## Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation

Optics Express, Vol. 16, Issue 16, pp. 11802-11807 (2008)

http://dx.doi.org/10.1364/OE.16.011802

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### Abstract

Planar chiral metamaterials comprising double-layer dielectricmetal-dielectric resonant structures in the shape of a gammadion are presented in the near-infrared regime. The unit cell of the doubly-periodic metamaterial design is optimized using the genetic algorithm for maximum circular dichroism and for maximum optical activity. A circular dichroism value in excess of 50% is predicted for the optimized design. Maximum polarization rotatory powers in terms of the minimum allowed transmittances are also obtained and presented.

© 2008 Optical Society of America

## 1. Introduction

1. A. Papakostas, A. Potts, D. M. Pagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. **90**, 107404 (2003). [CrossRef] [PubMed]

2. T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, “Optical activity in subwavelength-period arrays of chiral metallic particles,” Appl. Phys. Lett. **83**, 234–236 (2003). [CrossRef]

3. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. **95**, 227401 (2005). [CrossRef] [PubMed]

4. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. **97**, 167401 (2006). [CrossRef] [PubMed]

5. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. **97**, 177401 (2006). [CrossRef] [PubMed]

6. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electro-magnetic coupling,” Appl. Phys. Lett. **90**, 223113 (2007). [CrossRef]

7. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A **76**, 023811 (2007). [CrossRef]

8. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. **32**, 856–858 (2007). [CrossRef] [PubMed]

8. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. **32**, 856–858 (2007). [CrossRef] [PubMed]

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

## 2. Metamaterial design, analysis, and optimization methodologies

*p*in both the

*x*̂ and

*ŷ*directions. The resonator structure comprises two silver (Ag) layers of thickness

*t*separated by an alumina (Al

_{2}O

_{3}) layer of thickness

*d*. This is an example of the metal-dielectric-metal sandwich structures typically employed as planar magnetic resonators in optical negative-index metamaterials [10

10. 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]

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

12. D.-H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Near-infrared metamaterials with dual-band negative-index characteristics,” Opt. Express **15**, 1647–1652 (2007). [CrossRef] [PubMed]

*l*/2×

*w*and

*s*×

*r*connected at a right angle. A left-facing gammadion shown in Fig. 1(a) is employed in this study. The metamaterial is finally placed on an electrically thick glass substrate, which is treated as a half space in this study.

*z*̂ direction. For each circularly polarized incident wave, the four-fold rotational symmetry of the metamaterial structure with respect to the

*z*̂ axis guarantees that the reflected and transmitted fields have purely circular polarization states of the opposite and the same handednesses as the incident wave, respectively. A periodic version of the finite element-boundary integral fullwave technique [13

13. J. L. Volakis, A. Chatterjee, and L. C. Kempel, *Finite Element Method for Electromagnetics* (IEEE Press, Piscataway, NJ, 1998). [CrossRef]

*r*

_{±}and

*t*

_{±}, corresponding to the RCP/LCP incident light waves are evaluated at the top surface and the metamaterial-glass interface, respectively. Furthermore, the reflectance (

*R*

_{±}) and transmittance (

*T*

_{±}) are obtained from the associated values of

*r*

_{±}and

*t*

_{±}. Due to the four-fold structural symmetry, the four quantities

*r*

_{±}and

*t*

_{±}can be obtained from a single scattering analysis with an incident field linearly polarized either in the

*x*̂ or

*ŷ*direction. In the numerical analysis, alumina and glass are treated as lossless non-dispersive dielectric materials with relative permittivity values of 2.6244 and 2.25, respectively. Measured permittivity values reported in [14

14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**, 4370–4379 (1972). [CrossRef]

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

*f*. The value of

*f*is maximized through an evolutionary process within the solution space of the parameters to be determined. The GA has been previously employed to optimize the unit-cell geometry of optical metamaterials in the visible range to achieve a desired set of equivalent material parameter values [15

15. D.-H. Kwon and D. H. Werner, “Low-index metamaterial designs in the visible spectrum,” Opt. Express **15**, 9267–9272 (2007). [CrossRef] [PubMed]

*p*,

*l*,

*w*,

*r*,

*s*,

*t*, and

*d*– are optimized. The allowable ranges of these parameters are set to 0.3

*μ*m≤

*p*≤0.55

*μ*m, 0≤

*l*≤

*p*,0≤

*w*≤1,0≤

*r*≤(

*p*-

*w*)/2,0≤

*s*≤(

*l*-

*w*)/2,20 nm≤

*t*≤50 nm, and 20 nm≤

*d*≤50 nm. The ranges of

*l*,

*w*,

*r*, and

*s*permit a wide scope of sizes and shapes of the silver-alumina-silver resonator to be explored within the unit cell. At one extreme, no existence of any resonator structure is included (although this particular design realization is not interesting). At the other extreme, the entire unit cell volume may be filled with the resonator structure. It is noted that continuity of the gammadion structure across the unit cell boundaries is possible if

*l*=

*p*is satisfied. The target wavelength

*λ*for the optimal performance search is limited to 0.9

*μ*m≤

*λ*≤1.1

*μ*m in the near-IR range.

