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Optics Express

Optics Express

  • Editor: C. Martijin de Sterke
  • Vol. 19, Iss. 7 — Mar. 28, 2011
  • pp: 6348–6353
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Narrowband plasmonic excitation on gold hole-array nanostructures observed using spectroscopic ellipsometer

G. X. Li, Z. L. Wang, S. M. Chen, and K. W. Cheah  »View Author Affiliations


Optics Express, Vol. 19, Issue 7, pp. 6348-6353 (2011)
http://dx.doi.org/10.1364/OE.19.006348


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Abstract

Surface plasmon polaritons (SPPs) modes on gold hole-array nanostructures were studied using spectroscopy ellipsometer in reflection mode. Using background free techniques in the optical ellipsometer, clear SPP bands on gold nanostructure/air interface were measured in UV-Visible-Near infrared (NIR) regime (300 nm–1800 nm). Plasmonic excitation with bandwidth of 13 nm (FWHM) was observed in reflection measurement, and it is much narrower than that observed in transmission measurement mode. In addition, the plasmonic excitation bands were characterized in both amplitude and phase domain. Theoretical analysis using reciprocal lattice vector method and rigorous coupled wave analysis (RCWA) agreed well with the experimental results. By measuring the TM and TE waves simultaneously, the spectroscopic ellipsometer provides an important method to analyze both amplitude and phase information in plasmonic nanostructures and metamaterials.

© 2011 OSA

1. Introduction

In this work, we studied the SPP photonic bands on a gold hole-array nanostructure using the spectroscopic ellipsometer in reflection mode. In spectroscopic ellipsometer, the amplitude ratio and phase delay of reflected polarized light (p and s) is measured. By fitting the measured data, the refractive index and thickness of thin film sample could be obtained. The plasmonic modes on gold nanostructure are also characterized from analyzing the reflective spectra. Angle resolved ellipsometric experiment from 50 to 76 degrees were performed to map the plasmonic dispersion relationship. Narrow band (13 nm FWHM) plasmonic excitation at the gold/air surface was obtained in Visible-NIR regime. One advantage of spectroscopic ellipsometer is that it is background free in measurement process. Another is that the phase delay of the polarized light can also be monitored. Since the phase shift at plasmon resonance usually experience a sharp change, the phase information of plasmon excitation could be also used for sensing application [10

10. T. H. Reilly, S. H. Chang, J. D. Corbman, G. C. Schatz, and H. L. Rowlen, “Quantitative evaluation of plasmon enhanced Raman scattering from nanoaperture arrays,” J. Phys. Chem. C 111(4), 1689–1694 (2007). [CrossRef]

14

14. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

]. Theoretical analysis using dispersion relation and RCWA methods shows that the calculated and experimental results fit well with each other.

2. Device fabrication and ellipsometric plasmonic excitation

2.1. Device fabrication

In this work, the EOT gold nanostructure was studied in reflection mode. The gold hole-array nanostructure (shown in Fig. 1
Fig. 1 SEM image of two dimensional gold hole-array nanostructure on quartz substrate. Period: 800 nm; aperture size: 200 nm. Thickness of gold layer is 100 nm.
) was fabricated using standard e-beam lithography and metal lift-off process. First, a 10 nm thick chromium (Cr) layer was fabricated on a quartz substrate using RF sputtering method, then a ZEP520A thin film with thickness of about 550 nm was spun on the Cr layer, a ZEP520A dot array was formed on the substrate after pattering with e-beam lithography method, finally, a 100 nm thick gold layer was coated using thermal evaporator. The two dimensional gold hole-array nanostructures was obtained by removing the resist residue. The size of the gold nanostructure is 500 µm by 500 µm, and the period of the square hole-array is 800 nm with aperture size of 200 nm.

2.2. Ellipsometeric plasmonic excitation

Linear optical property of gold nanostructures was experimentally characterized using UV-Visible-NIR ellipsometer (SOPRA) in reflection mode. The white light from Xenon lamp is focused by a microlens system, the focal spot with diameter on the gold nanostructure is about 200 µm by 300 µm. Reflection of p (electric field parallel to incident plane) and s (electric field perpendicular to the incident plane) polarized light was collected by fiber coupled Visible-NIR spectrometer. Figure 2
Fig. 2 White light (red line) from Xenon lamp is focused on the patterned region of gold nanostructure at the incident angle of 50 degrees. The rainbow curves (indicated by blue line) are first and second order diffraction at the vertical incident plane of the UV-Visible-NIR spectroscopic ellipsometer.
shows the first and second order diffraction when white light is incident on the nanostructure at an angle of 50 degree.

