Abstract: We describe the plasmonic properties of a two-dimensionalperiodic metallic grating of macroscopic size obtained by gold deposition ona self-assembled silica opal. Structural characterization shows a transitionfrom microscopic order to isotropy at macroscopic scale. Optical reflectionspectra exhibit a dip of almost complete absorption due to coupling tosurface-plasmon-polaritons (SPP). This is explained by theoretical calcu-lations introducing a density of coupled SPP modes. We demonstrate, at agiven incidence angle, a broad continuum of coupled wavelengths over thevisible spectrum. This opens new possibilities in fields where light-plasmoncoupling is required over a broad range of wavelengths and incidenceorientations.
References and links1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830
(2003).2. E. Fort and S. Gresillon, “Surface enhanced fluorescence,” J. Phys. D 41, 013001 (2008).3. J. C. Brown and M. J. T. Milton, “Nanostructures and nanostructured substrates for surface enhanced Raman
scattering (SERS),” J. of Raman Spec. 39, 1313–1326 (2008).4. J. R. Lakowicz, “Plasmonics in biology and plasmon-controlled fluorescence,” Plasmonics 1, 5–33 (2006).5. S. Scarano, M. Mascini, A. P.F. Turner, and M. Minunni, “Surface plasmon resonance imaging for affinity-based
biosensors,” Biosensors and bioelectronics 25, 957–966 (2010).6. J. Vuckovic, M. Loncar, and A. Scherer, “Surface plasmon enhanced light-emitting diodes,” IEEE J. Quantum
Electron. 36, 1131–1144 (2000).7. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mat. 9, 205–213 (2010).8. R. Esteban, M. Laroche, and J.-J. Greffet, “Influence of metallic nanoparticles on upconversion processes,” J.
Appl. Phys. 105, 033107 (2009).9. C. Vion, P. Spinicelli, L. Coolen, C. Schwob, J.-M. Frigerio, J.-P. Hermier, and A. Maıtre, “Controlled modi-
fication of single colloidal CdSe/ZnS nanocrystal fluorescence through interactions with a gold surface,” Opt.Express 18, 7440-7455 (2010).
10. V. E. Ferry, M. A. Verschuuren, H. B. T. Li, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Improved red-response in thin film a-Si:H solar cells with soft-imprinted plasmonic back reflectors,” Appl. Phys. Lett. 95,183503 (2009).
11. W. Zhou, H. Gao, and T. W. Odom, “Toward broadband plasmonics : tuning dispersion in rhombic plasmoniccrystals,” ACS Nano 4, 1241–1247 (2010).
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24424
12. J. Zhang, Y.-J. Ye, X. Wang, P. Rochon, and M. Xiao, “Coupling between semiconductor quantum dots andtwo-dimensional surface plasmons,” Phys. Rev. B 72, 201306(R) (2005).
13. S. C. Kitson, W. L. Barnes, and J. R. Sambles, “Full photonic band gap for surface modes in the visible,” Phys.Rev. Lett. 77, 2670–2673 (1996).
14. C. Lopez, “Materials aspects of photonic crystals,” Adv. Mater. 15, 1679–1704 (2003).15. F. Marlow, Muldarisnur, P. Sharifi, R. Brinkmann, and C. Mendive, “Opals : status and prospects,” Angew. Chem.
Int. Ed. 48, 6212–6233 (2009).16. A. R. Tao, D. P. Ceperley, P. Sinsermsuksakul, A. R. Neureuther, and P. Yang, “Self-organized silver nanoparticles
for three-dimensional plasmonic crystals,” Nano Lett. 8, 4033–4038 (2008).17. H. W. Yan, C. F. Blanford, B. T. Holland, M. Parent, W. H. Smyrl, and A. Stein, “A chemical synthesis of periodic
macroporous NiO and metallic Ni,” Adv. Mater. 11, 1003–1006 (1999).18. O. D. Velev, P. M. Tessier, A. M. Lenhoff, and E. W. Kaler, “A class of porous metallic nanostructures,” Nature
401, 548 (1999).19. P. Jiang, J. Cizeron, J. F. Bertone, and V. L. Colvin, “Preparation of macroporous metal films from colloidal
crystals,” J. Am. Chem. Soc. 121, 7957–7958 (1999).20. A. V. Akimov, A. A. Meluchev, D. A. Kurdyukov, A. V. Scherbakov, A. Holst, and V. G. Golubev, “Plasmonic
effects and visible light diffraction in three-dimensional opal-metal photonic crystals,” Appl. Phys. Lett. 90,171108 (2007).
