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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 14771–14779
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Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms

Jeremy A. Bossard, Seokho Yun, Douglas H. Werner, and Theresa S. Mayer  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 14771-14779 (2009)
http://dx.doi.org/10.1364/OE.17.014771


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Abstract

Negative index metamaterial designs for the mid-infrared with low absorption and impedance mismatch losses are presented. A robust genetic algorithm is employed to optimize the flexible metamaterial structure for targeted refractive index and impedance values. A new figure of merit is introduced to evaluate the impedance match of the metamaterial to free space. Two designs are presented demonstrating low-loss characteristics for a thin metamaterial with two metal screens and a thick metamaterial stack with five screens. The device performance is analyzed when adding more screens to the structure, revealing that optimizing a thick stack produces a metamaterial with properties approaching those of a bulk material.

© 2009 OSA

1. Introduction

In recent years, there has been a substantial research interest in demonstrating metamaterials with a negative refractive index from the RF [1

1. 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(18), 4184–4187 (2000). [CrossRef] [PubMed]

3

3. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]

] through the optical [4

4. 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(24), 3356–3358 (2005). [CrossRef]

7

7. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

] regions of the electromagnetic spectrum. This research interest was sparked in 2000 when Pendry first proposed a ‘perfect’ flat lens with a refractive index of −1 that could in principle overcome the diffraction limit of conventional optics [8

8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

]. Experiments have proven that a negative index metamaterial (NIM) can be realized when the permeability and permittivity are simultaneously negative over the same wavelength range and that a flat lens constructed from such a metamaterial exhibits super-resolution [2

2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

, 3

3. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]

]. However, for infrared and optical wavelengths, there are problems that need to be addressed in order to realize a practical flat lens. First, the material losses due to absorption and impedance mismatches to the surrounding media for optical NIMs are quite high. Secondly, most optical NIM demonstrations have been thin structures, which are unsuitable for use in a flat lens. Recently, an optical NIM stack was fabricated that consists of many alternating layers of metal and dielectric insulator [7

7. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

], representing a step towards realizing a practical, optical NIM.

This paper presents an optimization strategy for realizing low-loss NIMs for the mid-IR spectrum targeting the atmospheric window from 3 μm to 5 μm with very small absorption losses and a good impedance match to free space. The primary goal of this research is to introduce a design tool and methodology for minimizing the losses in mid-IR NIMs. The proposed metamaterial structure consists of a stack of alternating layers of silver (Ag) metal and polyimide dielectric perforated by a two dimensional periodic pattern of air holes. The parallel metallic layers provide control over the permittivity and permeability, which can be adjusted by using a genetic algorithm (GA) optimization technique (see Fig. 1
Fig. 1 Flowchart showing the genetic algorithm synthesis procedure used to generate low-loss NIM stack designs.
) [9

9. R. L. Haupt, and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, NJ, 2007).

] to achieve both a negative refractive index and low loss, as quantified by the following figures of merit (FOM):
FOMn=|n'n"|,FOMZ=1|Z1|,
(1)
where n is the effective refractive index and Z is the effective impedance of the metamaterial normalized to the impedance of free space Z 0 . FOMn is the ratio of the real part of the index to the imaginary part and provides a measure of the absorption loss in the metamaterial. FOMZ describes the impedance match of the metamaterial to the surrounding medium (i.e. free space) and is often neglected in the NIM literature. By optimizing for large values of FOMn and FOMZ, a NIM design can be achieved with the smallest possible absorption and reflection.

This paper also examines the bulk properties (i.e., approaching those of an infinite stack) of the metamaterial by including an additional polyimide and Ag layer to designs optimized with two and five Ag screens. This analysis demonstrates that it is more effective to optimize a metamaterial stack with many layers in order to achieve a practical low-loss NIM. Optimizing a large stack also results in a metamaterial with properties approaching those of a bulk material.