Using the background free technique in spectroscopic ellipsometry, the polarization state of incident light is modulated by a rotating polarizer. By analyzing the amplitude and phase delay with an analyzer in the reflection direction, the complex ratio ρ of reflected polarized light (p and s) is written as:
ρ=RpRs=tan(ψ)exp(iΔ)
(1)
where ψ and Δ in Eq. (1) are the amplitude ratio and the phase shift of p and s polarized light respectively.

In Fig. 3(a)
Fig. 3 Measured dispersion relations of SPPs on gold hole-array nanostructure by UV-Visible-NIR ellipsometer. (a) Amplitude ratio (tan(ψ)) and (b) phase shift (cos(Δ)) of p and s polarized light are plotted as a relationship to incident angles and wavelength of incident light.
, the amplitude ratio (tan(ψ)) is plotted as a function of incident angles (50-76 degrees) and wavelength (300 nm-1800 nm) of incident light, Fig. 3(b) shows the relative phase shift (cos(Δ)) of p and s polarized light. Two narrow bands are found in both amplitude and phase spectra. The resonant wavelength in phase domain (Fig. 3(b)) usually experiences a phase jump when there is reflection dips in amplitude domain (Fig. 3(a)). Theoretical analysis in the following section shows that the two bands correspond to the first and second order grating coupled SPP excitation on gold/air surface. When SPPs are excited, p wave is absorbed and converted into SPPs and s wave has a slow varying response, so there is a resonant dip fortan(ψ). In the meantime, the phase of p wave is delayed compared to s wave, so there is a corresponding phase resonance in cos(Δ)diagram. The narrowband plasmonic excitation with bandwidth of ~13 nm in NIR regime was obtained.

3. Theoretical analysis

3.1. Grating coupled SPPs excitation

As the momentum of SPPs on the gold/air surface is larger than that of incident light, periodicity of gold hole-array nanostructures is used to couple light in free space into SPPs. The plasmonic excitation condition is defined by the following equations [22

22. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1988).

]:
ksp(ω)=k0(ω)sin(θ)+m2πpx+n2πpy
(2)
ksp(ω)=k0(ω)εmetalεairεmetal+εair
(3)
where ksp is the wavevector of SPP on gold/air interface, k0 is the vacuum wavevector, pxand py(800 nm) is the period of the gold hole arrays in x and y directions, m and nare integers. In the spectroscopic ellipsometer experiment, the in-plane reflection signals are collected, so only m is need to be considered in the calculations. In Fig. 4
Fig. 4 Red and blue lines are calculated SPP excitation bands using Eq. (2) and Eq. (3). The black and red dots are experiment data corresponding to first and second order grating coupled SPPs on gold/air surface in Fig. 3(a).
, it is shown that the first and second SPP bands are well fitted by Eq. (2) and Eq. (3). m1=1and m2=1correspond to the two SPP bands in NIR (red line) and Visible region (blue line). The SPPs propagate along the – x direction while m2=1representing the forward SPP waves in + x direction. At NIR region, the gold/air surface bound mode approaches the light line, the resonant dip in Fig. 4 may also come from the spoof plasmon phenomena [23

23. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

,24

24. F. J. García Vidal, L. Martín Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

].

