Abstract

We have recently shown that metamaterials composed of three-dimensional gold helices periodically arranged on a square lattice can be used as compact “thin-film” circular polarizers with one octave bandwidth. The physics of the motif of these artificial crystals is closely related to that of microwave sub-wavelength helical antennas in end-fire geometry. Here, we systematically study the dependence of the metamaterial’s chiral optical properties on helix pitch, helix radius, two-dimensional lattice constant, wire radius, number of helix pitches, and angle of incidence. Our numerical calculations show that the optical properties are governed by resonances of the individual helices, yet modified by interaction effects. Furthermore, our study shows possibilities and limitations regarding performance optimization.

© 2010 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition).
    [PubMed]
  2. K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 368(23), 621–644 (1920).
    [CrossRef]
  3. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
    [CrossRef] [PubMed]
  4. P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
    [CrossRef] [PubMed]
  5. M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag. 56(2), 390–401 (2008).
    [CrossRef]
  6. R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
    [CrossRef]
  7. Z.-Y. Zhang and Y.-P. Zhao, “Optical properties of helical and multiring Ag nanostructures: The effect of pitch height,” J. Appl. Phys. 104(1), 013517 (2008).
    [CrossRef]
  8. J. D. Kraus, and R. J. Marhefka, Antennas: For All Applications (McGraw-Hill, New York, 2003, 3rd edition).
  9. H.-S. Kitzerow, and C. Bahr, eds., Chirality in Liquid Crystals (Springer, Heidelberg, 2001, 1st edition).
  10. M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
    [CrossRef] [PubMed]
  11. M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
    [CrossRef]
  12. www.cst.com/Content/Products/MWS/Overview.aspx
  13. www.lumerical.com
  14. www.jcmwave.com
  15. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).
  16. D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design,” Opt. Express 16(16), 11822–11829 (2008).
    [CrossRef] [PubMed]

2009 (2)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

2008 (3)

Z.-Y. Zhang and Y.-P. Zhao, “Optical properties of helical and multiring Ag nanostructures: The effect of pitch height,” J. Appl. Phys. 104(1), 013517 (2008).
[CrossRef]

M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag. 56(2), 390–401 (2008).
[CrossRef]

D. H. Kwon, D. H. Werner, A. V. Kildishev, and V. M. Shalaev, “Material parameter retrieval procedure for general bi-isotropic metamaterials and its application to optical chiral negative-index metamaterial design,” Opt. Express 16(16), 11822–11829 (2008).
[CrossRef] [PubMed]

2007 (2)

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[CrossRef] [PubMed]

2003 (1)

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
[CrossRef] [PubMed]

1920 (1)

K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 368(23), 621–644 (1920).
[CrossRef]

Abdeddaïm, R.

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

Bade, K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

Belov, P. A.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
[CrossRef] [PubMed]

Decker, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Deubel, M.

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Gallas, B.

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

Gansel, J. K.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

Guida, G.

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

Kildishev, A. V.

Kwon, D. H.

Linden, S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Lindman, K. F.

K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 368(23), 621–644 (1920).
[CrossRef]

Priou, A.

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

Rill, M. S.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

Rivory, J.

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

Saile, V.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

Shalaev, V. M.

Silveirinha, M. G.

M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag. 56(2), 390–401 (2008).
[CrossRef]

Simovski, C. R.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
[CrossRef] [PubMed]

Thiel, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[CrossRef] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Tretyakov, S. A.

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
[CrossRef] [PubMed]

von Freymann, G.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[CrossRef] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Wegener, M.

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

M. Thiel, G. von Freymann, and M. Wegener, “Layer-by-layer three-dimensional chiral photonic crystals,” Opt. Lett. 32(17), 2547–2549 (2007).
[CrossRef] [PubMed]

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Werner, D. H.

Zhang, Z.-Y.

Z.-Y. Zhang and Y.-P. Zhao, “Optical properties of helical and multiring Ag nanostructures: The effect of pitch height,” J. Appl. Phys. 104(1), 013517 (2008).
[CrossRef]

Zhao, Y.-P.