2. Metamaterial structure

The metamaterial structure proposed here consists of stacked metallic screens sandwiching layers of dielectric. The metal-dielectric stack is perforated by air holes in a periodic pattern defined by a unit cell such as the one shown in Fig. 2
Fig. 2 13 x 13 pixel geometry for a negative index metamaterial with two metal screens separated by an insulator. The pixel size, Ag thickness, and polyimide thickness for this design are 107 nm, 75 nm, and 115 nm, respectively. (a) The top and side views of the unit cell, which is periodic in two dimensions. (b) 3D isometric view of the metamaterial.
. The unit cell geometry representing the stack and air hole locations is constrained to possess eight-fold symmetry, so that the metamaterial appears the same to normally incident waves polarized with the electric field directed vertically or horizontally with respect to the unit cell geometry. Thus, metamaterials with the proposed structure will have a polarization independent response at normal incidence, unlike the optical NIMs found in the literature, which are designed for linear polarization [4

4. 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(24), 3356–3358 (2005). [CrossRef]

7

7. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

]. The materials in the structure were chosen a priori to be Ag and polyimide because they both have low intrinsic losses in the mid-IR wavelength range from 2 μm to 5 μm. We have also previously studied these materials for use in planar metallo-dielectric filters for the far- and mid-IR spectra [10

10. J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antenn. Propag. 54(4), 1265–1276 (2006). [CrossRef]

, 11

11. Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett. 92(26), 263106 (2008). [CrossRef]

].

The Ag screens in the structure provide control over both the effective permittivity ε and permeability μ of the metamaterial. Operating under the same principals as the paired metallic nanowire arrays studied theoretically [12

12. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003). [CrossRef] [PubMed]

] and experimentally [4

4. 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(24), 3356–3358 (2005). [CrossRef]

] for use in optical NIMs, the neighboring layers of Ag in the proposed structure can form parallel plate magnetic resonators for H-field components transverse to the surface of the metamaterial. At resonance the transverse magnetic field excites a circulating current on the neighboring Ag patches, which, in turn, induces a magnetic field opposing the external magnetic field [4

4. 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(24), 3356–3358 (2005). [CrossRef]

]. Similarly, isolated metallic patches can provide electric resonances for transverse E-field components [4

4. 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(24), 3356–3358 (2005). [CrossRef]

, 12

12. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003). [CrossRef] [PubMed]

]. A fully connected geometry results in a Drude behavior for ε, similar to a metallic mesh that exploits the inherent Drude properties of a metal film while lowering the plasma frequency ω p of the effective permittivity by introducing air holes into the film [6

6. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]

]. The unit cell geometry is pixilated, so that complex structures can be considered in the design process. This provides great flexibility in controlling Lorentz and Drude characteristic resonances in the ε and μ profiles to simultaneously achieve a negative index with a small imaginary component (i.e., low absorption loss) and an impedance match to free space.

3. Design methodology

4. Numerical results

In order to demonstrate the effectiveness of the proposed design approach for synthesizing low loss NIMs, two examples will be presented. The first design consists of two Ag screens separated by a polyimide film, and the second design is a stack of five Ag screens separated by polyimide layers. Further analysis is presented to show the effect of adding another polyimide/Ag layer to the structure and to evaluate how well the effective n and Z values match the bulk properties of a cascaded metamaterial.

4.1 Low loss NIM with 2 metallic screens

The scattering parameters and effective n and Z for the design are shown in Fig. 3
Fig. 3 Effective and scattering parameters for the NIM design shown in Fig. 2: (a) Refractive index n and impedance normalized to free space Z. The optimization range (gray box) and optimum wavelength (vertical dashed line) are highlighted. (b) Reflection R, transmission T, and absorption A.
. It is notable that this design possesses broadband high transmission extending from the negative index region to shorter wavelengths where the index crosses zero and becomes positive (i.e., ZIM and PIM regions). Part of the reason for high transmission over a large wavelength range is that the normalized impedance Z has a broad band that is slowly varying around the free space impedance, giving a reflection coefficient lower than −10 dB from 2.53 μm to 3.04 μm in wavelength. Also, n” is small, resulting in low absorption from shorter wavelengths up to the optimum wavelength. The index approaches −1 at λ = 2.93 μm wavelength, where n = −1.04 + 0.21i and Z = 1.01 – 0.03i. The figures of merit at λ = 2.93 μm for this design are calculated to be FOMn = 5.0 and FOMZ = 31.6. The scattering parameter magnitudes at λ = 2.93 μm are transmission |T| = −1.1 dB, reflection |R| = −34.7 dB, and absorption |A| = −6.7 dB. The reflection null is indicative of an excellent impedance match to free space, and the absorption loss is minimized along with n”.

