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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 2 — Jan. 17, 2011
  • pp: 748–756
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Manipulating optical polarization by stereo plasmonic structure

J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu  »View Author Affiliations


Optics Express, Vol. 19, Issue 2, pp. 748-756 (2011)
http://dx.doi.org/10.1364/OE.19.000748


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Abstract

We theoretically study a particular plasmonic structure with stereo nanoholes array in metallic film, which has remarkable abilities to manipulate the optical polarizations at optical frequencies. The main property is that any linear polarization states including a complete 90° optical rotation can be obtained in transmission by proper structural design in combination of enhanced transmission efficiency. Together with the polarization change, surface plasmon propagation bounded on the surface of transmission side also can be modulated. Furthermore, an analytical Coupled Mode Method (CMM) is developed by introducing a frequency dependent coupling coefficient to describe such optical rotation property in stereo plasmonic systems.

© 2011 OSA

1. Introduction

Optical activity, the property of materials to rotate the polarization plane of linear polarized light, has attracted much attention in history. In natural materials like quarts [1

1. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999).

], optical activity is usually very weak as a consequence of molecular electric and magnetic polarization coupling. The recently emerging concept of metamaterial, by utilizing artificially trimmed metallic structures in subwavelength scale, opens up the possibility to achieve giant electromagnetic (EM) response in optical frequency region, and therefore inspired new ways to enhance and expand optical activity effects. The mainstream of this artificial optical activity is chiral metamaterials with helix structures for their scientific novelty [2

2. J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004). [CrossRef] [PubMed]

,3

3. M. Wegener and S. Linden, “Giving light yet another twist,” Physics 2, 3 (2009). [CrossRef]

], and probable application within optical region [4

4. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]

,5

5. 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]

]. Another type of design is to use planar metamaterials [6

6. J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]

,7

7. N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

] to realize polarization control, taking advantage of their broken symmetry and coupling effects. However, these artificial metallic ‘atoms’ always accompany great absorption with respect to these polarization controlled modes, which are revealed as the transmission minimums and forbid the transmitted far-field to be further utilized.

Inspired by the extraordinary optical transmission (EOT) effect associated with the surface plasmon polariton (SPP) excitations on metal surfaces [8

8. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

10

10. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005). [CrossRef]

], several approaches have been carried out to achieve optical activity by drilling special holes or grooves in metallic films based on particular plasmonic excitations [11

11. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]

15

15. T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 26113 (2010). [CrossRef]

] or similar mechanism in THz region [16

16. F. Miyamaru and M. Hangyo, “Strong optical activity in chiral metamaterials of metal screw hole arrays,” Appl. Phys. Lett. 89(21), 211105 (2006). [CrossRef]

,17

17. E. Lheurette, S. X. Wang, F. Garet, J. L. Coutaz, and D. Lippens, “Rotary power of a fishnet-related metamaterial at 0.5 THz,” 4th International Conference on Electromagnetic Materials in Microwaves and Optics, Karlsruhe pp. 321–323 (2010).

]. However, more effective and fruitful manipulation still remains challenges, especially in optical frequency. In this paper, we theoretically proposed a design of stereo-shaped nanoholes array drilled in metallic film, to bring the EOT effect to realize an efficient optical polarization control at will. Our numerical results definitely show that this structure can be designed to arbitrarily rotate the polarization states in optical transmissions for certain linearly polarized incidence. The excellent optical rotation modes are manifested as transmission peaks endowing our structure as an ultrathin polarization rotator. On the other hand, this SPP associated polarization change in the transmission side surface results in a change of surface wave propagation, which also indicates possible applications in future integrated optics. Moreover, we developed a commonly used Coupled Mode Method (CMM) [18

18. A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Holey metal films: From extraordinary transmission to negative-index behavior,” Phys. Rev. B 80(16), 165431 (2009). [CrossRef]

,19

19. C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007). [CrossRef]

] by introducing a frequency dependent conductive coupling coefficient, so that it gives a way in which CMM can be expanded to work in stereo plasmonic systems, as well as to provide a clear understanding of the mechanism of such efficient optical rotation. Good agreement with the numerical simulations indicates the validation of our developed analytical method.

