## Synthesizing low loss negative index metamaterial stacks for the mid-infrared using genetic algorithms

Optics Express, Vol. 17, Issue 17, pp. 14771-14779 (2009)

http://dx.doi.org/10.1364/OE.17.014771

Acrobat PDF (691 KB)

### 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

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. 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]

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]

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]

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]

*n*is the effective refractive index and

*Z*is the effective impedance of the metamaterial normalized to the impedance of free space

*Z*

_{0}. FOM

_{n}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. FOM

_{Z}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 FOM

_{n}and FOM

_{Z}, a NIM design can be achieved with the smallest possible absorption and reflection.

*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

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. 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]

*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. 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]

*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]

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]

**30**(24), 3356–3358 (2005). [CrossRef]

**30**(24), 3356–3358 (2005). [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]

*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]

*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

*n*and

*Z*include the unit cell dimension, the thicknesses of the Ag and polyimide layers, and the pixilated geometry differentiating between Ag/polyimide pixels and air holes. We employ a robust GA to optimize the metamaterial design parameters for a given

*n*and

*Z*[9]. GAs are proven to be an effective design tool for electromagnetics as they have been applied to a variety of metamaterials applications such as artificial magnetic conductors (AMCs) [13

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]

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]

*n*and

*Z*of the metamaterial. The first goal for the design is to achieve a refractive index of −1 with a large FOM

_{n}to minimize absorption loss in the metamaterial. The second goal is to obtain an impedance match to free space as indicated by a large FOM

_{Z}in order to minimize the reflection from the metamaterial. These goals are combined to obtain a cost function given bywhere

*n*

_{target}= −1 + 0i is the desired refractive index,

*Z*

_{target}= 1 + 0i is the desired normalized impedance for the metamaterial, and

*freqs*is a range of frequency points over which the GA will search for the best performance. While the weighting for each of these design goals is equal, one goal can be emphasized over the other using weighting coefficients. Also, a fitness function that integrates across frequency such as described in [24

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]

*ε*and

*μ*must be obtained in order to realize a design with high FOM

_{n}and FOM

_{Z}. The GA is an excellent tool for evolving a complex geometry with balanced absorption and impedance losses, where the loss mechanisms are difficult to interpret and fine-tune using simple physical models.

## 4. Numerical results

*n*and

*Z*values match the bulk properties of a cascaded metamaterial.

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]

### 4.1 Low loss NIM with 2 metallic screens

_{n}) [5

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]

**455**(7211), 376–379 (2008). [CrossRef] [PubMed]

_{n}and high FOM

_{Z}. They also possess eight-fold symmetry for a non-polarized response at normal incidence.

*n*and

*Z*for the design are shown in Fig. 3 . 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 FOM

_{n}= 5.0 and FOM

_{Z}= 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

_{Z}) of the metamaterial, which is one of the goals sought by the GA. Also, this geometry possesses eight-fold symmetry and polarization insensitivity for normal incidence, an advantage over the fishnet structures previously considered in the literature.

*n*and

*Z*as well as the scattering magnitudes are shown plotted in Fig. 5 . At

*λ*= 2.86 μm the optimum effective parameters are

*n*= −0.99 + 0.13i and

*Z*= 1.01 – 0.08i. At this wavelength FOM

_{n}= 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, FOM

_{Z}= 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 FOM

_{n}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

*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 FOM

_{n}= 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 FOM

_{Z}= 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.

*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 FOM

_{n}= 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 FOM

_{Z}= 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

_{n}= 5.0 and 7.6 and FOM

_{Z}= 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 FOM

_{n}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. 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]

_{Z}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

## 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. |

2. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science |

3. | A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. |

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. |

5. | G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780nm wavelength,” Opt. Lett. |

6. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. |

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 |

8. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

9. | R. L. Haupt, and D. H. Werner, |

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. |

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. |

12. | V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, “Plasmon modes and negative refraction in metal nanowire composites,” Opt. Express |

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. |

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. |

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. |

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. |

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 |

18. | D. J. Kern, D. H. Werner, and M. Lisovich, “Metaferrites: Using electromagnetic bandgap structures to synthesize metamaterial ferrites,” IEEE Trans. Antenn. Propag. |

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. |

20. | D.-H. Kwon, L. Li, J. A. Bossard, M. G. Bray, and D. H. Werner, “Zero index metamaterials with checkerboard structure,” Elec. Lett. |

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. |

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. |

23. | W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE |

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. |

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 |

26. | C. M. Soukoulis, S. Linden, and M. Wegener, “Physics. Negative refractive index at optical wavelengths,” Science |

**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

- 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]
- 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]
- 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]
- 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]
- G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780nm wavelength,” Opt. Lett. 32(1), 53–55 (2007). [CrossRef]
- 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]
- 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]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000). [CrossRef] [PubMed]
- R. L. Haupt, and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, NJ, 2007).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- W. B. Weir, “Automatic measurement of complex dielectric constant and permeability at microwave frequencies,” Proc. IEEE 62(1), 33–36 (1974). [CrossRef]
- 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]
- 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]
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