4.2 Low loss NIM stack with 5 metallic screens

The effective n and Z as well as the scattering magnitudes are shown plotted in Fig. 5
Fig. 5 Effective and scattering parameters for the NIM in Fig. 4: (a) Refractive index n and normalized impedance Z. The optimization range (gray box) and optimum wavelength (vertical dashed line) are highlighted. (b) Reflection R, transmission T, and absorption A from a normally incident wave.
. At λ = 2.86 μm the optimum effective parameters are n = −0.99 + 0.13i and Z = 1.01 – 0.08i. At this wavelength FOMn = 7.6, which is higher than the figure of merit for the design containing only two Ag screens, meaning that this design will have lower absorption per unit thickness. On the other hand, FOMZ = 12.4 is lower than the first design, resulting in a higher reflection. The scattering parameter magnitudes at the optimum wavelength λ = 2.86 μm are transmission |T| = −1.3 dB, reflection |R| = −23.6 dB, and absorption |A| = −5.9 dB. Despite the better FOMn for this design, the transmission is slightly lower because this design has approximately double the thickness of the two-screen design, resulting in an increased absorption. Nevertheless, the transmission properties are still remarkably good. The excellent performance of this design indicates that for practical, thicker NIMs at mid-IR wavelengths, the losses can be minimized by optimizing a metamaterial stack in its entirety. In moving from 2 metal screens to 5 metal screens, the number of generations required for convergence doubled, and the computation time required on the cluster increased by nearly 5 times. Thus, further increasing the number of screens in the optimization is expected to greatly increase the computational resources required for the GA to converge on a solution.

4.3 Effect of adding a metallic screen

In order to evaluate how closely the effective parameters for the two designs match the desired bulk metamaterial properties, the effect of adding an Ag screen to each design will be analyzed. Figure 6
Fig. 6 Metamaterial cross-section and refractive index when adding a third metallic screen to the design in Fig. 2: (a) Cross-section view of structure. (b) Refractive index n for two (blue curves) and three (green curves) metal screens.
shows a cross-sectional view of the first design when adding a metal screen and an overlay plot showing the effect of the third screen on n. While the NIM band for the modified metamaterial is still present, the location of the band has shifted and the loss characteristics have changed significantly. The optimum wavelength where n’ = −1 has shifted to λ = 2.86 μm, where n = −1.03 + 0.22i and Z = 1.85 – 0.04i. The scattering magnitudes at this wavelength are |T| = −3.0 dB, |R| = −7.7 dB, and |A| = −4.8 dB. The reduced FOMn = 4.64 as well as the increased metamaterial thickness has contributed to a higher absorption, and the poor impedance match has resulted in a small FOMZ = 1.13 and much higher reflection. The drastic changes seen in n and Z when increasing the number of metal screens in this design indicate that the effective properties are strongly affected by the coupling with the third screen. Hence, this design does not possess bulk-like effective properties.

The results of adding a metal screen to the second design are shown in Fig. 7
Fig. 7 Metamaterial structure and refractive index when adding an additional metal screen to the design in Fig. 4: (a) Cross-section view showing the device with five and six metal layers. (b) Refractive index n for the device with five (blue curves) and six (green curves) metal screens. The performance of this design does not change significantly when another metal screen is added.
. As can be seen in the overlay showing the index for the five screen design and the modified design, the NIM band has not changed (moved) significantly and retains its loss characteristics at the optimum wavelength. At λ = 2.85 μm the optimum effective parameters for the modified structure are n = 0.99 + 0.14i and Z = 1.27 – 0.14i, and the scattering magnitudes at this wavelength are |T| = −1.9 dB, |R| = −13.2 dB, and |A| = −5.0 dB. The slightly lower NIM FOMn = 7.07 and the increased metamaterial size contribute to an increased absorption, and the impedance match is not as good as the original design, resulting in a higher reflection and lower FOMZ = 3.3. However, this design still performs very well with the added Ag screen, indicating that by optimizing for a larger metamaterial stack, the resulting design yields effective properties approaching those of a bulk material.