2. Modeling and numerical approaches

Numerical simulations are performed by commercial software CST Microwave Studio using Finite Integration Method. The metal material is defined as gold with complex permittivity described by the Drude mode ε=1-ωp 2/(ω 2 + iωγ), whose plasma frequency is ωp=1.37×1016 rad/s and collision frequency is γ=12.24×1013 rad/s, considering the increased loss in the nanoscale system [20

20. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

,21

21. T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface-plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016606 (2007). [CrossRef] [PubMed]

]. To be noted this definition is used in the following analytical approach. Periodic boundary conditions are set in x and y directions, representing the periodically arranged nanohole array. Incidence is an electrically y-polarized plane wave propagating along + z direction and hence, the boundary condition in z direction is set as open. Probes along x and y directions are located 3μm from the structure to detect the transmission components of different polarizations, at which position the transmitted electromagnetic field has already been uniform within concerned frequency range, because the sample is a subwavelength structure and the diffraction effect in far field area is well prohibited.

From simulation results, our structures show the ability to arbitrarily rotate the polarization state to any direction by carefully designing the stereo holes. For examples, in cases of structures with total rotation angles equal 45° and 60°, Figs. 2(a)
Fig. 2 Numerical result of polarization control of stereo structures with different rotation angles of 45° and 60°. (a) Transmission spectra with polarization perpendicular to long axis of last layer. (b) Spectra of the corresponding rotated azimuth angle and ellipticity angle.
and 2(b) give the spectrum of transmission intensity with polarization along the designed 45° and 60° direction under y-polarized illuminations, as well the their rotated azimuth angle and ellipticity. Relative strong optical transmittances are clearly observed as two peaks at wavelength of about 720 and 800 nm. When normalized to the nanohole occupation area, the transmittances are greatly higher than one unit, indicating an enhancement effect. Moreover, the optical rotation modes of about 720 nm are almost independent of structures, which are well reflected from the transmission peaks and good matches to the desired rotation angle for these 45° and 60° samples [see Fig. 2(b)]. Both of them exhibit good linearity (elliptical angles < 4°) in transmissions within the spectra we concerned. It is reasonable that we also can obtain a corresponding rotated polarization state about 720 nm wavelength for any other rotated structure. This means a fully control of transmitted polarization will be accomplished. In the following, we will elaborately show the result of 90° rotation structure (shown in Fig. 1), which is expect to achieve a totally polarization conversion from vertical to horizontal.

Figure 3(a)
Fig. 3 Numerical results of transmission properties for 90° rotation structure. (a) Transmission spectra detected in x- and y-polarization under y-polarized incidence (here h=300nm). (b) Transmittance of Ex for different total thicknesses, as h=150nm, 300nm, 450nm, 750nm, respectively. (c) E field Distributions of distinct modes marked out in (b).
illustrates the polarized transmission spectra in the original (Tyy) and it orthogonal (Tyx) polarization states when a y-polarized light incident onto a 90° rotation structure (h=300nm), in which both complete polarization conversion (because Tyy are almost zero) and about 70% maximum transmittance (Tyx) are observed belonging to this polarization conversion. Split transmission peaks are considered from the plasmonic coupling between two metal surfaces [22

22. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001). [CrossRef] [PubMed]

]. Peak shift with respect to the metal film thickness given in Fig. 3(b) provides positive support that thicker metallic layer (from 150 to 450nm) reduces coupling strength and hence decrease peak gap. Field distributions of peak modes are shown in Fig. 3(c), and in phase and out-of phase coupling between SPPs give rise to splitting of peaks (marked as ① and ②). Incidentally, new peak in smaller wavelength (658nm) for the large thickness case (h = 750nm) is found corresponding to Fabry-Perot (F-P) cavity mode due to the elongated hole channel to meet a certain resonance condition, which is well reflected from the strong field concentrated inside the twisted nanohole channel. Detailed field distributions for these modes are shown in Fig. 3(c).