21. J. C. Hulteen, and R. P. Van Duyne, “Nanosphere lithography : a materials general fabrication process for periodicparticlearray surfaces,” J. Vac. Sci. Technol. A 13, 1553–1558 (1995).
22. P. Zhang, Z. Wang, H. Dong, J. Sun, J. Wu, H.-T. Wang, S. Zhu, N. Ming, and J. Zi, “The anomalous infraredtransmission of gold films on two-dimensional colloidal crystals,” Adv. Mater. 18, 1612–1616 (2006).
23. C. Farcau and S. Astilean, “Probing the unusual optical transmission of silver films deposited on two-dimensionalregular arrays of polystyrene microspheres,” J. Opt. A 9, S345–S349 (2007).
24. R. M. Cole, J. J. Baumberg, F. J. Garcia de Abajo, S. Mahajan, M. Abdelsalam, and P. N. Bartlett, “Understandingplasmons in nanoscale voids,” Nano Lett. 7, 2094–2100 (2007).
25. S. Mahajan, M. Abdelsalam, Y. Suguwara, S. Cintra, Andrea Russell, J. Baumberg, and P. Bartlett, “Tuningplasmons on nano-structured substrates for NIR-SERS,” Phys. Chem. Chem. Phys. 9, 104–109 (2007).
26. N. N. Lal, B. F. Soares, J. K. Sinha, F. Huang, S. Mahajan, P. N. Bartlett, N. C. Greenham, and J. J. Baumberg,“Enhancing solar cells with localized plasmons in nanovoids,” Opt. Express 19, 11256–11263 (2011).
27. L. Landstrom, D. Brodoceanu, K. Piglmayer, and D. Bauerle, “Extraordinary optical transmission through metal-coated colloidal monolayers,” Appl. Phys. A 84, 373–377 (2006).
28. Z.-B. Wang, Y.-H. Ye, Y.-A. Zhang, and J.-Y. Zhang, “Visible transmission through metal-coated colloidal crys-tals,” Appl. Phys. A 97, 225–228 (2009).
29. L. Landstrom, D. Brodoceanu, D. Bauerle, F. J. Garcia-Vidal, S. G. Rodrigo, and L. Martin-Moreno, “Extraordi-nary transmission through metal-coated monolayers of microspheres,” Opt. Express 17, 761–772 (2009).
30. B. Ding, M. E. Pemble, A. V. Korovin, U. Peschel, and S. G. Romanov, “Three-dimensional photonic crystalswith an active surface : gold film terminated opals,” Phys. Rev. B 82, 035119 (2010).
31. W. Mu, D.-K. Hwang, R. P. H. Chang, M. Sukharev, D. B. Tice, and J. B. Ketterson, “Surface-enhanced Ramanscattering from silver-coated opals,” J. Chem. Phys. 134, 124312 (2011).
32. J. Stropp, G. Trachta, G. Brehm, and S. Schneider, “A new version of AgFON substrates for high-throughputanalytical SERS applications,” J. Raman Spectrosc. 34, 26–32 (2003).
33. K. Liu, C. Sun, N. C. Linn, B. Jiang, and P. Jiang, “Wafer-scale surface-enhanced Raman scattering substrateswith highly reproducible enhancement,” J. Phys. Chem. C 113, 14804 (2009).
34. A. N. Gruzintsev, G. A. Emel’chenko, V. M. Masalov, M. Romanelli, C. Barthou, P. Benalloul, and A. Maıtre,“Luminescent properties of opals,” Inorg. Mater. 44, 159–164 (2008).
35. C. Vion, C. Barthou, P. Benalloul, C. Schwob, L. Coolen, A. Gruzintev, G. Emelchenko, W. Masalov, J.-M.Frigerio, and A. Maıtre, “Manipulating emission of CdTeSe nanocrystals embedded in three-dimensional pho-tonic crystals,” J. Appl. Phys. 105, 113120 (2009).
36. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep.408, 131-314 (2005).
