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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 17 — Aug. 17, 2009
  • pp: 14586–14598
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Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence

Ewold Verhagen, L. Kuipers, and Albert Polman  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 14586-14598 (2009)
http://dx.doi.org/10.1364/OE.17.014586


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Abstract

Upconversion luminescence from erbium ions placed in the near field of subwavelength aperture arrays is used to investigate field enhancement of incident near-infrared light in such nanostructures. We study field enhancement due to the excitation of both propagating and localized surface plasmon resonances in arrays of square and annular apertures in a Au film. The conversion of 1480 nm excitation light to 980 nm emission is shown to be enhanced up to a factor 450 through a subwavelength hole array. The effects of array periodicity and aperture size are investigated. It is shown that a Fano model can describe both far-field transmission and near-field intensity. The upconversion enhancement reveals the wavelength and linewidth of the surface plasmon modes that are responsible for extraordinary transmission in such arrays. Angle-dependent measurements on annular aperture arrays prove that the field enhancement due to localized resonances is independent of the incident angle. These experiments provide insight in the mechanisms responsible for extraordinary transmission and are important for applications that aim to exploit near-field enhancement in nanostructured metal films.

© 2009 Optical Society of America

1. Introduction

There has been a large interest in subwavelength aperture arrays in metallic films ever since the first report of extraordinary transmission through such structures [1

1. 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).

]. Much effort has been dedicated to elucidating the fundamental principles that govern the far-field properties of aperture arrays [2

2. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).

, 3

3. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys.79(4) (2007).

]. Additionally, the enhancement of the near field in aperture arrays due to the excitation of optical resonances has been recognized to yield many possible applications. Among those applications are efficient sensing [4

4. A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-Enhanced Raman Scattering,” Nano Lett. 4(10), 2015–2018 (2004).

, 5

5. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005).

], strong control over light extraction [6

6. Y. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Opt. Lett. 28(7), 507–509 (2003).

, 7

7. A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C.-W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, “Surface Plasmon-Quantum Dot Coupling from Arrays of Nanoholes,” J. Phys. Chem. B 110(16), 8307–8313 (2006).

] and the enhancement of nonlinear effects [8

8. M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure Appl. Opt. 7(2), S118–S123 (2005).

11

11. W. Fan, S. Zhang, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array,” Opt. Express 14(21), 9570–9575 (2006).

]. Broadly speaking, two types of resonances can be distinguished that are responsible for the main transmission peaks observed in far-field transmission spectra as well as for the accompanying enhancement of the near field. The first type relies on the resonant excitation of surface waves (surface plasmon polaritons (SPPs) for optical frequencies) propagating along the metal film surface. As the excitation is due to grating diffraction, this effect depends strongly on incident angle and wavelength. The responsible surface waves can be described as eigenmodes of the corrugated metal surface [12

12. P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt. 7(8), 422–426 (2005).

]. Secondly, properly shaped apertures can support localized plasmonic modes that can lead to very large transmission [13

13. K. J. Klein 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).

, 14

14. F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95(10), 103901 (2005).

]. In particular, arrays of annular apertures exhibit a strong transmission resonance [15

15. F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).

17

17. W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).

]. This resonance is associated to the cutoff condition for the TE11 mode propagating inside individual apertures [18

18. F. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B: Lasers Opt. 79(1), 1–8 (2004).

21

21. M. I. Haftel, C. Schlockermann, and G. Blumberg, “Enhanced transmission with coaxial nanoapertures: Role of cylindrical surface plasmons,” Phys. Rev. B74(23) (2006).

]. A single aperture can be viewed as a truncated waveguide. Bounded by the air and substrate outside the metal film, it forms a low quality factor optical cavity. At cutoff, the wavevector of the TE11 mode propagating inside this waveguide approaches zero, which results in a cavity resonance that is independent of the metal film thickness. Because of the localized nature of the mode, this transmission resonance is independent of incident angle and polarization [22

22. D. Van Labeke, D. Gérard, B. Guizal, F. I. Baida, and L. Li, “An angle-independent Frequency Selective Surface in the optical range,” Opt. Express 14(25), 11945–11951 (2006).

], which is a large benefit for many applications. Moreover, the resonance has a wide bandwidth.

In this work, we investigate field enhancement in aperture arrays supporting both types of resonances using the photoluminescence from emitters placed in the near field of the metallic nanostructures. The emitters are erbium ions located in the sapphire substrate at an average depth of 35 nm below the structured Au film. The Er ions can convert infrared radiation with a free-space wavelength of 1480 nm to emission at shorter wavelengths (most notably at 980 nm) through an upconversion process [23

23. F. Auzel, “Upconversion and Anti-Stokes Processes with f and d Ions in Solids,” Chem. Rev. 104(1), 139–174 (2004).

, 24

24. G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79(3), 1258–1266 (1996).

]. The upconversion luminescence emitted into the far field is used as a direct probe of the local field intensity at the position of the Er ions. We find that the emitted upconversion luminescence from Er ions excited through hole arrays supporting propagating surface plasmon resonances can be enhanced up to a factor of 450. We investigate the influence of hole size and array periodicity on the field enhancement, and show the connection between far-field transmission and near-field intensity in a Fano model. Annular aperture arrays that exhibit localized plasmon resonances also lead to upconversion enhancements, albeit of smaller magnitude. We experimentally demonstrate that the field enhancement due to the excitation of such modes is independent of incident angle.