Another important feature of this stereo plasmonic structure is the ability to change the propagation of SPP waves bounded on the metal surface of transmission side. It is verified by surface field distributions in Figs. 4(a)
Fig. 4 Magnetic field distributions on the metal surfaces of a stereo structure containing 5×5 period array with h=300nm and θ=90° at λ=769nm: (a) Hx and (b) Hy at incident side z=0, (c) Hx and (d) Hx at transmission side z=h, where Hmax=0.002A/m.
-4(d) from the sample of h=300 nm, where an excited SPP wave along ±y directions on the incident surface (z=0), corresponding to a y-polarized incidence, is transferred to propagating along ±x directions on the transmission surface (z=300 nm) (all are indicated by the magnetic field components). This phenomenon explains that near-field polarization rotation effect causes SPP propagation change. In this sense, this structure also acts like a polarized coupler that can couple the far field incidence into a modulated propagation SPP wave, further implying it to have promising application in photonic integrations.

3. Analytical approach and discussions

In this section, we will focus on the underlying physics of such polarization control by this stereo plasmonic structure. The mechanism of this polarization manipulation is obvious different the natural optical activities, in which coupling effect between electric and magnetic dipoles results in a non-diagonalized susceptibility tensor. Then, our structure cannot be described by effective EM parameters (ε and μ) like the metamaterial, mostly due to the light (EM field) can only touches the first layer and the responses of the inner layers mainly arises from the plasmonic coupling. Although numerical results have provided us the major phenomena and intuitive explanations, it is necessary to explore this structure in more scientific sense within the framework of plasmonic EOT system.

Now we come back to find out a proper form of η. Since our assumption to achieve the field in different layers is simply by multiplying this coefficient, η must be a complicated function of kz and in a reasonable form of η(kz)=η 0[exp(ikzh)+const], where kz is responsible for the phase component. For simplicity, we expand kz(ω) to 1st order approximation in the neighborhood of ω 0,
kz(ω)=kz0+kzω|ω=ω0(ωω0)+...,
(4)
where ω 0 is a parameter correlated with thickness h, hence we get the form of η as
η(ω)=η0[eC(ωω0)eiD(ωω0)+c],
(5)
where parameters C and D are real and defined as kzω|ω=ω0h=D+iC. To determine unknown parameters A and B in Eqs. (2a)-(2c), following boundary conditions are applied.
HxI|z=0=Hx(1)|z=0,HyIII|z=h=HyII|z=h,
(6a)
EyI+ZHxI|z=0=Ey(1)+ZHx(1)|z=0,ExIIIZHyIII|z=h+=ExIIZHyII|z=h+,
(6b)
where Z is the notation of surface impedance of metal as Z=μ0c/εm. It is essential to find that fields in former layers combine together to work on the boundary conditions
ExII=Eξ(2)|z=h+Eξ(3)|z=h×cos(θ2),HyII=Hς(2)|z=h+Hς(3)|z=h×cos(θ2),
(7)
where θ equals to 90° for these polarization conversion cases. By solving Eqs. (6)-(7), zeroth ordered transmission is calculated in the following form as [19

19. C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007). [CrossRef]

],
T=|t0F(λ)|2,
(8)
where the parameters are defined as

t0=4wσ(1+εm1/2)2,F(λ)=η(λ)eikzh'δ++eikzh'δ1(1θ+)(1+θ),
(9a)
δ±=η(λ)+12e±ikzh',θ±=σ±εm1/2sinckybmwtmh'mλm+εm1/2,h'=h3.
(9b)

Figure 5(b) gives the results of polarized transmittance of field Ex with our method for thicknesses of 270nm, 300nm and 330nm, which show good agreement with the simulated results [see Fig. 5(c)] both in peak positions and the splitting evolution with respect to the total thickness. The fitting parameters in coupling coefficient η in form of Eq. (5) are: (a) ω 0=675THz, C=35 and D=135 for h=270nm; (b) ω 0=653THz, C=25 and D=100 for h=300nm; (c) ω 0=633THz, C=21 and D=82 for h=330nm, and const=2.3, η 0=0.1 are constants for all thicknesses. Therefore, this developed Coupled Mode Method is valid to deal with this stereo structure, and indicates more applications in some other similar complicated plasmonic system.