5. Conclusion

A flexible metamaterial platform consisting of stacked metal and dielectric screens perforated with a periodic array of air holes was presented along with a synthesis procedure for realizing low loss NIMs. The metamaterial structure provides control over the electric and magnetic responses of the device, and GA optimization can be used to exploit this flexibility to achieve a negative index along with low absorption and impedance mismatch losses. Designs were presented to demonstrate that these low loss characteristics can be achieved both for thin metamaterials with two metal screens as well as for thicker metamaterial stacks with many alternating metal and dielectric layers. These designs possessed high figures of merit with FOMn = 5.0 and 7.6 and FOMZ = 31.6 and 12.4, respectively, as well as low transmission attenuations of −1.1 dB and −1.3 dB. While the values obtained for FOMn represent the state of the art when compared with experimental IR/optical NIMs found in the literature [6

6. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]

, 25

25. C. García-Meca, R. Ortuño, R. Salvador, A. Martínez, and J. Martí, “Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths,” Opt. Express 15(15), 9320–9325 (2007). [CrossRef] [PubMed]

, 26

26. C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]

], introducing FOMZ as a second optimization goal advances the field by minimizing reflection losses due to impedance mismatch. Further analysis conducted by adding a metal screen to both designs revealed that by optimizing a thicker metamaterial stack, the recovered effective properties n and Z are approaching those of a bulk metamaterial. In the future metamaterials with larger stacks will be investigated theoretically and experimentally for low loss and bulk effective properties as well as the extension of this design strategy to near-IR and optical wavelengths.

Acknowledgements

This work was supported by the Penn State MRSEC under NSF grant DMR-0820404.

References and links

1.

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(18), 4184–4187 (2000). [CrossRef] [PubMed]

2.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]

3.

A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]

4.

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(24), 3356–3358 (2005). [CrossRef]

5.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780nm wavelength,” Opt. Lett. 32(1), 53–55 (2007). [CrossRef]

6.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]

7.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]

8.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]

9.

R. L. Haupt, and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, NJ, 2007).

10.

J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antenn. Propag. 54(4), 1265–1276 (2006). [CrossRef]

11.

Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett. 92(26), 263106 (2008). [CrossRef]

12.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003). [CrossRef] [PubMed]

13.

D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, “The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces,” IEEE Trans. Antenn. Propag. 53(1), 8–17 (2005). [CrossRef]

14.

D. J. Kern, D. H. Werner, M. J. Wilhelm, and K. H. Church, “Genetically engineered multiband high-impedance frequency selective surfaces,” Microw. Opt. Technol. Lett. 38(5), 400–403 (2003). [CrossRef]

15.

Y. Yuan, C. H. Chan, K. F. Man, and K. M. Luk, “Meta-material surface design using the hierarchical genetic algorithm,” Microw. Opt. Technol. Lett. 39(3), 226–230 (2003). [CrossRef]

16.

D. J. Kern and D. H. Werner, “A genetic algorithm approach to the design of ultra-thin electromagnetic bandgap absorbers,” Microw. Opt. Technol. Lett. 38(1), 61–64 (2003). [CrossRef]

17.

P. Y. Chen, C. H. Chen, H. Wang, J. H. Tsai, and W. X. Ni, “Synthesis design of artificial magnetic metamaterials using a genetic algorithm,” Opt. Express 16(17), 12806–12818 (2008). [CrossRef] [PubMed]

18.

D. J. Kern, D. H. Werner, and M. Lisovich, “Metaferrites: Using electromagnetic bandgap structures to synthesize metamaterial ferrites,” IEEE Trans. Antenn. Propag. 53(4), 1382–1389 (2005). [CrossRef]

19.

