossRef]
- I. V. Shadrivov, A. N. Reznik, and Y. S. Kivshar, “Magnetoinductive waves in arrays of split-ring resonators,” Physica B 394, 180–183 (2007). [CrossRef]
- A. Sihvola, Electromagnetic Mixing Formulas and Applications (IEE, 1999).
- A. Sihvola, “Mixing rules,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 9.1.
- S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, 2003).
- O. Ouchetto, Q. Cheng-Wei, S. Zouhdi, L. Le-Wei, and A. Razek, “Homogenization of 3-D periodic bianisotropic metamaterials,” IEEE Trans. Microwave Theory Tech. 54, 3893–3898 (2006). [CrossRef]
- A. M. Nicolson and G. F. Ross, “Measurement of the intrinsic properties of materials by time-domain techniques,” IEEE Trans. Instrum. Meas. 19, 377–382 (1970). [CrossRef]
- W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62, 33–36 (1974). [CrossRef]
- A. H. Boughriet, C. Legrand, and A. Chapoton, “Noniterative stable transmission/reflection method for low-loss material complex permittivity determination,” IEEE Trans. Microwave Theory Tech. 45, 52–57 (1997). [CrossRef]
- C. R. Simovski, “On the extraction of local material parameters of metamaterials from experimental or simulated data,” in Theory and Phenomena of Metamaterials, F. Capolino, ed. (CRC Press, 2009), p. 11.1.
- S. A. Ramakrishna and T. M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials (CRC Press and SPIE Press, 2009).
- H. Nemec, C. Kadlec, F. Kadlec, P. Kuzel, R. Yahiaoui, U. C. Chung, C. Elissalde, M. Maglione, and P. Mounaix, “Resonant magnetic response of TiO2 microspheres at terahertz frequencies,” Appl. Phys. Lett. 100, 061117 (2012). [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.