4. Conclusions

A kind of stereo plasmonic structure is theoretically proposed and intensively studied in this paper, which is proved to having strong ability in manipulating transmitted optical polarization as well as near field SPP propagation. Our numerical results reveal considerable strong polarized transmission intensity and versatile SPP mode associated with the coupling effect and F-P like cavity mode, which all contribute to such an optical rotation property. It is rightly due to this particular stereo-hole design that breaks the mirror symmetry of the structure and gives rise to the partially matched coupling for the plasmonic modes between layers. Based on this mechanism, we developed the Coupled Mode Method by introducing a frequency dependent coupling coefficient so as to analytically deal with this stereo plasmonic system. Besides the scientific contribution, this kind of stereo plasmonic system with good optical functionality suggests practical applications in nano-optics with the development of advanced fabrication technology.

Acknowledgments

This work is supported by the State Key Program for Basic Research of China (Nos. 2010CB630703, 2009CB930501), the National Natural Science Foundation of China (Nos. 10704036, 10974090, 60990320 and 11021403), and the National Undergraduates Innovation Program of China.

References and links

1.

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999).

2.

J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004). [CrossRef] [PubMed]

3.

M. Wegener and S. Linden, “Giving light yet another twist,” Physics 2, 3 (2009). [CrossRef]

4.

M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]

5.

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]

6.

J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]

7.

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]

8.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]

9.

K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004). [CrossRef] [PubMed]

10.

K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005). [CrossRef]

11.

R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]

12.

A. V. Krasavin, A. S. Schwanecke, N. I. Zheludev, M. Reichelt, T. Stroucken, S. W. Koch, and E. M. Wright, “Polarization conversion and “focusing” of light propagating through a small chiral hole in a metallic screen,” Appl. Phys. Lett. 86(20), 201105 (2005). [CrossRef]

13.

T. Li, H. Liu, S. M. Wang, X. G. Yin, F. M. Wang, S. N. Zhu, and X. A. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008). [CrossRef]

14.

A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008). [CrossRef] [PubMed]

15.

T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 26113 (2010). [CrossRef]

16.

F. Miyamaru and M. Hangyo, “Strong optical activity in chiral metamaterials of metal screw hole arrays,” Appl. Phys. Lett. 89(21), 211105 (2006). [CrossRef]

17.

E. Lheurette, S. X. Wang, F. Garet, J. L. Coutaz, and D. Lippens, “Rotary power of a fishnet-related metamaterial at 0.5 THz,” 4th International Conference on Electromagnetic Materials in Microwaves and Optics, Karlsruhe pp. 321–323 (2010).

18.

A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Holey metal films: From extraordinary transmission to negative-index behavior,” Phys. Rev. B 80(16), 165431 (2009). [CrossRef]

19.

C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007). [CrossRef]

20.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]

21.

T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface-plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016606 (2007). [CrossRef] [PubMed]

22.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001). [CrossRef] [PubMed]

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics
(260.5430) Physical optics : Polarization

ToC Category:
Optics at Surfaces

History
Original Manuscript: November 9, 2010
Revised Manuscript: December 20, 2010
Manuscript Accepted: December 22, 2010
Published: January 5, 2011

Citation
J. Xu, T. Li, F. F. Lu, S. M. Wang, and S. N. Zhu, "Manipulating optical polarization by stereo plasmonic structure," Opt. Express 19, 748-756 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-748