## 3. Strong circular dichroism

*A*

_{±}are the absorbances for the RCP and LCP incident waves, which are given by

*A*

_{±}=1-

*R*

_{±}-

*T*

_{±}. The second equality in (1) follows from

*R*

_{+}=

*R*

_{-}, which can be obtained from the reciprocity theorem for structures having four-fold rotational symmetry and a normally incident plane wave [7

7. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A **76**, 023811 (2007). [CrossRef]

*f*=0.563 with

*T*

_{+}=0.591 and

*T*

_{-}=0.028 at

*λ*=1.087

*μ*m. The optimized geometrical parameter values were found to be

*p*=534 nm,

*l*=437 nm,

*w*=194 nm,

*r*=97.1 nm,

*s*=24.3 nm,

*t*=24.0 nm, and

*d*=20.0 nm. The optimized metamaterial geometry and the transmittance spectra for the two circular polarizations are shown in Fig. 2. The transmittance curves for

*T*

_{±}lie on top of each other away from the optimal wavelength 1.087

*μ*m, around which

*T*

_{+}and

*T*

_{-}change sharply in opposite directions. At the optimal wavelength, the absorbance values were found to be

*A*

_{+}=0.090 and

*A*

_{-}= 0.653. Since, based on reciprocity, the values

*R*

_{±}=0.318 are both the same, then it follows that the difference in the transmittances relies completely on loss, which is in accordance with the observation made in [4

4. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. **97**, 167401 (2006). [CrossRef] [PubMed]

8. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. **32**, 856–858 (2007). [CrossRef] [PubMed]

**32**, 856–858 (2007). [CrossRef] [PubMed]

*d*forced to zero. Without the alumina spacer layer, there is no magnetic resonance to cause strong absorption. Even the design optimized for strong CD produced (results not shown) a meager fitness value of

*f*=0.0026, which practically amounts to a non-existent CD.

## 4. Large polarization rotation

*t*

_{±}be written as

*t*

_{±}=|

*t*

_{±}|exp(

*iϕ*

_{±}), where an exp(-

*iωt*) time convention is assumed. For a linearly polarized illumination at normal incidence, the polarization rotation angle

*θ*and the ellipticity

*τ*of the transmitted wave are given by [7

7. B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A **76**, 023811 (2007). [CrossRef]

*θ*is measured from the polarization direction of the incident electric field. The maximum norm of practical importance for

*θ*is equal to 90°.

6. E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electro-magnetic coupling,” Appl. Phys. Lett. **90**, 223113 (2007). [CrossRef]

*T*

_{±}as low as -30 dB [5

5. A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. **97**, 177401 (2006). [CrossRef] [PubMed]

*T*

_{±}are permitted, a polarization rotation by 90° may be easily obtained because only a small amount of polarization-sensitive response will be necessary to make

*θ*large. This condition is satisfied if the two curves for

*t*

_{±}in the complex plane traverse the origin in opposite directions as a function of wavelength or frequency. Therefore, it is expected that the maximum achievable polarization rotation will be a decreasing function of the minimum transmittance required during the optimization.

*T*

_{min}by requiring

*T*

_{±}≥

*T*

_{min}during the optimization. Six different values were used for

*T*

_{min}from 0 to 0.5 at an interval of 0.1. The converged fitnesses, optimized parameter values, and polarization rotation performances are summarized in Table 1 together with the associated values for

*T*

_{±}and

*τ*for each choice of

*T*

_{min}. First, it can be observed that polarization rotations close to 90° can be obtained with values of

*T*

_{min}ranging from zero up to 30%. Beyond 30%, the maximum value of

*θ*decreases and the polarization rotation power is limited. Secondly, the optimized planar chiral structure is connected across the unit cell boundary for

*T*

_{min}=0.2 and 0.3 because

*l*=

*p*. This shows that isolated planar chiral structures are not a requirement for strong polarization rotations. For all other designs, the gammadion resonators are physically separated from one another.

*T*

_{min}=0.5 are shown in Fig. 3. The total thickness of the metamaterial is found to be 120 nm. The maximum polarization rotation of 21.0 ° is realized at

*λ*=1.093

*μ*m (Fig. 3(c)) with the values of transmittance

*T*

_{+}=0.561 and

*T*

_{-}=0.511 (Fig. 3(b)). In terms of the specific rotation, this amounts to a giant rotatory power of 1.75×10

^{5°}/mm. Around

*λ*=1.093

*μ*m,

*T*

_{±}are steeply decreasing functions of

*λ*and they fall below the minimum requirement of 50% transmittance at longer wavelengths. The value of the ellipticity is equal to 0.023 at the optimal wavelength (Fig. 3(d)), indicating that the polarization of the transmitted light, resulting from linearly polarized incident light, will be close to linear.

