## Self-organization approach for THz polaritonic metamaterials |

Optics Express, Vol. 20, Issue 13, pp. 14663-14682 (2012)

http://dx.doi.org/10.1364/OE.20.014663

Acrobat PDF (5467 KB)

### Abstract

In this paper we discuss the fabrication and the electromagnetic (EM) characterization of anisotropic eutectic metamaterials, consisting of cylindrical polaritonic LiF rods embedded in either KCl or NaCl polaritonic host. The fabrication was performed using the eutectics directional solidification self-organization approach. For the EM characterization the specular reflectance at far infrared, between 3 THz and 11 THz, was measured and also calculated by numerically solving Maxwell equations, obtaining good agreement between experimental and calculated spectra. Applying an effective medium approach to describe the response of our samples, we predicted a range of frequencies in which most of our systems behave as homogeneous anisotropic media with a hyperbolic dispersion relation, opening thus possibilities for using them in negative refractive index and imaging applications at THz range.

© 2012 OSA

## 1. Introduction

1. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature **417**, 156–159 (2002). [CrossRef] [PubMed]

2. S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. **46**, R101–R112 (2001). [CrossRef] [PubMed]

3. D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, *Terahertz Science and Technology for Military and Security Applications* (World Scientific Publishing Co. Pte. Ltd., 2007). [CrossRef]

5. V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series **25**, 321–326 (2007). [CrossRef]

6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of *ε* and *μ*,” Sov. Phys. Usp. **10**, 509–514 (1968). [CrossRef]

7. J. B. Pendry, “Negative refraction makes perfect lens,” Phys. Rev. Lett. **85**, 3966–3969 (2000). [CrossRef] [PubMed]

8. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. **47**, 2075–2084 (1999). [CrossRef]

10. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. **84**, 4184–4187 (2000). [CrossRef] [PubMed]

11. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter **14**, 4035–4044 (2002). [CrossRef]

13. L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. **99**, 043102 (2006). [CrossRef]

13. L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. **99**, 043102 (2006). [CrossRef]

15. 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**, 3717–3734 (2005). [CrossRef]

12. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. **99**, 107401 (2007). [CrossRef] [PubMed]

16. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. **90**, 077405 (2003). [CrossRef] [PubMed]

22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science **315**, 1686–1686 (2007). [CrossRef] [PubMed]

21. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express **15**, 15886–15891 (2007). [CrossRef] [PubMed]

24. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B **74**, 075103 (2006). [CrossRef]

22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science **315**, 1686–1686 (2007). [CrossRef] [PubMed]

25. A. Fang, T. Koschny, and C. M. Soukoulis, “Optical anisotropic metamaterials: negative refraction and focusing,” Phys. Rev. B **79**, 245127 (2009). [CrossRef]

16. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. **90**, 077405 (2003). [CrossRef] [PubMed]

22. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science **315**, 1686–1686 (2007). [CrossRef] [PubMed]

26. G. A. Wurtz, W. Dickson, D. O’Connor, R. Atkinson, W. Hendren, P. Evans, R. Pollard, and A. V. Zayats, “Guided plasmonic modes in nanorod assemblies: strong electromagnetic coupling regime,” Opt. Express **16**, 7460–7470 (2008). [CrossRef] [PubMed]

21. H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express **15**, 15886–15891 (2007). [CrossRef] [PubMed]

**315**, 1686–1686 (2007). [CrossRef] [PubMed]

27. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. **7**, 31–37 (2008). [CrossRef]

30. D. B. Burckel, J. R. Wendt, G. A. Ten Eyck, A. R. Ellis, I. Brener, and M. B. Sinclair, “Fabrication of 3D metamaterial resonators using self-aligned membrane projection lithography,” Adv. Mater. **22**, 3171–3175 (2010). [CrossRef] [PubMed]

31. C. Rockstuhl, F. Lederer, C. Etrich, T. Pertsch, and T. Scharf, “Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum,” Phys. Rev. Lett. **99**, 017401 (2007). [CrossRef] [PubMed]