37. The SPP skin depth δ is obtained from the experimentally measured θ and λ by (i) considering that the peak inρ(λ ) (Fig. 5(b)) corresponds to values of φ = 10 o, (ii) calculating the experimental kSPP through the momentumconservation in eq. 1 with k// = (2π/λ )sinθ with φ = 10 o, and (iii) using the energy conservation conditionk2
0 = (2π/λ )2 = k2SPP +(1/δ )2 to find δ .
38. M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436(1976).
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24425
1. Introduction
Coupling to a metallic surface can be used for the enhancement of optical emission or ab-sorption [1, 2], with applications in fields such as surface-enhanced Raman scattering (SERS)[3], bio-imaging [4, 5], light-emitting diodes (LED) [6], photovoltaics [7, 8] or single-photonsources [9]. In order to take advantage of surface-plasmon-polariton (SPP) modes, which arenot coupled to far-field radiative modes in the case of a planar metallic surface, many studieshave introduced a periodic corrugation to the metallic surface. The phase-matching conditionis then fulfilled by the grating wave vector. For instance, LED or solar-cell devices have beenproposed with a corrugated metal surface for SPP-assisted in- or out-coupling [6, 10].
The realization of such plasmonic crystals with a sub-micrometric period often involves cleanroom technologies (e-beam lithography and nano-imprint [11]), although other techniques havebeen used, such as holography [12, 13]. For many applications, in particular for solar cells asreviewed in Ref. [7], it is necessary to obtain plasmonic samples of macroscopic size, withbroadband coupling to visible light and little dependence on the sample orientation.
Self-assembly provides an interesting bottom-up alternative for the fabrication of orderednanostructures. Opal samples (three-dimensionally ordered stacks of sub-micrometer balls)have been the most studied. Their fabrication, which uses soft chemistry reactions for the syn-thesis of silica balls and self-assembly for the ordering of the lattice, is now a mature technol-ogy [14, 15]. Three-dimensional metallic structures have also been fabricated either by directself-assembly of metallic nanoparticles [16] or by metal deposition in a dielectric opal used asa template (inverse opal [17–20]).
Self-assembled silica balls have also been used for the fabrication of two-dimensional metal-lic gratings.
In some cases, a monolayer of silica balls served as a mask for the evaporation of triangularnanoparticles [21–23] or as a mould for the electrodeposition of spherical nanovoids. This lattertype of structures has been the subject of comprehensive optical studies [24] which evidenceda dominant role of localized surface plasmon (LSP) modes, and applications for SERS [25] orsolar cells [26] were demonstrated.
In other cases, a metallic layer was deposited on top of self-assembled colloidal spheres.For thin opal slabs covered by a thin metallic film, extraordinary optical transmission (EOT)was demonstrated and attributed to SPP mediation [27,28], and combined photonic-crystal andEOT effects were studied [29,30]. With thicker metallic layers, the opal is purely a template forfabricating an opaque two-dimensional corrugated metallic grating. This is the approach whichis followed in the present study. Such structures have been used in SERS experiments : good-quality wafer-scale samples, reproducible spectra and very large enhancements were evidenced[31–33]. There has been however no extensive characterization of their optical properties. Thisis the purpose of the present article.
In this paper, we describe the fabrication of a plasmonic crystal of centimetric size, by evap-orating a thick layer of gold on an artificial silica opal used as a periodic template. We combinestructural characterization (atomic-force and electron microscopies) with optical angle- andpolarization-resolved characterizations. We analyze the role of disorder inside our plasmoniccrystal and show that its macroscopic properties are little sensitive to its in-plane orientation.A strong broadband absorption by SPP modes is measured, with absorptions as high as 95 %.The broadband nature of the plasmon coupling is related to the dispersive character of the SPPmodes.
In the first section, we present the fabrication and the structural characterization of our sam-ples, and explain how the corrugation depth can be tuned through the deposition parameters.We examine further the two-dimensional order of the samples in the second section by analyz-ing electron microscopy images, and show a transition from microscopic order to macroscopic
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24426
isotropy. We present in the third section an optical reflectometric characterization of the sam-ples and evidence both LSP and SPP modes, with a very strong absorption from the SPP mode.In the last section, we theoretically define and calculate a density of coupled SPP modes andshow that broadband coupling to the SPP modes can be expected.