*d*forced to zero to eliminate the possibility of resonance. The optimization for

*T*

_{min}=0.1 resulted in

*f*=0.414 with

*θ*=-0.96°, verifying that a resonance and the associated loss are essential in producing strong polarization rotations.

## 5. Conclusion

*λ*= 1.087

*μ*m for the optimized design, which is larger by an order of magnitude than those in previously reported designs. Maximum polarization rotatory powers were studied for the first time in relation to the minimum allowed transmittances. Strong polarization rotations close to 90° were obtained subject to the restriction that minimum transmittance values be less than 30%. Higher required transmittances were seen to result in weaker polarization rotation powers. However, a strong polarization rotation in excess of 20° was predicted for a 120 nm-thick metamaterial even when a 50% minimum transmittance restriction was enforced.

## Acknowledgments

## References and links

1. | A. Papakostas, A. Potts, D. M. Pagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. |

2. | T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, “Optical activity in subwavelength-period arrays of chiral metallic particles,” Appl. Phys. Lett. |

3. | M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, “Giant optical activity in quasi-two-dimensional planar nanostructures,” Phys. Rev. Lett. |

4. | V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, “Asymmetric propagation of electromagnetic waves through a planar chiral structure,” Phys. Rev. Lett. |

5. | A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, “Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure,” Phys. Rev. Lett. |

6. | E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, “Giant optical gyrotropy due to electro-magnetic coupling,” Appl. Phys. Lett. |

7. | B. Bai, Y. Svirko, J. Turunen, and T. Vallius, “Optical activity in planar chiral metamaterials: Theoretical study,” Phys. Rev. A |

8. | M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. |

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

10. | 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. |

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

12. | D.-H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Near-infrared metamaterials with dual-band negative-index characteristics,” Opt. Express |

13. | J. L. Volakis, A. Chatterjee, and L. C. Kempel, |

14. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

15. | D.-H. Kwon and D. H. Werner, “Low-index metamaterial designs in the visible spectrum,” Opt. Express |

**OCIS Codes**

(050.1930) Diffraction and gratings : Dichroism

(160.4760) Materials : Optical properties

(260.5430) Physical optics : Polarization

**ToC Category:**

Metamaterials

**History**

Original Manuscript: March 17, 2008

Revised Manuscript: July 14, 2008

Manuscript Accepted: July 16, 2008

Published: July 23, 2008

**Citation**

Do-Hoon Kwon, Pingjuan L. Werner, and Douglas H. Werner, "Optical planar chiral metamaterial designs for strong circular dichroism and polarization rotation," Opt. Express **16**, 11802-11807 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-16-11802

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### References

- A. Papakostas, A. Potts, D. M. Pagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, "Optical manifestations of planar chirality," Phys. Rev. Lett. 90, 107404 (2003). [CrossRef] [PubMed]
- T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, "Optical activity in subwavelength-period arrays of chiral metallic particles," Appl. Phys. Lett. 83, 234-236 (2003). [CrossRef]
- M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, "Giant optical activity in quasi-two-dimensional planar nanostructures," Phys. Rev. Lett. 95, 227401 (2005). [CrossRef] [PubMed]
- V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, "Asymmetric propagation of electromagnetic waves through a planar chiral structure," Phys. Rev. Lett. 97, 167401 (2006). [CrossRef] [PubMed]
- A. V. Rogacheva, V. A. Fedotov, A. S. Schwanecke, and N. I. Zheludev, "Giant gyrotropy due to electromagnetic-field coupling in a bilayered chiral structure," Phys. Rev. Lett. 97, 177401 (2006). [CrossRef] [PubMed]
- E. Plum, V. A. Fedotov, A. S. Schwanecke, N. I. Zheludev, and Y. Chen, "Giant optical gyrotropy due to electromagnetic coupling," Appl. Phys. Lett. 90, 223113 (2007). [CrossRef]
- B. Bai, Y. Svirko, J. Turunen, and T. Vallius, "Optical activity in planar chiral metamaterials: Theoretical study," Phys. Rev. A 76, 023811 (2007). [CrossRef]
- M. Decker, M. W. Klein, M. Wegener, and S. Linden, "Circular dichroism of planar chiral magnetic metamaterials," Opt. Lett. 32, 856-858 (2007). [CrossRef] [PubMed]
- R. L. Haupt and D. H. Werner, Genetic Algorithms in Electromagnetics (Wiley, Hoboken, NJ, 2007). [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]
- G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (2007). [CrossRef]
- D.-H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, "Near-infrared metamaterials with dual-band negative-index characteristics," Opt. Express 15, 1647-1652 (2007). [CrossRef] [PubMed]
- J. L. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics (IEEE Press, Piscataway, NJ, 1998). [CrossRef]
- P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
- D.-H. Kwon and D. H. Werner, "Low-index metamaterial designs in the visible spectrum," Opt. Express 15, 9267-9272 (2007). [CrossRef] [PubMed]

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