34. D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization,” Adv. Funct. Mater. **20**, 1116–1124 (2010). [CrossRef]

34. D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization,” Adv. Funct. Mater. **20**, 1116–1124 (2010). [CrossRef]

35. J. Llorca and V. M. Orera, “Directionally solidified eutectic ceramic oxides,” Prog. Mater. Sci. **51**, 711–809 (2006). [CrossRef]

36. V. M. Orera, J. I. Peña, P. B. Oliete, R. I. Merino, and A. Larrea, “Growth of eutectic ceramic structures by directional solidification methods,” J. Cryst. Growth (2011), [CrossRef] .

34. D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization,” Adv. Funct. Mater. **20**, 1116–1124 (2010). [CrossRef]

33. V. M. Orera and A. Larrea, “NaCl-assisted growth of micrometer-wide long single crystalline fluoride fibres,” Opt. Mater. **27**, 1726–1729 (2005). [CrossRef]

## 2. Eutectic metamaterial samples obtained

*ω*is the phonon-polariton resonance frequency, and

_{T}*ε*

_{∞}and

*ε*

_{0}are the limiting values of the dielectric function at frequencies much larger than (

*ε*

_{0}−

*ε*

_{∞})

^{1/2}

*ω*, and at zero frequency, respectively. The fitting parameters obtained from the fitting procedure for the three materials are shown in Table 1.

_{T}### 2.1. Sample preparation

33. V. M. Orera and A. Larrea, “NaCl-assisted growth of micrometer-wide long single crystalline fluoride fibres,” Opt. Mater. **27**, 1726–1729 (2005). [CrossRef]

*Alfa Aesar*), 99.5% pure KCl (

*Merk*) and 99.99% pure NaCl (

*Alfa Aesar*) were used as starting powders. They were mixed in their eutectic composition: 91 wt% of KCl and 9 wt% of LiF for the LiF rods in KCl (samples named below as LK#), and 71 wt% NaCl and 29 wt% LiF for the LiF in NaCl (samples named LN#). The numbers in the sample acronym indicate the interphase spacing. The growth was done in carbon-glass crucibles under an Ar atmosphere, pulling them out from the hot region of the furnace through a thermal gradient of 40 C/cm, at different pulling rates. Modifying the pulling rate has as a result the modification of size and inter-spacing of the LiF rods formed. Larger pulling rates result to smaller length-scale systems. The volume percent of fibers (LiF) remains fixed by the eutectic composition (6.9% for LiF in KCl and 25% for LiF in NaCl).

*μ*m or 0.25

*μ*m, for microstructural characterization. Under the naked eye the slices looked as in Fig. 2(a). They appear rather transparent to transmitted light along the solidification direction, as corresponds to well aligned microstructures. Figures 2(c) (transmission optical micrograph) and 2(d) (scanning electron microscopy (SEM) image) show images of typical transverse cross sections of both eutectics, where the dark phase is LiF and the bright one is NaCl [Fig. 2(c)] and KCl [Fig. 2(d)]. As expected, the microstructure (see Fig. 2) consists of LiF rods embedded in a KCl or NaCl matrix. In Fig. 2(b) we show a SEM image, where one can appreciate the continuity of the LiF rods coming out of a humidity corroded longitudinal section of KCl-LiF. In fact, LiF fibers as long as several millimeters result [33

33. V. M. Orera and A. Larrea, “NaCl-assisted growth of micrometer-wide long single crystalline fluoride fibres,” Opt. Mater. **27**, 1726–1729 (2005). [CrossRef]

39. A. Larrea and V. M. Orera, “Porous crystal structures obtained from directionally solidified eutectic precursors,” J. Cryst. Growth **300**, 387–393 (2007). [CrossRef]

*μ*m (grown at slower pulling rates). Such a case is shown in Fig. 3(b), concerning a LiF-KCl sample of interphase spacing 23.3

*μ*m, where the diameter distribution shows clearly two peaks, indicating two different populations of diameters.

