Abstract

We show that employing localized surface plasmon resonators to probe environmental media will always lead to dissimilar optical sensitivities to permittivity and permeability. We find that while the permittivity sensitivities of diverse plasmonic structures display a geometry-independent universal scaling relation, the permeability sensitivities are highly dependent on the metals’ geometries and resonant modes. Similar results are also found in mixed real/spoof localized surface plasmon resonators, and the phenomena can be universally scaled to the normalized effective plasmon frequencies. Importantly, the results put a fundamental constraint for all plasmonic-assisted nonlinear magneto-optical phenomena, including the Faraday effect, magneto-optical Kerr effect, and Cotton–Mouton effect.

© 2014 Optical Society of America

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References

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  1. P. W. Anderson, Phys. Rev. 130, 439 (1963).
    [CrossRef]
  2. Y. K. Chang, Z. X. Lou, K. D. Chang, and C. W. Chang, Opt. Express 21, 1804 (2013).
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  4. V. V. Temnov, Nat. Photonics 6, 728 (2012).
    [CrossRef]
  5. J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
    [CrossRef]
  6. M. M. Miller and A. A. Lazarides, J. Phys. Chem. B 109, 21556 (2005).
    [CrossRef]
  7. C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
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  8. J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
    [CrossRef]
  9. J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
    [CrossRef]
  10. A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
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2013

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Y. K. Chang, Z. X. Lou, K. D. Chang, and C. W. Chang, Opt. Express 21, 1804 (2013).
[CrossRef]

2012

V. V. Temnov, Nat. Photonics 6, 728 (2012).
[CrossRef]

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

2011

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

2008

C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
[CrossRef]

2005

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

M. M. Miller and A. A. Lazarides, J. Phys. Chem. B 109, 21556 (2005).
[CrossRef]

2004

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

1963

P. W. Anderson, Phys. Rev. 130, 439 (1963).
[CrossRef]

Akimov, I. A.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Anderson, P. W.

P. W. Anderson, Phys. Rev. 130, 439 (1963).
[CrossRef]

Bayer, M.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Belotelov, V. I.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Chang, C. W.

Chang, K. D.

Chang, Y. K.

Chen, C. Y.

C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
[CrossRef]

Chin, J. Y.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Dregely, D.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Garcia-Vidal, F. J.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Giessen, H.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Gopal, A. V.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Kasture, S.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Koschny, T.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Kotov, V. A.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Lazarides, A. A.

M. M. Miller and A. A. Lazarides, J. Phys. Chem. B 109, 21556 (2005).
[CrossRef]

Lou, Z. X.

Martin-Moreno, L.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Miller, M. M.

M. M. Miller and A. A. Lazarides, J. Phys. Chem. B 109, 21556 (2005).
[CrossRef]

Moreno, E.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

Pendry, J. B.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

Pohl, M.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Pors, A.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

Soukoulis, C. M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Steinle, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Stritzker, B.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Temnov, V. V.

V. V. Temnov, Nat. Photonics 6, 728 (2012).
[CrossRef]

Vengurlekar, A. S.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Wehlus, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Weiss, T.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Wu, S. C.

C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
[CrossRef]

Yakovlev, D. R.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Yen, T. J.

C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
[CrossRef]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Zvezdin, A. K.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Appl. Phys. Lett.

C. Y. Chen, S. C. Wu, and T. J. Yen, Appl. Phys. Lett. 93, 034110 (2008).
[CrossRef]

J. Phys. Chem. B

M. M. Miller and A. A. Lazarides, J. Phys. Chem. B 109, 21556 (2005).
[CrossRef]

Nat. Commun.

J. Y. Chin, T. Steinle, T. Wehlus, D. Dregely, T. Weiss, V. I. Belotelov, B. Stritzker, and H. Giessen, Nat. Commun. 4, 1599 (2013).
[CrossRef]

Nat. Nanotechnol.

V. I. Belotelov, I. A. Akimov, M. Pohl, V. A. Kotov, S. Kasture, A. S. Vengurlekar, A. V. Gopal, D. R. Yakovlev, A. K. Zvezdin, and M. Bayer, Nat. Nanotechnol. 6, 370 (2011).

Nat. Photonics

V. V. Temnov, Nat. Photonics 6, 728 (2012).
[CrossRef]

Opt. Express

Phys. Rev.

P. W. Anderson, Phys. Rev. 130, 439 (1963).
[CrossRef]

Phys. Rev. Lett.

A. Pors, E. Moreno, L. Martin-Moreno, J. B. Pendry, and F. J. Garcia-Vidal, Phys. Rev. Lett. 108, 223905 (2012).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, Phys. Rev. Lett. 95, 223902 (2005).
[CrossRef]

Science

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, Science 305, 847 (2004).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(Top) Simulation procedures for determining the wavelength redshifts (Δλm) of an SRR when immersed into dielectric (ε=1, μ=2) or magnetic (ε=1, μ=2) media. Except for exchanging the media, all other simulated configurations, including the incident wave polarizations, remain unchanged. (Bottom) Normalized frequency-dependent ε sensitivity or μ sensitivity for various plasmonic metal structures and harmonic modes (SRR, split-ring resonator; Rod, nanorod; CSRR, split-ring resonator with complementary structures). Prediction of the standing wave model is plotted as a dashed line.

Fig. 2.
Fig. 2.

(a) The ratio of ε sensitivity to μ sensitivity as a function of plasmon frequencies [1 (rectangle), 1/2 (up triangle), 1/5 (down triangle), and 1/10 (star) of ωp,Au], harmonic modes, and resonant frequency (normalized to the respective plasmon frequencies). (b) The saturation of resonant frequencies with reducing sizes of an SRR is similar to the curve of the ratios of ε sensitivity to μ sensitivity. (c) Normalized effective plasmon frequency (ωp,eff/ωp,Au) for different spoof SRRs shown in the inset. (d) The ratio of ε sensitivity to μ sensitivity as a function of resonant frequencies (normalized to ωp,Au) for SRRs and spoof SRRs. Here the resonant frequencies of SRRs and spoof SRRs are tuned by varying L and r, respectively.

Fig. 3.
Fig. 3.

Universal relation for the ratio of ε sensitivity to μ sensitivity as a function of resonant frequencies. The resonant frequency is normalized to the plasmon frequency (1, 1/2, and 1/5 of ωp,Au, respectively) for SRRs and to ωp,eff [determined from Fig. 2(c)] for spoof SRRs, respectively. When the spoof SRR is made by PEC, identical ε and μ sensitivities are observed (dashed line).

Fig. 4.
Fig. 4.

Ratio of electric field (E) to magnetic field (B) of SRRs as a function of resonant frequencies. Inset shows that the electric field and the magnetic field are probed at the gap and the center of the SRR, respectively. The E/B ratio for an SRR made of PEC (gray dashed line) and gold (orange solid line) are shown for comparison.

Equations (3)

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

γ=iω2με(mπa)2(nπb)2,
εsensitivityμsensitivity=με(L+LeL),
U=U012ε0εijEiEj12μ0μijHiHj13ε0χijk(2)EiEjEk13ε0μ0ηijk(2)EiEjHk13ε0μ0ςijk(2)EiHjHk14ε0χijkl(3)EiEjEkEl+,

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