We note that enhancing the strength of the upconversion process with plasmonic nanostructures is a valuable goal in itself. Upconversion is of importance in lasers [25

25. W. von Klitzing, E. Jahier, R. Long, F. Lissillour, V. Lefevre-Seguin, J. Hare, J.-M. Raimond, and S. Haroche, “Very low threshold green lasing in microspheres by upconversion of IR photons,” J. Opt. B: Quantum Semiclassical Opt. 2(2), 204–206 (2000).

27

27. T. Lu, L. Yang, R. V. A. van Loon, A. Polman, and K. J. Vahala, “On-chip green silica upconversion microlaser,” Opt. Lett. 34(4), 482–484 (2009).

], display technology [28

28. E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A Three-Color, Solid-State, Three-Dimensional Display,” Science 273(5279), 1185–1189 (1996).

], and luminescent probes in microscopy [29

29. S. F. Lim, R. Riehn, W. S. Ryu, N. Khanarian, C.-k. Tung, D. Tank, and R. H. Austin, “In Vivo and Scanning Electron Microscopy Imaging of Upconverting Nanophosphors in Caenorhabditis elegans,” Nano Lett. 6(2), 169–174 (2006).

]. Moreover, it has been proposed as a possible route to enhance the efficiency of silicon solar cells. By converting part of the infrared solar radiation that is not captured by a silicon solar cell to radiation with shorter wavelengths, this part of the solar spectrum could be absorbed as well [30

30. T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by upconversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).

, 31

31. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).

]. However, all of these applications are hindered by the fact that the upconversion process is nonlinear in the excitation power and — in the case of rare earth ions — by the fact that typical absorption cross sections are small. Both facts limit the upconversion efficiency, especially at small pump powers. By making use of the enhanced fields of plasmonic resonances (which have large cross sections) as an intermediate step in the excitation of the emitters by incident light, their cross section can be effectively enhanced. This could lead to an increased upconversion efficiency [31

31. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).

34

34. V. K. Rai, L. de S. Menezes, C. B. de Araújo, L. R. P. Kassab, D. M. da Silva, and R. A. Kobayashi, “Surface-plasmon-enhanced frequency upconversion in Pr3+ doped tellurium-oxide glasses containing silver nanoparticles,” J. Appl. Phys. 103(9) (2008).

], from which all of the above applications might benefit.

2. Methods

The arrays of holes in a Au film are fabricated by electron beam lithography and liftoff. The structures are patterned in a layered resist stack of 300 nm photoresist (S1813), 20 nm Ge and 100 nm negative electron beam resist (Ma-N 2401). The pattern is transferred to the layers underneath by reactive ion etching. The 110 nm thick Au film is evaporated directly on the substrate. The photoresist is finally stripped in a liftoff process. The size of each aperture array is 50×50 µm2. Many arrays are fabricated, of which the period as well as aperture size and shape are varied. Two general aperture shapes are considered: square and annular (also termed coaxial). Figures 1(a,b) show SEM micrographs of details of both an array of square holes and an array of annular apertures. The annular apertures are designed to be square rather than circular, but these two types of hole shape are known to exhibit comparable behavior [37

37. A. Moreau, G. Granet, F. Baida, and D. V. Labeke, “Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11(10), 1131–1136 (2003).

].

The measurement geometry is schematically depicted in Fig. 1(c). The arrays are illuminated from the air side of the Au film at normal incidence with a numerical aperture of 0.02, effectively illuminating individual arrays completely. The excitation source is a fiber-pigtailed 1480 nm CW diode pump laser (Fitel). To record broad-band transmission spectra, a fiber-coupled halogen lamp is used. Light from the sample is collected through the substrate using a microscope objective (NA=0.75), and focused on the entrance facet of a 100 µm core diameter optical fiber. Because the magnification of the microscope is 12.5×, only light originating from the center of the illumination spot is detected, and the illumination within this collection spot can therefore be considered as homogeneous. The collected Er upconversion emission or white light transmission is then led to a spectrograph and a Si CCD detector to record spectra for visible wavelengths, or to a spectrograph and a InGaAs photodiode array detector to record infrared transmission spectra.

For the angle-dependent measurements reported in section 5, the illumination optics are replaced by a microscope objective with an NA of 0.75. By limiting the width of the beam entering the back aperture of the objective, the illumination NA is effectively reduced to 0.1. The illumination angle is then controlled by displacing the beam that enters the objective with respect to the optical axis.

Fig. 1. (a) and (b) SEM micrographs of details of fabricated arrays of square and annular apertures, respectively. Scale bars are 1 µm. (c) Schematic depiction of the measurement geometry. The sample is illuminated with 1480 nm pump light, and upconversion luminescence from Er ions implanted in the sapphire substrate is collected through the substrate. (d) Er3+ 4f level diagram indicating the upconversion mechanism that leads to the population of Er3+ levels emitting at wavelengths of 980, 660, and 550 nm under 1480 nm excitation.