*μ*m, were chosen for optical characterization. The geometrical features of the samples chosen are listed in Table 2 for the KCl-LiF samples and in Table 3 for NaCl-LiF ones. The errors indicate standard deviation of the corresponding magnitude. In the case of KCl-LiF systems, the volume filling fraction of LiF was 6.95% and the diameters were within the range 0.8

*μ*m − 6.4

*μ*m, while the separation distances between cylinders were within the range 2.8

*μ*m – 23.3

*μ*m (see Table 2). For the NaCl-LiF systems the volume filling fraction of LiF was 25%, with diameters of the cylinders between 2.0

*μ*m – 10.7

*μ*m and separation distances 3.6

*μ*m – 20.3

*μ*m (see Table 3). Standard deviation of the evaluated microstructural magnitudes are larger in LiF-KCl than in LiF-NaCl. This is particularly evident for the interphase spacing as obtained from FFT images. Also, the almost hexagonal ordering tends to extend a bit further in distance in LiF-NaCl than in LiF-KCl. This is consistent with qualitative observations in other fibrous directionality solidified eutectics, suggesting that small volume of the dispersed phase (as in LiF-KCl or MgO-CaF

_{2}[40

40. A. Larrea, L. Contreras, R. I. Merino, J. Llorca, and V. M. Orera, “Microstructure and physical properties of CaF2-MgO eutectics produced by the Bridgman method,” J. Mat. Res. **15**, 1314–1319 (2000). [CrossRef]

**27**, 1726–1729 (2005). [CrossRef]

## 3. Experimental setup and both theoretical and numerical tools employed

### 3.1. Experimental setup used to measure reflectance

*Bruker IFS 66v/S FT-IR*spectrometer. Longitudinal slices (i.e. cuts parallel to the rods) of thickness around 1 mm were cut and dry-polished for optical measurements. Typically the surface of the slices was 10×10 mm

^{2}. Only the sample LN3.6 had smaller area (around 4×10 mm

^{2}), since the well aligned region for this fast-pulled out sample had a smaller size. The reflectance for both parallel polarization (incident electric field,

**E**

*, parallel to the rod axes) and perpendicular polarization (*

_{inc}**E**

*perpendicular to the rod axes) was measured, as indicated in Fig. 4(a) and 4(b) respectively, with the wave vector of the incident radiation,*

_{inc}**k**

*, being always perpendicular to the axes of the rods, i.e. in the plane of periodicity. The reflectance measurements were performed at incidence angle*

_{inc}*θ*= 13° in respect to the vector normal to the interface (see Fig. 4), which is the smallest achievable angle of incidence of the instrument.

_{inc}### 3.2. Models used for numerical calculations of the reflectance

*CST Microwave Studio*, which solves numerically Maxwell equations in both time- and frequency-domain, employing the Finite Integration Technique based on the space and time discretization of Maxwell’s equations in their integral form.

### 3.3. Analytical model: effective medium approach

**E**) is perpendicular to the cylinders axes is the well known Maxwell Garnett model, suitable for dispersed particles inside a matrix [42, 43]. The Maxwell Garnett formula for the effective dielectric response function in two dimensions is given by where

*φ*is the volume filling fraction of the cylinders, and

*ε*and

_{host}*ε*are the permittivities of the host and the cylinders, respectively. When

_{cyl}**E**is parallel to the cylinder axes, the appropriate formula for the effective dielectric function is the average dielectric function [44

44. A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B **57**, 277–288 (1998). [CrossRef]

## 4. Electromagnetic characterization results and discussion

### 4.1. Reflectance from KCl-LiF eutectic metamaterial systems

*ε*] < 0: around 5 THz and around 10 THz. The lower-frequency region corresponds to the reflectance due to the KCl matrix, while the higher-frequency region is due to the contribution of the LiF rods. For the perpendicular polarization (right column), we observe that Maxwell Garnett formula predicts Re[

*ε*] < 0 in a single broader frequency region, from 4.2 THz up to 6.2 THz, with a peak at around 4.5 THz, where Re[

*ε*] is less negative and the losses are smaller than those for smaller frequencies.

