Abstract

We theoretically calculate the electromagnetic response of metallic rod dimers for the arbitrary planar arrangement of rods in the dimer. It is shown that dimers without an in-plane symmetry axis exhibit elliptical dichroism and act as “atoms” in planar chiral metamaterials. Because of a very simple geometry of the rod dimer, such planar metamaterials are much easier to fabricate than conventional split-ring or gammadion-type structures and lend themselves to a simple analytical treatment based on a coupled dipole model. Dependencies of the metamaterial’s directional asymmetry on the dimer’s geometry are established analytically and confirmed in numerical simulations.

© 2011 Optical Society of America

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  1. M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
    [CrossRef] [PubMed]
  2. V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
    [CrossRef] [PubMed]
  3. E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
    [CrossRef]
  4. J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
    [CrossRef]
  5. E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Tünnermann, and T. Pertsch, Opt. Express 19, 6269 (2011).
    [CrossRef] [PubMed]
  6. S. V. Zhukovsky, V. M. Galynsky, and A. V. Novitsky, Opt. Lett. 34, 1988 (2009).
    [CrossRef] [PubMed]
  7. A. Moroz, J. Opt. Soc. Am. B 26, 517 (2009).
    [CrossRef]
  8. F. I. Fedorov, Theory of Gyrotropy (Nauka i Tekhnika, 1976).
  9. L. M. Barkovsky, Sov. Phys. Crystallogr. 21, 245 (1976).
  10. G. N. Borzdov, J. Math. Phys. 38, 6328 (1997).
    [CrossRef]
  11. Ansys HFSS, http://www.ansoft.com/products/hf/hfss/.
  12. C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
    [CrossRef]
  13. S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
    [CrossRef]
  14. C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

2011 (1)

2010 (1)

C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
[CrossRef]

2009 (5)

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

S. V. Zhukovsky, V. M. Galynsky, and A. V. Novitsky, Opt. Lett. 34, 1988 (2009).
[CrossRef] [PubMed]

A. Moroz, J. Opt. Soc. Am. B 26, 517 (2009).
[CrossRef]

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

2008 (1)

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

2006 (1)

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

2005 (1)

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

1997 (1)

G. N. Borzdov, J. Math. Phys. 38, 6328 (1997).
[CrossRef]

1976 (2)

F. I. Fedorov, Theory of Gyrotropy (Nauka i Tekhnika, 1976).

L. M. Barkovsky, Sov. Phys. Crystallogr. 21, 245 (1976).

Barkovsky, L. M.

L. M. Barkovsky, Sov. Phys. Crystallogr. 21, 245 (1976).

Borzdov, G. N.

G. N. Borzdov, J. Math. Phys. 38, 6328 (1997).
[CrossRef]

Boyd, R. W.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Canfield, B. K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Chen, Y.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Chigrin, D. N.

C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

Chipouline, A.

E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Tünnermann, and T. Pertsch, Opt. Express 19, 6269 (2011).
[CrossRef] [PubMed]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Dolgaleva, K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Fedorov, F. I.

F. I. Fedorov, Theory of Gyrotropy (Nauka i Tekhnika, 1976).

Fedotov, V. A.

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Galynsky, V. M.

Hübner, U.

Ino, Y.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Jefimovs, K.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Kauranen, M.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Kremers, C.

C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

Kuwata-Gonokami, M.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Lederer, F.

C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
[CrossRef]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Menzel, C.

C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
[CrossRef]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Mladyonov, P. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Moroz, A.

Novitsky, A. V.

Pertsch, T.

E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Tünnermann, and T. Pertsch, Opt. Express 19, 6269 (2011).
[CrossRef] [PubMed]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Petschulat, J.

E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Tünnermann, and T. Pertsch, Opt. Express 19, 6269 (2011).
[CrossRef] [PubMed]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Plum, E.

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

Prosvirnin, S. L.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Pshenay-Severin, E.

Rockstuhl, C.

C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
[CrossRef]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Rogacheva, A. V.

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Saito, N.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Svirko, Y.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Tünnermann, A.

E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Hübner, A. Tünnermann, and T. Pertsch, Opt. Express 19, 6269 (2011).
[CrossRef] [PubMed]

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

Turunen, J.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Vallius, T.

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, Phys. Rev. Lett. 95, 227401 (2005).
[CrossRef] [PubMed]

Volkov, S. N.

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Zheludev, N. I.

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

V. A. Fedotov, P. L. Mladyonov, S. L. Prosvirnin, A. V. Rogacheva, Y. Chen, and N. I. Zheludev, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Zhukovsky, S. V.