Upconversion emission from the Er ions is used as a probe of the local intensity of the 1480 nm excitation laser light. A level diagram of the 4f energy levels in Er3+ is shown in Fig. 1(d). The pump light excites Er ions to the first excited state, from which multiple upconversion processes can occur to populate higher Er levels [23

23. F. Auzel, “Upconversion and Anti-Stokes Processes with f and d Ions in Solids,” Chem. Rev. 104(1), 139–174 (2004).

, 24

24. G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79(3), 1258–1266 (1996).

]. Two neighboring Er ions that are both excited can exchange energy in a dipole-dipole interaction to promote one to the 4I9/2 level. The excited Er ion then quickly relaxes to the second excited state (4I11/2), which can emit a photon with a wavelength of 980 nm (see Fig. 1(d)). This process, based on Förster transfer between two excited Er ions, is called cooperative upconversion. A competing process is excited state absorption, in which a second pump photon is directly absorbed by an Er ion residing in the first excited state. Excited state absorption is especially strong for large incident fluxes. At small pump powers, both processes will result in a quadratic dependence of the 980 nm upconversion photoluminescence on the excitation power. However, at higher excitation powers the pump power dependence can deviate from this quadratic dependence due to saturation of the Er levels. Higher order upconversion processes can also populate Er levels emitting at wavelengths of 660 nm and 550 nm (see Fig. 1(d)), but in this work we will focus on the emission from the 4I11/2 level at 980 nm. Because the emission wavelength is spectrally separated from the excitation wavelength, plasmon resonances will not simultaneously affect both excitation and emission channels. It is however impossible to exclude any effects on the upconversion emission due to the presence of the metal nanostructures, such as an altered branching ratio due to a changed local density of states at the emission wavelength [33

33. T. Aisaka, M. Fujii, and S. Hayashi, “Enhancement of upconversion luminescence of Er doped Al2O3v films by Ag island films,” Appl. Phys. Lett.92(13) (2008).

] or emission into preferred directions due to grating diffraction. The effect of the latter is suppressed by collecting with a large numerical aperture. As we will show, it is possible to ascribe all observations in this paper to modifications of the Er excitation rate due to a variation in pump intensity in the near field of the aperture arrays.

3. Field enhancement in hole arrays: dependence on structural parameters

We first focus our attention to arrays of square-shaped holes. Figure 2 shows a white light transmission spectrum of an array with a periodicity of 810 nm and a hole diameter of 290 nm, normalized to the transmittance through the sample without the Au film. It shows three distinct transmission peaks for wavelengths longer than 800 nm. These maxima have been attributed to the excitation of surface plasmon polaritons that are excited when the condition

kSPP=k0sinθ0+2πiax̂+2πjaŷ
(1)

is satisfied [1

1. 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).

, 39

39. 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, 6779 (1998).

, 40

40. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004). [PubMed]

]. Here k 0 and θ 0 are the free-space wavevector and angle of incidence, respectively. The array pitch is given by a. The integers i and j together specify the diffraction order (i, j) that couples to SPPs with wavevector kSPP. It is important to note that kSPP is a priori unknown, since it is an eigenmode of the corrugated surface (i.e. a pole of the scattering matrix of the array), and it depends on the exact geometry of the structure [12

12. P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt. 7(8), 422–426 (2005).

]. The two peaks with longest wavelengths correspond to excitation of the surface plasmon mode at the metal/sapphire surface, and they are therefore expected to enhance the field at the position of the Er ions.

Fig. 2. (a) Transmission spectrum of a hole array in a Au film with a pitch of 810 nm. The red dotted curve is a fit of the Fano model described in section 4. The vertical gray lines indicate the resonance frequencies deduced from the Fano model, and the dashed gray lines depict the Rayleigh conditions for different diffraction orders. (b) Transmission spectra around the (±1,0) peak at the Au/Al2O3 interface for various array periods. (c) Evolution of the same transmission peak with increasing hole size (indicated as diameter/period.)

The resonance wavelengths can be precisely tuned by varying the array periodicity, as can be seen for the transmission peak associated to excitation of the surface wave at the Al2O3 interface by the (±1,0) diffraction order in Fig. 2(b). The wavelength of the transmission maximum is a linear function of the periodicity to close approximation, since the SPP dispersion is nearly linear in this frequency regime. In the following experiment the periodicity is chosen such that the transmission peak coincides with the excitation wavelength of 1480 nm (see dashed line in Fig. 2(b)). This periodicity is 810 nm, as in Fig. 2(a). The upconversion photoluminescence spectrum as collected from that particular array is depicted by the red curve in Fig. 3, at an excitation power of 200 W/cm2. Emission from four different Er manifolds that are all populated through upconversion processes is observed, at wavelengths of 550, 660, 810 and 980 nm. Also plotted is the luminescence spectrum obtained under equal experimental conditions in the absence of gold (through an aperture in the Au film of 50×50 µm2), multiplied by a factor 10. Clearly, the upconversion emission on the hole array is strongly enhanced with respect to that reference. In the following, we define the ‘upconversion enhancement’ caused by an array as the ratio of the collected upconversion photoluminescence intensity on that array and the detected upconversion emission in a reference measurement in the absence of the Au film.