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References

  1. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, England, 1999).
  2. J. B. Pendry, “A chiral route to negative refraction,” Science 306(5700), 1353–1355 (2004). [CrossRef] [PubMed]
  3. M. Wegener and S. Linden, “Giving light yet another twist,” Physics 2, 3 (2009). [CrossRef]
  4. M. Decker, M. W. Klein, M. Wegener, and S. Linden, “Circular dichroism of planar chiral magnetic metamaterials,” Opt. Lett. 32(7), 856–858 (2007). [CrossRef] [PubMed]
  5. 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]
  6. J. M. Hao, Y. Yuan, L. X. Ran, T. Jiang, J. A. Kong, C. T. Chan, and L. Zhou, “Manipulating electromagnetic wave polarizations by anisotropic metamaterials,” Phys. Rev. Lett. 99(6), 063908 (2007). [CrossRef] [PubMed]
  7. N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009). [CrossRef]
  8. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  9. K. J. Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes,” Phys. Rev. Lett. 92(18), 183901 (2004). [CrossRef] [PubMed]
  10. K. L. van der Molen, K. J. Klein Koerkamp, S. Enoch, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Role of shape and localized resonances in extraordinary transmission through periodic arrays of subwavelength holes: Experiment and theory,” Phys. Rev. B 72(4), 045421 (2005). [CrossRef]
  11. R. Gordon, A. G. Brolo, A. McKinnon, A. Rajora, B. Leathem, and K. L. Kavanagh, “Strong polarization in the optical transmission through elliptical nanohole arrays,” Phys. Rev. Lett. 92(3), 037401 (2004). [CrossRef] [PubMed]
  12. A. V. Krasavin, A. S. Schwanecke, N. I. Zheludev, M. Reichelt, T. Stroucken, S. W. Koch, and E. M. Wright, “Polarization conversion and “focusing” of light propagating through a small chiral hole in a metallic screen,” Appl. Phys. Lett. 86(20), 201105 (2005). [CrossRef]
  13. T. Li, H. Liu, S. M. Wang, X. G. Yin, F. M. Wang, S. N. Zhu, and X. A. Zhang, “Manipulating optical rotation in extraordinary transmission by hybrid plasmonic excitations,” Appl. Phys. Lett. 93(2), 021110 (2008). [CrossRef]
  14. A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101(4), 043902 (2008). [CrossRef] [PubMed]
  15. T. Li, S. M. Wang, J. X. Cao, H. Liu, and S. N. Zhu, “Cavity-involved plasmonic metamaterial for optical polarization conversion,” Appl. Phys. Lett. 97, 26113 (2010). [CrossRef]
  16. F. Miyamaru and M. Hangyo, “Strong optical activity in chiral metamaterials of metal screw hole arrays,” Appl. Phys. Lett. 89(21), 211105 (2006). [CrossRef]
  17. E. Lheurette, S. X. Wang, F. Garet, J. L. Coutaz, and D. Lippens, “Rotary power of a fishnet-related metamaterial at 0.5 THz,” 4th International Conference on Electromagnetic Materials in Microwaves and Optics, Karlsruhe pp. 321–323 (2010).
  18. A. Mary, S. G. Rodrigo, L. Martin-Moreno, and F. J. Garcia-Vidal, “Holey metal films: From extraordinary transmission to negative-index behavior,” Phys. Rev. B 80(16), 165431 (2009). [CrossRef]
  19. C. P. Huang, Q. J. Wang, and Y. Y. Zhu, “Dual effect of surface plasmons in light transmission through perforated metal films,” Phys. Rev. B 75(24), 245421 (2007). [CrossRef]
  20. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005). [CrossRef] [PubMed]
  21. T. Li, H. Liu, F. M. Wang, J. Q. Li, Y. Y. Zhu, and S. N. Zhu, “Surface-plasmon-induced optical magnetic response in perforated trilayer metamaterial,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(1), 016606 (2007). [CrossRef] [PubMed]
  22. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86(6), 1114–1117 (2001). [CrossRef] [PubMed]

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