*k*,

_{host}R*k*and

_{cyl}R*k*are all much smaller than unity (

_{eff}R*k*denotes the wavenumber in each material and

*R*the cylinder radius). In this limit the main contribution to the cylinder scattering in the parallel polarization case is the isotropic scattering term (of zero angular momentum) and no cylinder resonance exists in frequencies below the LiF polaritonic-resonance frequency (

*f*= 9.22 THz).

_{T}*μ*m, as shown in Fig. 7(a), where we show the single-cylinder extinction cross-section [45] for a LiF cylinder of radius 0.4, 1.05, 1.6 and 3.3

*μ*m, (for

**E**parallel to cylinder axis). As can be seen from Fig. 7(a), as we go to cylinders of larger radii, the lowest-frequency resonance (coming from the isotropic scattering), which for very small radius is located at

*f*, moves to frequencies below

_{T}*f*and additional resonances start to appear in the close-by regime. This is due to the large values of the LiF permittivity below

_{T}*f*, which make the quantity

_{T}*k*

_{host}*R*,

*k*<< 1 but

_{eff}R*k*

_{cyl}*R*≈ 1, a correct homogenization approach should take into account the full single-cylinder scattering (not only the first/isotropic term) and not the limit

*k*

_{cyl}*R*→ 0. Such an approach, known as extended Maxwell Garnett approach [46

46. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B **39**, 9852–9858 (1989). [CrossRef]

47. R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. **182**, 273–279 (2000). [CrossRef]

15. 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**, 3717–3734 (2005). [CrossRef]

11. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter **14**, 4035–4044 (2002). [CrossRef]

12. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. **99**, 107401 (2007). [CrossRef] [PubMed]

11. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter **14**, 4035–4044 (2002). [CrossRef]

*μ*m, as in our LK11.2 system, the negative permittivity regime predicted by the averaging approach lies between 7 and 9 THz, coinciding with the second reflection peak of the sample LK11.2 (see Fig. 6), and showing that even in that system an homogeneous effective medium approximation can be applied.

*d*=5.4

*μ*m [the average diameter of the left peak of the distribution shown in Fig. 3(b)], (ii)

*d*=6.6

*μ*m (the average value of the diameter for the entire distribution) and (iii)

*d*=7.8

*μ*m [the right peak in Fig. 3(b)]. The results are presented in Fig. 9, separated in two columns: left one for parallel polarization and right one for perpendicular polarization. As in Fig. 6, the first row corresponds to the real (red) and imaginary (blue) parts of the effective dielectric permittivity for each polarization case, using average and Maxwell Garnett formulas. We clearly see in Fig. 9 that the agreement between experiment and numerical results is poor, mainly for the parallel polarization (left column in Fig. 9), and that the reflection results deviate strongly from the predictions of the simple homogeneous effective medium models employed. In fact the presence in the simulations of many distinct, narrow and closely aligned reflectance peaks indicates (not confirms though) failure of any homogeneous effective medium approach, thus being clear that this specific sample does not possesses a hyperbolic dispersion relation.

### 4.2. Reflectance from NaCl-LiF eutectic metamaterial systems

*Microwave Studio*) reflection data for four representative samples: LN20.3, LN10.5, LN6.1 and LN3.6.

*ε*] < 0 for both parallel and perpendicular polarizations, in respect to the axes of the cylinders. For a direct comparison of the reflection results with the effective medium predictions, we have added in the last row of Fig. 10 the reflection from a thick “effective” homogeneous slab (green line), with the effective parameters obtained through Eqs. (3) and (2), using in this case the LiF and NaCl permittivities directly (without fit) from Palik data [37].

*ε*]≈ 0.

## 5. Polaritonic systems as indefinite media

41. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B **84**, 035128 (2011). [CrossRef]

*ω*(

**k**), for the ordinary (left equation) and the extraordinary (right equation) wave, respectively (considering the cylinder axes along

*ẑ*-direction).