Fig. 3. Er upconversion spectra obtained from a hole array with a pitch of 810 nm (red) and from a reference in the absence of the Au film (black) under 1480 nm pumping at 200 W/cm2. Spectral resolution is ~20 nm. The inset depicts the dependence of the 980 nm emission on 1480 nm pump power, measured on the array (red) and on the reference (black).

We note that the measured upconversion enhancement does not directly reflect the average field enhancement at the position of the Er ions. The pump power dependence of the upconversion luminescence intensity is not a simple function such as a power law with a known exponent, which would make extraction of the pump power enhancement straightforward. The measured 980 nm upconversion emission as a function of 1480 nm pump power density is plotted on a double-logarithmic scale in the inset of Fig. 3, both on the array (red) and on the reference (black). For low pump powers, the upconversion luminescence can be seen to scale roughly quadratically with the excitation power as expected, but for larger pump powers saturation clearly occurs. By comparing the two curves, we can deduce a better estimate of the pump power enhancement on the array. We extract the pump powers for which the collected upconversion luminescence intensities on the array and on the reference are equal. The ratio of these pump powers represents the average field intensity enhancement at the position of the Er ions, since it tells us how much the pump intensity on the array can be diminished with respect to that of the reference, to still result in the same amount of emission. We find a field intensity enhancement of a factor 40. For practical reasons we will use the aforementioned upconversion enhancement to compare the field enhancement on different arrays. We note that the upconversion luminescence emitted at shorter wavelengths is even more strongly enhanced, as the corresponding Er levels are populated through higher order nonlinear upconversion processes. In the following, only the upconversion enhancement from the level emitting at a wavelength of 980 nm is considered.

We now systematically vary the periodicity and the hole diameter. Figure 4 shows the upconversion enhancement at an incident flux of 2 W/cm2 as a function of array periodicity and hole size (expressed as the hole diameter divided by the period). By varying the period in this range, both the (±1,0) and the (±1,±1) transmission resonances corresponding to SPPs at the Au/sapphire interface can be tuned to the excitation wavelength, at periods of approximately 800 and 1150 nm, respectively (see arrows in Fig. 4).

Fig. 4. 980 nm upconversion enhancement (under 1480 nm pumping at 2 W/cm2) at an emission wavelength of 980 nm on hole arrays as a function of array period and hole size. Every point in the figure is derived from measurements such as in Fig. 3 on a corresponding array.

For a given enhancement peak, a strong dependence of the upconversion luminescence on the aperture size can be seen in Fig. 4. For the resonance excited with a period of ~800 nm, maximum field enhancement is observed for a hole size that is 0.36 times the period, giving rise to a 450-fold upconversion enhancement. For larger holes, the field enhancement gradually decreases. Increasing the hole size will increase the evanescent tunneling of light through the holes as well as their scattering strength. Therefore the fraction of light coupled to SPPs will increase with increasing diameter. This becomes apparent as a monotonous increase of the far-field transmittance with increasing diameter [41

41. K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).

], that is depicted in Fig. 2(c). The near-field enhancement represented by the data in Fig. 4 on the other hand reveals the existence of an optimum hole size. The stronger coupling between far-field radiation and SPPs for larger holes results in a widening and a redshift of the transmission peak. Both effects can be observed in the data in Fig. 4, as well as in the transmission spectra in Fig. 2(c). Unlike the far-field transmittance, the near-field enhancement does not only scale with the fraction of light coupled to SPPs, but also with the resonance linewidth. A larger quality factor of the SPP resonance results in a stronger build-up of optical energy close to the array. A trade-off therefore exists between quality factor and coupled fraction as the hole size is varied, resulting in an optimum hole size that yields maximum field enhancement. Note that this optimum strongly depends on other parameters as well; most notably the film thickness and the illumination geometry. If the array would have been illuminated from the substrate side of the film, the exciting radiation would not have needed to tunnel through the apertures before exciting SPPs at the Au/sapphire interface, likely resulting in a stronger field enhancement at a smaller optimum hole size compared to the geometry studied here.

4. The Fano model: far field transmission and near field enhancement

We also investigate the relation between far-field transmittance and near-field enhancement by comparing their dependence on array periodicity. Figure 5 (red circles) shows the upconversion enhancement as a function of period for a hole diameter of 0.42 times the period from Fig. 4. Again, every data point represents a measurement on an array with a different periodicity. Also indicated is the transmittance at the excitation wavelength of 1480 nm on those same arrays. While both data sets show two maxima at similar periods (at 800 nm and ~1150 nm), striking differences between the shapes of the curves can be observed. The transmission peaks are wider, shifted to smaller pitches (corresponding to a spectral redshift), and pronouncedly more asymmetric than the peaks observed in the near-field enhancement probed by the upconversion emission.

Fig. 5. Comparison between the 980 nm upconversion enhancement (red) and the transmittance at 1480 nm (black) as a function of the hole array period (hole diameter/period=0.42). Each data point is measured on a different array. The curves are fits of a Fano model to the data. The resonance wavelengths and widths derived from the Fano model fitted to the transmittance data are imposed on the Fano model that is fitted to the upconversion enhancement data. The Fano model correctly predicts both the position and linewidth of the surface plasmon resonances, which are revealed by the upconversion enhancement.

These differences can be fully explained in terms of the Fano model [42

42. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).