M. A. Gingrich and D. H. Werner, “Synthesis of low/zero index of refraction metamaterials from frequency selective surfaces using genetic algorithms,” IEE Electron. Lett. 41(23), 1266–1267 (2005). [CrossRef]

20.

D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, “Zero index metamaterials with checkerboard structure,” Elec. Lett. 43(6), 319–320 (2007). [CrossRef]

21.

T. F. Eibert, J. L. Volakis, D. R. Wilton, and D. R. Jackson, “Hybrid FE/BI modeling of 3-D doubly periodic structures utilizing triangular prismatic elements and an MPIE formulation accelerated by the Ewald transformation,” IEEE Trans. Antenn. Propag. 47(5), 843–850 (1999). [CrossRef]

22.

A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37(22), 5271–5283 (1998). [CrossRef]

23.

W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62(1), 33–36 (1974). [CrossRef]

24.

J. Radovanović, V. Milanović, Z. Ikonić, and D. Indjin, “Application of the genetic algorithm to the optimized design of semimagnetic semiconductor-based spin-filters,” J. Phys. D Appl. Phys. 40(17), 5066–5070 (2007). [CrossRef]

25.

C. García-Meca, R. Ortuño, R. Salvador, A. Martínez, and J. Martí, “Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths,” Opt. Express 15(15), 9320–9325 (2007). [CrossRef] [PubMed]

26.

C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science 315(5808), 47–49 (2007). [CrossRef] [PubMed]

OCIS Codes
(160.3918) Materials : Metamaterials
(310.4165) Thin films : Multilayer design

ToC Category:
Metamaterials

History
Original Manuscript: May 26, 2009
Revised Manuscript: July 25, 2009
Manuscript Accepted: July 28, 2009
Published: August 5, 2009

Citation
Jeremy A. Bossard, Seokho Yun, Douglas H. Werner, and Theresa S. Mayer, "Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms," Opt. Express 17, 14771-14779 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14771


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References

  1. 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(18), 4184–4187 (2000). [CrossRef] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001). [CrossRef] [PubMed]
  3. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. 92(11), 117403 (2004). [CrossRef] [PubMed]
  4. 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(24), 3356–3358 (2005). [CrossRef]
  5. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780nm wavelength,” Opt. Lett. 32(1), 53–55 (2007). [CrossRef]
  6. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006). [CrossRef] [PubMed]
  7. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008). [CrossRef] [PubMed]
  8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  9. R. L. Haupt, and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, NJ, 2007).
  10. J. A. Bossard, D. H. Werner, T. S. Mayer, J. A. Smith, Y. Tang, R. P. Drupp, and L. Li, “The design and fabrication of planar multiband metallodielectric frequency selective surfaces for infrared applications,” IEEE Trans. Antenn. Propag. 54(4), 1265–1276 (2006). [CrossRef]
  11. Y. Tang, J. A. Bossard, D. H. Werner, and T. S. Mayer, “Single-layer metallodielectric nanostructures as dual-band midinfrared filters,” Appl. Phys. Lett. 92(26), 263106 (2008). [CrossRef]
  12. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express 11(7), 735–745 (2003). [CrossRef] [PubMed]
  13. D. J. Kern, D. H. Werner, A. Monorchio, L. Lanuzza, and M. Wilhelm, “The design synthesis of multiband artificial magnetic conductors using high impedance frequency selective surfaces,” IEEE Trans. Antenn. Propag. 53(1), 8–17 (2005). [CrossRef]
  14. D. J. Kern, D. H. Werner, M. J. Wilhelm, and K. H. Church, “Genetically engineered multiband high-impedance frequency selective surfaces,” Microw. Opt. Technol. Lett. 38(5), 400–403 (2003). [CrossRef]
  15. Y. Yuan, C. H. Chan, K. F. Man, and K. M. Luk, “Meta-material surface design using the hierarchical genetic algorithm,” Microw. Opt. Technol. Lett. 39(3), 226–230 (2003). [CrossRef]
  16. D. J. Kern and D. H. Werner, “A genetic algorithm approach to the design of ultra-thin electromagnetic bandgap absorbers,” Microw. Opt. Technol. Lett. 38(1), 61–64 (2003). [CrossRef]
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