Z.-Y. Zhang and Y.-P. Zhao, “Optical properties of helical and multiring Ag nanostructures: The effect of pitch height,” J. Appl. Phys. 104(1), 013517 (2008).
[CrossRef]

Adv. Mater. (1)

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, “Polarization stop bands in chiral polymeric three-dimensional photonic crystals,” Adv. Mater. 19(2), 207–210 (2007).
[CrossRef]

Ann. Phys. (1)

K. F. Lindman, “Über eine durch ein isotropes System von spiralförmigen Resonatoren erzeugte Rotationspolarisation der elektromagnetischen Wellen,” Ann. Phys. 368(23), 621–644 (1920).
[CrossRef]

Appl. Phys. Lett. (1)

R. Abdeddaïm, G. Guida, A. Priou, B. Gallas, and J. Rivory, “Negative permittivity and permeability of gold square nanospirals,” Appl. Phys. Lett. 94(8), 081907 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

M. G. Silveirinha, “Design of linear-to-circular polarization transformers made of long densely packed metallic helices,” IEEE Trans. Antenn. Propag. 56(2), 390–401 (2008).
[CrossRef]

J. Appl. Phys. (1)

Z.-Y. Zhang and Y.-P. Zhao, “Optical properties of helical and multiring Ag nanostructures: The effect of pitch height,” J. Appl. Phys. 104(1), 013517 (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

P. A. Belov, C. R. Simovski, and S. A. Tretyakov, “Example of bianisotropic electromagnetic crystals: the spiral medium,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5), 056622 (2003).
[CrossRef] [PubMed]

Science (1)

J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science 325(5947), 1513–1515 (2009).
[CrossRef] [PubMed]

Other (7)

E. Hecht, Optics (Addison-Wesley, San Francisco, 2002, 4th edition).
[PubMed]

J. D. Kraus, and R. J. Marhefka, Antennas: For All Applications (McGraw-Hill, New York, 2003, 3rd edition).

H.-S. Kitzerow, and C. Bahr, eds., Chirality in Liquid Crystals (Springer, Heidelberg, 2001, 1st edition).

www.cst.com/Content/Products/MWS/Overview.aspx

www.lumerical.com

www.jcmwave.com

I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston, 1994).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Scheme of one lateral unit cell of a chiral metamaterial composed of left-handed gold helices arranged in a square lattice on a glass substrate. The relevant structure parameters are illustrated. We consider propagation of light along the helix axis. N = 1 helix pitch is shown.

Fig. 2
Fig. 2

Intensity transmittance and intensity conversion spectra (note the different vertical scales) for circularly polarized incident light propagating along the helix axis (compare Fig. 1). Results for left-handed circular polarization (LCP) and right-handed circular polarization (RCP) of light are shown. The metal helices are left-handed. Parameters are R = 0.6 µm, r = 0.1 µm, a = 2 µm, and p = 2 µm. The gold is described by the free-electron Drude model. The number of helix pitches, N, is varied as indicated.

Fig. 3
Fig. 3

As Fig. 2, N = 1, but the helix pitch, p, is varied as indicated. p = 0 µm corresponds to a planar, hence non-chiral, split-ring resonator with 100 nm gap width.

Fig. 5
Fig. 5

As Fig. 2, N = 1, but the metal helix radius, R, is varied as indicated.

Fig. 6
Fig. 6

As Fig. 2, N = 1, but the metal wire radius, r, is varied as indicated.

Fig. 8
Fig. 8

Intensity reflectance and conversion spectra for the parameters and the geometry shown in Fig. 2. For usual Fresnel-type reflection, LCP (RCP) incident light turns into RCP (LCP) reflected light. Thus, in reflection geometry, by “conversion” we refer to, e.g., the ratio of LCP reflected light intensity and LCP incident light intensity. The red curves correspond to the behavior of an ideal metal mirror.

Fig. 4
Fig. 4

As Fig. 2, N = 1, but the square lattice constant, a, is varied as indicated.

Fig. 7
Fig. 7

As Fig. 2, N = 1, but the angle of incidence, α, is varied from normal incidence to 40 degrees with respect to the surface normal in steps of 10 degrees. The inset on the left-hand side illustrates the oblique-incidence geometry.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

λ 2 π R × [ 3 4 , 4 3 ] .

Metrics