]. The response of a subwavelength hole array can be described as that of multiple discrete states (the surface plasmon modes resonantly excited by various diffraction orders) coupled to a continuum (all far-field scattering states) [43

43. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).

, 44

44. C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).

]. The array can scatter light to the far field either directly or by first exciting surface plasmons and subsequently radiating to the far field. These nonresonant and resonant channels can interfere to produce asymmetric transmission spectra when both contributions are of approximately equal magnitude, as the resonant channel acquires an opposite phase as the frequency crosses the resonance [42

42. U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).

]. The spectral shape, generalized to a system of multiple resonances with resonance frequencies ωr and linewidths γr is given by [17

17. W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).

]

T(ω)=Ta(1+Σrqrεr)21+(Σrεr1)2,withεr=ωωrγr2,
(2)

5. Field enhancement in arrays of annular apertures: propagating and localized resonances

Fig. 6. (a) Transmission spectra of annular aperture arrays for increasing aperture size (array period 800 nm). The black curve is the transmittance of an array of square holes with the same period. (b) 980 nm upconversion enhancement (1480 nm pump at 2 W/cm2) as a function of the main parameters describing the shape of the annular apertures: the sum of D 1 and D 2, and the width of the air gap W expressed as a fraction of the total aperture size D 2.

Finally, we investigate the effect of the angle of incidence on the field enhancement due to either propagating or localized resonances. Figure 7 shows the measured upconversion enhancement on three different aperture arrays as a function of angle of incidence as described in section 2. The incident light is p-polarized. As expected, the upconversion enhancement on array A, which is associated to the excitation of propagating SPPs, shows a strong dependence on the incident angle, vanishing for angles larger than 10°. Note that the maximum enhancement at normal incidence is now reduced compared to that in Fig. 6(b) due to the use of a larger NA. The maximum enhancement on array B is observed for an incident angle of ~6°. For this array, the resonance was not tuned exactly to the laser wavelength at normal incidence. Instead, Eq. 1 is satisfied at a slightly different angle. The upconversion enhancement diminishes less rapidly for larger angles than for array A, since the resonance width is larger in this case. Nonetheless, still a clear angle-dependence is observed. Array C does not show an effect of the incident angle on the upconversion enhancement, which is ~10 for the angular range studied here. This shows that the field enhancement due to localized plasmonic resonances in annular aperture arrays is indeed independent on the incident angle.

Fig. 7. 980 nm upconversion enhancement as a function of incident angle for three different annular aperture arrays specified in Fig. 6 (1480 nm pump at 16 W/cm2). The field enhancement that is caused by a localized resonance (array C) is independent of the angle of incidence.

6. Conclusions

We have shown that Er upconversion luminescence can be used to probe the field enhancement in subwavelength aperture arrays. Field enhancement due to the excitation of both propagating and localized resonances in aperture arrays was studied. In hole arrays supporting propagating resonances, an enhancement of the 980 nm upconversion luminescence of Er ions under 1480 nm pumping by a factor 450 is demonstrated. This maximum upconversion enhancement is achieved for a hole size that balances SPP coupling efficiency and resonance linewidth. We note that the field enhancement can be further increased by changing the experimental geometry. The evanescent tunneling of the excitation light incident from the air side of the sample to excite SPPs at the substrate side of the sample (where the Er ions are located) limits the measured upconversion enhancement in the present geometry.

We confirm that the Fano model accurately predicts the frequencies and linewidths of the resonances that cause the extraordinary transmission phenomena. These properties are revealed by observing the Er upconversion enhancement. The relative strength of the resonant contribution to the near-field enhancement with respect to the non-resonant contribution is much larger than the ratio of both contributions in far-field transmission spectra. This results in much more symmetric lineshapes of the upconversion enhancement. The transmission peaks are significantly redshifted from the spectral position of maximal field enhancement.

This work reveals basic mechanisms governing near-field enhancement in metallic subwavelength aperture arrays, which is important for many practical applications of such nanostructures. In doing so, it sheds light on the mechanisms behind far-field extraordinary transmission properties as well.

Acknowledgements

This work was made possible by the fabrication and characterization facilities of the Amsterdam nanoCenter. It is part of the Joint Solar Programme (JSP) of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse organisatie voorWetenschappelijk Onderzoek (NWO). The JSP is co-financed by gebied Chemische Wetenschappen of NWO and Stichting Shell Research.

References and links

1.

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).

2.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445(7123), 39–46 (2007).

3.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys.79(4) (2007).

4.

A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, “Nanohole-Enhanced Raman Scattering,” Nano Lett. 4(10), 2015–2018 (2004).

5.

M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, “Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays,” Opt. Lett. 30(10), 1210–1212 (2005).

6.

Y. Liu and S. Blair, “Fluorescence enhancement from an array of subwavelength metal apertures,” Opt. Lett. 28(7), 507–509 (2003).

7.

A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C.-W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, “Surface Plasmon-Quantum Dot Coupling from Arrays of Nanoholes,” J. Phys. Chem. B 110(16), 8307–8313 (2006).

8.

M. Airola, Y. Liu, and S. Blair, “Second-harmonic generation from an array of sub-wavelength metal apertures,” J. Opt. A: Pure Appl. Opt. 7(2), S118–S123 (2005).

9.