3.2. RCWA method

To numerically simulate the whole reflection spectra as shown in Fig. 3(a), rigorous coupled wave analysis (RCWA) method and practical parameters of materials [25

25. J. B. Johnson and R. W. Christy, “Optical constants of the nobel metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

,26

26. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

] was utilized. The angle resolved reflection spectra of p and s polarized light is calculated, and then amplitude ratio of reflection (Ep/Es) is plotted in Fig. 5(a)
Fig. 5 (a) Ratio of reflection spectra of p and s polarized light is calculated using RCWA method. (b) For 50 degree incident angle, the theoretical calculation is compared with experimental data (amplitude and phase information). The narrowband SPP excitation is well simulated.
. It is shown that the spectroscopic ellipsometric result (Fig. 3) can also be well simulated by RCWA method. The experimental (blue line) and theoretical (red line) results agreed well with each other (Fig. 5(b)). In addition, a clear plasmonic dip with FWHM of ~13 nm is experimentally observed at the NIR regime (with Q factor of ~130), such narrowband plasmonic excitation is close to the theoretical limit (~5 nm). The bandwidth expected to be narrower if there is less imperfection in sample fabrication process. From the another point of view, as the optical interference are concluded in the collected signals, the sharp resonance may be attributed to the plasmonic resonance and Fano resonance effects [27

27. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

,28

28. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

].

4. Conclusions

In summary, we have introduced the spectroscopic ellipsometer to study the plasmonic excitation on gold hole-array nanostructures. The amplitude and phase property of narrowband plasmonic excitation was experimentally measured using the background free spectroscopic ellipsometry method. Narrow band (Q factor ~130) plasmonic excitation was realized and could be tuned in the Visible-NIR regime by scanning the incident angle of light. Grating coupled plasmon excitation and RCWA methods were used to simulate the SPP band structures, calculated results agree well with the experimental data.

Our work has shown that the reflection mode in spectroscopic ellipsometer is useful for measuring narrowband plasmonic excitation and phase change in metallic nanostructures. By measuring the s and p polarized light reflected from the plasmonic device simultaneously, the optical response of a plasmonic device could be tuned in real time and this will be important issue for practical application.

Acknowledgments

This work is supported by Hong Kong Research Grant Council with group research grant HKUST3/06C. The authors would like to acknowledge Prof. Edwin Pun and Dr. Polis Wong for their support in device fabrication.

References and links

1.

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

2.

F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]

3.

F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

4.

J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]

5.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000). [CrossRef]

6.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]

7.

A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia de Abajo, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]

8.

T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]

9.

H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009). [CrossRef]

10.

T. H. Reilly, S. H. Chang, J. D. Corbman, G. C. Schatz, and H. L. Rowlen, “Quantitative evaluation of plasmon enhanced Raman scattering from nanoaperture arrays,” J. Phys. Chem. C 111(4), 1689–1694 (2007). [CrossRef]

11.

G. A. Baker and D. S. Moore, “Progress in plasmonic engineering of surface-enhanced Raman-scattering substrates toward ultra-trace analysis,” Anal. Bioanal. Chem. 382(8), 1751–1770 (2005). [CrossRef] [PubMed]

12.

S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. 29(20), 2378–2380 (2004). [CrossRef] [PubMed]

13.

A. J. Haes, S. L. Zou, G. C. Schatz, and R. P. Van Duyne, “A nanoscale optical biosensor: the long range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles,” J. Phys. Chem. B 108(1), 109–116 (2004). [CrossRef]

14.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

15.

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]

16.

N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2(9), 564–570 (2008). [CrossRef]

17.

N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010). [CrossRef] [PubMed]

18.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008). [CrossRef]

19.

T. Xu, Y. K. Wu, X. G. Luo, and L. G. Luo, “Plasmonic nanoresonators for high-resolution colour fitering and spectral imaging,” Nat. Commun. 1, 59–63 (2010). [CrossRef] [PubMed]

20.

A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28(6), 423–425 (2003). [CrossRef] [PubMed]

21.

T. Xu, X. Jiao, and S. Blair, “Third-harmonic generation from arrays of sub-wavelength metal apertures,” Opt. Express 17(26), 23582–23588 (2009). [CrossRef]

22.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1988).

23.

J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]

24.

F. J. García Vidal, L. Martín Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]

25.