**E**parallel to the rods (metal-like behavior), while it is positive for

**E**perpendicular to the rods (dielectric behavior). In this region thus, the sample will behave as an anisotropic uniaxial medium with a negative permittivity component (indefinite medium), and thus it will be characterized by a hyperbolic dispersion relation. Hyperbolic dispersion relation, as was discussed in the introduction, gives great possibilities for subwavelength imaging applications. Such a dispersion relation has been discussed and realized so far only in the case of metallodielectric systems, while it has been discussed only recently [41

41. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B **84**, 035128 (2011). [CrossRef]

48. P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B **67**, 113103 (2003). [CrossRef]

*μ*m to 3.2

*μ*m – see Table 2).

41. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B **84**, 035128 (2011). [CrossRef]

49. K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B **68**, 075209 (2003). [CrossRef]

50. K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Field expulsion and reconfiguration in polaritonic photonic crystals,” Phys. Rev. Lett. **90**, 196402 (2003). [CrossRef] [PubMed]

## 6. Conclusions

## Acknowledgments

## References and links

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34. | D. A. Pawlak, S. Turczynski, M. Gajc, K. Kolodziejak, R. Diduszko, K. Rozniatowski, J. Smalc, and I. Vendik, “How far are we from making metamaterials by self-organization,” Adv. Funct. Mater. |

35. | J. Llorca and V. M. Orera, “Directionally solidified eutectic ceramic oxides,” Prog. Mater. Sci. |

36. | V. M. Orera, J. I. Peña, P. B. Oliete, R. I. Merino, and A. Larrea, “Growth of eutectic ceramic structures by directional solidification methods,” J. Cryst. Growth (2011), [CrossRef] . |

37. | E. D. Palik, |

38. | V. M. Orera, A. Larrea, R. I. Merino, M. A. Rebolledo, J. A. Valles, R. Gotor, and J. I. Peña, “Novel photonic materials made from ionic eutectic compounds,” Acta Phys. Slovaca |

39. | A. Larrea and V. M. Orera, “Porous crystal structures obtained from directionally solidified eutectic precursors,” J. Cryst. Growth |

40. | A. Larrea, L. Contreras, R. I. Merino, J. Llorca, and V. M. Orera, “Microstructure and physical properties of CaF2-MgO eutectics produced by the Bridgman method,” J. Mat. Res. |

41. | S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B |

42. | J. C. Maxwell Garnett, “Colours in metal glasses and metal films,” Phil. Trans. R. Soc. London Ser. A |

43. | A. Sihvola, |

44. | A. Kirchner, K. Busch, and C. M. Soukoulis, “Transport properties of random arrays of dielectric cylinders,” Phys. Rev. B |

45. | J. A. Straton, |

46. | W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B |

47. | R. Ruppin, “Evaluation of extended Maxwell-Garnett theories,” Opt. Commun. |

48. | P. A. Belov, R. Marqués, S. I. Maslovski, I. S. Nefedov, M. Silveirinha, C. R. Simovski, and S. A. Tretyakov, “Strong spatial dispersion in wire media in the very large wavelength limit,” Phys. Rev. B |

49. | K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Phonon-polariton excitations in photonic crystals,” Phys. Rev. B |

50. | K. C. Huang, P. Bienstman, J. D. Joannopoulos, K. A. Nelson, and S. Fan, “Field expulsion and reconfiguration in polaritonic photonic crystals,” Phys. Rev. Lett. |

**OCIS Codes**

(160.1190) Materials : Anisotropic optical materials

(160.4670) Materials : Optical materials

(160.4760) Materials : Optical properties

(220.4000) Optical design and fabrication : Microstructure fabrication

(160.1245) Materials : Artificially engineered materials

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: January 12, 2012

Revised Manuscript: April 19, 2012

Manuscript Accepted: April 23, 2012

Published: June 15, 2012

**Citation**

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, "Self-organization approach for THz polaritonic metamaterials," Opt. Express **20**, 14663-14682 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-14663

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