J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, “Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays,” Phys. Rev. Lett. 97(14), 146102 (2006).

10.

W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, “Second Harmonic Generation from a Nanopatterned Isotropic Nonlinear Material,” Nano Lett. 6(5), 1027–1030 (2006).

11.

W. Fan, S. Zhang, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array,” Opt. Express 14(21), 9570–9575 (2006).

12.

P. Lalanne, J. C. Rodier, and J. P. Hugonin, “Surface plasmons of metallic surfaces perforated by nanohole arrays,” J. Opt. A: Pure Appl. Opt. 7(8), 422–426 (2005).

13.

K. J. Klein 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).

14.

F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Martín-Moreno, “Transmission of Light through a Single Rectangular Hole,” Phys. Rev. Lett. 95(10), 103901 (2005).

15.

F. I. Baida and D. Van Labeke, “Light transmission by subwavelength annular aperture arrays in metallic films,” Opt. Commun. 209, 17–22 (2002).

16.

F. I. Baida and D. Van Labeke, “Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays,” Phys. Rev. B 67(15), 155314 (2003).

17.

W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, “Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays,” Phys. Rev. Lett. 94(3), 033902 (2005).

18.

F. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, “Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands,” Appl. Phys. B: Lasers Opt. 79(1), 1–8 (2004).

19.

S. M. Orbons and A. Roberts, “Resonance and extraordinary transmission in annular aperture arrays,” Opt. Express 14(26), 12623–12628 (2006).

20.

F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, “Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes,” Phys. Rev. B74(20) (2006).

21.

M. I. Haftel, C. Schlockermann, and G. Blumberg, “Enhanced transmission with coaxial nanoapertures: Role of cylindrical surface plasmons,” Phys. Rev. B74(23) (2006).

22.

D. Van Labeke, D. Gérard, B. Guizal, F. I. Baida, and L. Li, “An angle-independent Frequency Selective Surface in the optical range,” Opt. Express 14(25), 11945–11951 (2006).

23.

F. Auzel, “Upconversion and Anti-Stokes Processes with f and d Ions in Solids,” Chem. Rev. 104(1), 139–174 (2004).

24.

G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, “Upconversion in Er-implanted Al2O3 waveguides,” J. Appl. Phys. 79(3), 1258–1266 (1996).

25.

W. von Klitzing, E. Jahier, R. Long, F. Lissillour, V. Lefevre-Seguin, J. Hare, J.-M. Raimond, and S. Haroche, “Very low threshold green lasing in microspheres by upconversion of IR photons,” J. Opt. B: Quantum Semiclassical Opt. 2(2), 204–206 (2000).

26.

E. Heumann, S. Bär, K. Rademaker, G. Huber, S. Butterworth, A. Diening, and W. Seelert, “Semiconductorlaser-pumped high-power upconversion laser,” Appl. Phys. Lett. 88(6) (2006).

27.

T. Lu, L. Yang, R. V. A. van Loon, A. Polman, and K. J. Vahala, “On-chip green silica upconversion microlaser,” Opt. Lett. 34(4), 482–484 (2009).

28.

E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, “A Three-Color, Solid-State, Three-Dimensional Display,” Science 273(5279), 1185–1189 (1996).

29.

S. F. Lim, R. Riehn, W. S. Ryu, N. Khanarian, C.-k. Tung, D. Tank, and R. H. Austin, “In Vivo and Scanning Electron Microscopy Imaging of Upconverting Nanophosphors in Caenorhabditis elegans,” Nano Lett. 6(2), 169–174 (2006).

30.

T. Trupke, M. A. Green, and P. Würfel, “Improving solar cell efficiencies by upconversion of sub-band-gap light,” J. Appl. Phys. 92(7), 4117–4122 (2002).

31.

F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, “On the use of localized plasmon polaritons in solar cells,” Phys. Status Solidi A 205(12), 2844–2861 (2008).

32.

S. Baluschev, F. Yu, T. Miteva, S. Ahl, A. Yasuda, G. Nelles, W. Knoll, and G. Wegner, “Metal-Enhanced UpConversion Fluorescence: Effective Triplet-Triplet Annihilation near Silver Surface,” Nano Lett. 5(12), 2482–2484 (2005).

33.

T. Aisaka, M. Fujii, and S. Hayashi, “Enhancement of upconversion luminescence of Er doped Al2O3v films by Ag island films,” Appl. Phys. Lett.92(13) (2008).

34.

V. K. Rai, L. de S. Menezes, C. B. de Araújo, L. R. P. Kassab, D. M. da Silva, and R. A. Kobayashi, “Surface-plasmon-enhanced frequency upconversion in Pr3+ doped tellurium-oxide glasses containing silver nanoparticles,” J. Appl. Phys. 103(9) (2008).

35.

URL: www.srim.org.

36.

G. N. van den Hoven, E. Snoeks, A. Polman, J.W. M. van Uffelen, Y. S. Oei, and M. K. Smit, “Photoluminescence characterization of Er-implanted Al2O3 films,” Appl. Phys. Lett. 62(24), 3065–3067 (1993).

37.

A. Moreau, G. Granet, F. Baida, and D. V. Labeke, “Light transmission by subwavelength square coaxial aperture arrays in metallic films,” Opt. Express 11(10), 1131–1136 (2003).