S. V. Zhukovsky, V. M. Galynsky, and A. V. Novitsky, Opt. Lett. 34, 1988 (2009).
[CrossRef] [PubMed]

C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

Appl. Phys. Lett. (1)

E. Plum, V. A. Fedotov, and N. I. Zheludev, Appl. Phys. Lett. 94, 131901 (2009).
[CrossRef]

J. Math. Phys. (1)

G. N. Borzdov, J. Math. Phys. 38, 6328 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (3)

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, and T. Pertsch, Phys. Rev. A 78, 043811 (2008).
[CrossRef]

C. Menzel, C. Rockstuhl, and F. Lederer, Phys. Rev. A 82, 053811 (2010).
[CrossRef]

S. N. Volkov, K. Dolgaleva, R. W. Boyd, K. Jefimovs, J. Turunen, Y. Svirko, B. K. Canfield, and M. Kauranen, Phys. Rev. A 79, 043819 (2009).
[CrossRef]

Phys. Rev. Lett. (2)

M. Kuwata-Gonokami, N. Saito, Y. Ino, M. Kauranen, K. Jefimovs, T. Vallius, J. Turunen, and Y. Svirko, 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, Phys. Rev. Lett. 97, 167401 (2006).
[CrossRef] [PubMed]

Sov. Phys. Crystallogr. (1)

L. M. Barkovsky, Sov. Phys. Crystallogr. 21, 245 (1976).

Other (3)

C. Kremers, S. V. Zhukovsky, and D. N. Chigrin, in Theoretical and Computational Nanophotonics: Proceedings of the 2nd International Workshop, D.N.Chigrin, ed., AIP Conference Proceedings Series (American Institute of Physics, 2009), Vol.  1176, p. 118.

Ansys HFSS, http://www.ansoft.com/products/hf/hfss/.

F. I. Fedorov, Theory of Gyrotropy (Nauka i Tekhnika, 1976).

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Figures (4)

Fig. 1
Fig. 1

Example of (a) 3D and (b) 2D enantiomeric meta-atoms; (c) difference in transmission for LH-/RH- polarized wave for copper split-ring versus “straightened split-ring” (rod dimer) structure.

Fig. 2
Fig. 2

(a) Geometry of an arbitrary planar rod dimer under study. (b) Scattering cross-section of a parallelepiped-shaped copper rod with size 13 mm × 0.8 mm × 0.8 mm determined by numerical simulations and from Eq. (1), ab initio (unfitted), and using best-fit parameters. Numerical results for a 13 mm long ring segment are included for comparison.

Fig. 3
Fig. 3

(a) Refractive indices for two corotating elliptically polarized eigenwaves h 1 , 2 of N ^ H in the effective medium given by Eq. (6). (b) Transmission and absorption for incident wave with polarization given by h 1 , 2 . (c) Absolute value of the complex projection coefficients C 1 , 2 for RH (solid) and LH (dashed) circularly polarized incident wave. (d) Analytically calculated difference in transmission for LH-/RH-polarized incident wave. Here a 1 = 13 mm , a 2 = 10 mm , d = 10 mm , ϕ = 45 ° , and ψ = 0 ° .

Fig. 4
Fig. 4

Numerical (top) and analytical (bottom) dependence of Δ T R L on (a) inter-rod distance d, (b) difference in rod length a 1 a 2 , (c) rod misalignment angle ϕ, and (c) rod displacement angle ψ for ϕ = 90 ° (as the dimer changes between T- and L-shaped). Unless specified otherwise, a 1 = 13 mm , a 2 = 10 mm , d = 6 mm , ϕ = 45 ° , and ψ = 0 ° .

Equations (7)

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

α ^ j = f j μ j μ j ω j 2 ω 2 i ω ( γ j + δ j ω 2 ) α j μ j μ j ,
d 1 , 2 = α ^ 1 , 2 [ E 0 + ( k 2 / ε 0 ) G ^ ( R ) d 2 , 1 ] ,
G ^ ( R ) = e i k R 4 π R [ ( 1 + i k R 1 k 2 R 2 ) I ^ + 3 3 i k R k 2 R 2 k 2 R 2 R R R 2 ] G I I ^ + G R r r ,
α ^ eff = α 1 μ 1 μ 1 + α 2 μ 2 μ 2 + α 1 α 2 κ ( μ 1 μ 2 + μ 2 μ 1 ) 1 α 1 α 2 κ 2 α 1 eff μ 1 μ 1 + α 2 eff μ 2 μ 2 + α 3 eff ( μ 1 μ 2 + μ 2 μ 1 ) ,
κ = ( k 2 / ε 0 ) [ G I ( μ 1 · μ 2 ) + G R ( μ 1 · r ) ( μ 2 · r ) ] .
ε ^ eff = I ^ + [ α 1 eff / ( 2 ε 0 V cell ) ] ( c + c + c c + ) ,
η ± = [ α 3 eff ± ( α 3 eff ) 2 α 1 eff α 2 eff ] ( α 1 eff ) 1 .

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