J. B. Johnson and R. W. Christy, “Optical constants of the nobel metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]

26.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

27.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]

28.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

OCIS Codes
(220.4241) Optical design and fabrication : Nanostructure fabrication
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Optics at Surfaces

History
Original Manuscript: February 10, 2011
Revised Manuscript: February 21, 2011
Manuscript Accepted: February 21, 2011
Published: March 18, 2011

Citation
G. X. Li, Z. L. Wang, S. M. Chen, and K. W. Cheah, "Narrowband plasmonic excitatio on gold hole-array nanostructures observed using spectroscopic ellipsometer," Opt. Express 19, 6348-6353 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-7-6348


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References

  1. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]
  2. F. J. García de Abajo, “Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]
  3. F. J. Garcia-Vidal, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]
  4. J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]
  5. E. Popov, M. Neviere, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62(23), 16100–16108 (2000). [CrossRef]
  6. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58(11), 6779–6782 (1998). [CrossRef]
  7. A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia de Abajo, “Evanescently coupled resonance in surface plasmon enhanced transmission,” Opt. Commun. 200(1-6), 1–7 (2001). [CrossRef]
  8. T. Li, H. Liu, F. M. Wang, Z. G. Dong, S. N. Zhu, and X. Zhang, “Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission,” Opt. Express 14(23), 11155–11163 (2006). [CrossRef] [PubMed]
  9. H. Liu, T. Li, Q. J. Wang, Z. H. Zhu, S. M. Wang, J. Q. Li, S. N. Zhu, Y. Y. Zhu, and X. Zhang, “Extraordinary optical transmission induced by excitation of a magnetic plasmon propagation mode in a diatomic chain of slit-hole resonators,” Phys. Rev. B 79(2), 024304 (2009). [CrossRef]
  10. T. H. Reilly, S. H. Chang, J. D. Corbman, G. C. Schatz, and H. L. Rowlen, “Quantitative evaluation of plasmon enhanced Raman scattering from nanoaperture arrays,” J. Phys. Chem. C 111(4), 1689–1694 (2007). [CrossRef]
  11. G. A. Baker and D. S. Moore, “Progress in plasmonic engineering of surface-enhanced Raman-scattering substrates toward ultra-trace analysis,” Anal. Bioanal. Chem. 382(8), 1751–1770 (2005). [CrossRef] [PubMed]
  12. S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. 29(20), 2378–2380 (2004). [CrossRef] [PubMed]
  13. A. J. Haes, S. L. Zou, G. C. Schatz, and R. P. Van Duyne, “A nanoscale optical biosensor: the long range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles,” J. Phys. Chem. B 108(1), 109–116 (2004). [CrossRef]
  14. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]
  15. A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009). [CrossRef] [PubMed]
  16. N. Yu, J. Fan, Q. J. Wang, C. Pflügl, L. Diehl, T. Edamura, M. Yamanishi, H. Kan, and F. Capasso, “Small-divergence semiconductor lasers by plasmonic collimation,” Nat. Photonics 2(9), 564–570 (2008). [CrossRef]
  17. N. Yu, Q. J. Wang, M. A. Kats, J. A. Fan, S. P. Khanna, L. Li, A. G. Davies, E. H. Linfield, and F. Capasso, “Designer spoof surface plasmon structures collimate terahertz laser beams,” Nat. Mater. 9(9), 730–735 (2010). [CrossRef] [PubMed]
  18. E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008). [CrossRef]
  19. T. Xu, Y. K. Wu, X. G. Luo, and L. G. Luo, “Plasmonic nanoresonators for high-resolution colour fitering and spectral imaging,” Nat. Commun. 1, 59–63 (2010). [CrossRef] [PubMed]
  20. A. Nahata, R. A. Linke, T. Ishi, and K. Ohashi, “Enhanced nonlinear optical conversion from a periodically nanostructured metal film,” Opt. Lett. 28(6), 423–425 (2003). [CrossRef] [PubMed]
  21. T. Xu, X. Jiao, and S. Blair, “Third-harmonic generation from arrays of sub-wavelength metal apertures,” Opt. Express 17(26), 23582–23588 (2009). [CrossRef]
  22. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1988).
  23. J. B. Pendry, L. Martín-Moreno, and F. J. García-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305(5685), 847–848 (2004). [CrossRef] [PubMed]
  24. F. J. García Vidal, L. Martín Moreno, and J. B. Pendry, “Surfaces with holes in them: new plasmonic metamaterials,” J. Opt. A, Pure Appl. Opt. 7(2), S97–S101 (2005). [CrossRef]
  25. J. B. Johnson and R. W. Christy, “Optical constants of the nobel metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
  26. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
  27. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef] [PubMed]
  28. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]

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