38.

J. Kalkman, L. Kuipers, A. Polman, and H. Gersen, “Coupling of Er ions to surface plasmons on Ag,” Appl. Phys. Lett. 86, 041113 (2005).

39.

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, 6779 (1998).

40.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92, 107401 (2004). [PubMed]

41.

K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, “Influence of hole size on the extraordinary transmission through subwavelength hole arrays,” Appl. Phys. Lett. 85(19), 4316–4318 (2004).

42.

U. Fano, “Effects of Configuration Interaction on Intensities and Phase Shifts,” Phys. Rev. 124(6), 1866–1878 (1961).

43.

M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, “Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes,” Phys. Rev. B 67(8), 085415 (2003).

44.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225, 331–336 (2003).

45.

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66(7–8), 163–182 (1944).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(300.2530) Spectroscopy : Fluorescence, laser-induced
(050.6624) Diffraction and gratings : Subwavelength structures

ToC Category:
Diffraction and Gratings

History
Original Manuscript: July 6, 2009
Revised Manuscript: July 29, 2009
Manuscript Accepted: July 30, 2009
Published: August 3, 2009

Citation
Ewold Verhagen, L. Kuipers, and Albert Polman, "Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence," Opt. Express 17, 14586-14598 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-14586


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References

  1. 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).
  2. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445(7123), 39-46 (2007).
  3. F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79(4) (2007).
  4. A. G. Brolo, E. Arctander, R. Gordon, B. Leathem, and K. L. Kavanagh, "Nanohole-Enhanced Raman Scattering," Nano Lett. 4(10), 2015-2018 (2004).
  5. M. Tanaka, F. Miyamaru, M. Hangyo, T. Tanaka, M. Akazawa, and E. Sano, "Effect of a thin dielectric layer on terahertz transmission characteristics for metal hole arrays," Opt. Lett. 30(10), 1210-1212 (2005).
  6. Y. Liu and S. Blair, "Fluorescence enhancement from an array of subwavelength metal apertures," Opt. Lett. 28(7), 507-509 (2003).
  7. A. G. Brolo, S. C. Kwok, M. D. Cooper, M. G. Moffitt, C.-W. Wang, R. Gordon, J. Riordon, and K. L. Kavanagh, "Surface Plasmon-Quantum Dot Coupling from Arrays of Nanoholes," J. Phys. Chem. B 110(16), 8307-8313 (2006).
  8. M. Airola, Y. Liu, and S. Blair, "Second-harmonic generation from an array of sub-wavelength metal apertures," J. Opt. A: Pure Appl. Opt. 7(2), S118-S123 (2005).
  9. J. A. H. van Nieuwstadt, M. Sandtke, R. H. Harmsen, F. B. Segerink, J. C. Prangsma, S. Enoch, and L. Kuipers, "Strong Modification of the Nonlinear Optical Response of Metallic Subwavelength Hole Arrays," Phys. Rev. Lett. 97(14), 146102 (2006).
  10. W. Fan, S. Zhang, N.-C. Panoiu, A. Abdenour, S. Krishna, R. M. Osgood, K. J. Malloy, and S. R. J. Brueck, "Second Harmonic Generation from a Nanopatterned Isotropic Nonlinear Material," Nano Lett. 6(5), 1027-1030 (2006).
  11. W. Fan, S. Zhang, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Second harmonic generation from patterned GaAs inside a subwavelength metallic hole array," Opt. Express 14(21), 9570-9575 (2006).
  12. P. Lalanne, J. C. Rodier, and J. P. Hugonin, "Surface plasmons of metallic surfaces perforated by nanohole arrays," J. Opt. A: Pure Appl. Opt. 7(8), 422-426 (2005).
  13. K. J. Klein 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).
  14. F. J. García-Vidal, E. Moreno, J. A. Porto, and L. Mart’?n-Moreno, "Transmission of Light through a Single Rectangular Hole," Phys. Rev. Lett. 95(10), 103901 (2005).
  15. F. I. Baida and D. Van Labeke, "Light transmission by subwavelength annular aperture arrays in metallic films," Opt. Commun. 209, 17-22 (2002).
  16. F. I. Baida and D. Van Labeke, "Three-dimensional structures for enhanced transmission through a metallic film: Annular aperture arrays," Phys. Rev. B 67(15), 155314 (2003).
  17. W. Fan, S. Zhang, B. Minhas, K. J. Malloy, and S. R. J. Brueck, "Enhanced Infrared Transmission through Subwavelength Coaxial Metallic Arrays," Phys. Rev. Lett. 94(3), 033902 (2005).
  18. F. Baida, D. Van Labeke, G. Granet, A. Moreau, and A. Belkhir, "Origin of the super-enhanced light transmission through a 2-D metallic annular aperture array: a study of photonic bands," Appl. Phys. B: Lasers Opt. 79(1), 1-8 (2004).
  19. S. M. Orbons and A. Roberts, "Resonance and extraordinary transmission in annular aperture arrays," Opt. Express 14(26), 12623-12628 (2006).
  20. F. I. Baida, A. Belkhir, D. Van Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74(20) (2006).
  21. M. I. Haftel, C. Schlockermann, and G. Blumberg, "Enhanced transmission with coaxial nanoapertures: Role of cylindrical surface plasmons," Phys. Rev. B 74(23) (2006).
  22. D. Van Labeke, D. Gérard, B. Guizal, F. I. Baida, and L. Li, "An angle-independent Frequency Selective Surface in the optical range," Opt. Express 14(25), 11945-11951 (2006).
  23. F. Auzel, "Upconversion and Anti-Stokes Processes with f and d Ions in Solids," Chem. Rev. 104(1), 139-174 (2004).
  24. G. N. van den Hoven, E. Snoeks, A. Polman, C. van Dam, J. W. M. van Uffelen, and M. K. Smit, "Upconversion in Er-implanted Al2O3 waveguides," J. Appl. Phys. 79(3), 1258-1266 (1996).
  25. W. von Klitzing, E. Jahier, R. Long, F. Lissillour, V. Lefevre-Seguin, J. Hare, J.-M. Raimond, and S. Haroche, "Very low threshold green lasing in microspheres by up-conversion of IR photons," J. Opt. B: Quantum Semiclassical Opt. 2(2), 204-206 (2000).
  26. E. Heumann, S. Bär, K. Rademaker, G. Huber, S. Butterworth, A. Diening, and W. Seelert, "Semiconductorlaser-pumped high-power upconversion laser," Appl. Phys. Lett. 88(6) (2006).
  27. T. Lu, L. Yang, R. V. A. van Loon, A. Polman, and K. J. Vahala, "On-chip green silica upconversion microlaser," Opt. Lett. 34(4), 482-484 (2009).
  28. E. Downing, L. Hesselink, J. Ralston, and R. Macfarlane, "A Three-Color, Solid-State, Three-Dimensional Display," Science 273(5279), 1185-1189 (1996).
  29. S. F. Lim, R. Riehn, W. S. Ryu, N. Khanarian, C.-k. Tung, D. Tank, and R. H. Austin, "In Vivo and Scanning Electron Microscopy Imaging of Upconverting Nanophosphors in Caenorhabditis elegans," Nano Lett. 6(2), 169-174 (2006).
  30. T. Trupke, M. A. Green, and P. W¨urfel, "Improving solar cell efficiencies by up-conversion of sub-band-gap light," J. Appl. Phys. 92(7), 4117-4122 (2002).
  31. F. Hallermann, C. Rockstuhl, S. Fahr, G. Seifert, S. Wackerow, H. Graener, G. v. Plessen, and F. Lederer, "On the use of localized plasmon polaritons in solar cells," Phys. Status Solidi A 205(12), 2844-2861 (2008).
  32. S. Baluschev, F. Yu, T. Miteva, S. Ahl, A. Yasuda, G. Nelles, W. Knoll, and G. Wegner, "Metal-Enhanced Up-Conversion Fluorescence: Effective Triplet-Triplet Annihilation near Silver Surface," Nano Lett. 5(12), 2482-2484 (2005).
  33. T. Aisaka, M. Fujii, and S. Hayashi, "Enhancement of upconversion luminescence of Er doped Al2O3v films by Ag island films," Appl. Phys. Lett. 92(13) (2008).
  34. V. K. Rai, L. de S. Menezes, C. B. de Araújo, L. R. P. Kassab, D. M. da Silva, and R.  A. Kobayashi, "Surface plasmon-enhanced frequency upconversion in Pr3+ doped tellurium-oxide glasses containing silver nanoparticles," J. Appl. Phys. 103(9) (2008).
  35. URL: www.srim.org.
  36. G. N. van den Hoven, E. Snoeks, A. Polman, J.W. M. van Uffelen, Y. S. Oei, and M. K. Smit, "Photoluminescence characterization of Er-implanted Al2O3 films," Appl. Phys. Lett. 62(24), 3065-3067 (1993).
  37. A. Moreau, G. Granet, F. Baida, and D. V. Labeke, "Light transmission by subwavelength square coaxial aperture arrays in metallic films," Opt. Express 11(10), 1131-1136 (2003).
  38. J. Kalkman, L. Kuipers, A. Polman, and H. Gersen, "Coupling of Er ions to surface plasmons on Ag," Appl. Phys. Lett. 86, 041113 (2005).
  39. 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, 6779 (1998).
  40. W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, "Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film," Phys. Rev. Lett. 92, 107401 (2004). [PubMed]
  41. K. L. van der Molen, F. B. Segerink, N. F. van Hulst, and L. Kuipers, "Influence of hole size on the extraordinary transmission through subwavelength hole arrays," Appl. Phys. Lett. 85(19), 4316-4318 (2004).
  42. U. Fano, "Effects of Configuration Interaction on Intensities and Phase Shifts," Phys. Rev. 124(6), 1866-1878 (1961).
  43. M. Sarrazin, J.-P. Vigneron, and J.-M. Vigoureux, "Role ofWood anomalies in optical properties of thin metallic films with a bidimensional array of subwavelength holes," Phys. Rev. B 67(8), 085415 (2003).
  44. C. Genet, M. P. van Exter, and J. P. Woerdman, "Fano-type interpretation of red shifts and red tails in hole array transmission spectra," Opt. Commun. 225, 331 - 336 (2003).
  45. H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66(7-8), 163-182 (1944).

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