2. Sample fabrication
The principle of the sample fabrication (Fig. 1(a)), is to evaporate a layer of gold onto a self-assembled periodical array of silica spheres (artificial opal). The gold thickness is larger thanthe SPP skin depth, so the gold layer is optically infinite : the silica structure is used purely as atemplate to impose a periodic corrugation to the gold layer.
b ) c )
0 1position (μm)
0
100
heig
ht (n
m)
h
500 nm
a )
opal template
silica smoothergold (150 to 500 nm)
(0 to 200 nm)
Fig. 1. (a) General structure of the fabricated samples : a gold layer evaporated on an artifi-cial opal, with an optional silica smoothing layer. (b) AFM image of a sample with 500 nmgold layer (and no smoothing layer). (c) Profile of the sample along the purple line indicatedin (b). A groove depth h = 90 nm is measured.
In a first step, we characterized the opal template, fabricated following the sedimentationprotocol described in [34]. The opal lattice is face-centered cubic, with its (111) planes parallelto the sample surface. Thus, the surface appears as a compact two-dimensional triangular lattice.The diameter of the spheres was estimated to a = 395 ± 5 nm by reflectometry as previouslydescribed in [35].
In a second step, the gold layer was evaporated on the silica balls template. Our typical sam-ple size was 1-2 cm. An atomic force microscopy (AFM) image of a sample with 500-nm goldthickness is displayed in Fig. 1(b). It shows that the opal surface is completely covered by thegold layer, in agreement with Ref. [31] where a similar silver deposition was characterized.The template two-dimensional structure is preserved in the corrugated surface and well-definedgrooves are observed (the sharpness of the junctions between the grooves was possibly under-estimated due to the AFM tip size, which is of the order of 20 nm). We measure by AFM aspheres diameter of 390±10 nm, in agreement with the value obtained by reflectometry.
An AFM profile of the sample is shown in Fig. 1(c). We define the groove depth h as theamplitude of this curve. A value of h = 90±10 nm was obtained for this sample.
The groove depth is a key parameter for adjusting the SPP dispersion relation. As comparedto the 500-nm-gold sample, h can be reduced by using thinner gold depositions, or increasedby previous addition of a silica smoothing sublayer (Fig. 1(a)). By varying the two layer thick-nesses (as summarized in Table 1), we were able to tune the groove depth h from 55 nm to150 nm.
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24427
Table 1. Control of the groove depth h (measured by AFM) by the thickness of the goldand silica layers.
Let us analyze more closely the two-dimensional grating order, with the example of the samesample as in Fig. 1. A 20x20 μm2 scanning electron microscopy (SEM) image is shown inFig. 2(a). It reveals the good homogeneity of the gold deposition and the almost-perfect flatnessof the opal template.
We plot in Fig. 2(b) the two-dimensional Fourier transform (FT) of the sample SEM image,for the overall 60x60 μm2 image, and for two 40x40 and 20x20 μm2 sub-portions (the latterbeing the one shown in Fig. 2(a)).
a ) b ) 20 x 20 μm
40 x 40 μm
60 x 60 μmc )
0 50 100
0.98
1A
(φ) (
norm
.)
φ (°) kx (μm )0 10-10
-1
ky (μ
m )
010
-10
-1ky
(μm
)0
10-1
0
-1ky
(μm
)0
10-1
0
-1
20 x 20 μm
φ40 μm
60 μm
20 μm
Fig. 2. (a) SEM image of a plasmonic sample with a gold layer of 500 nm. (b) FTs of threesample portions of sizes 60x60, 40x40 and 20x20 μm2. (c) Autocorrelation curves A(φ) ofthe three FTs, as defined in the text.
For the smallest portion, the six reciprocal nodes appear clearly and form a hexagon. Weextract from it a spheres diameter of a = 390±10 nm, which matches well with the values of390 and 395 nm previously obtained respectively by AFM and reflectometry. This portion ofthe sample is thus practically a single crystalline domain. For the larger portions, the FT patternis no longer hexagonal and tends to become a circle due to the presence of several orderedmonodomains with different random orientations.
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24428
In order to clarify the growing complexity of the FT patterns, we plot their angular autocorre-lation in Fig. 2(c). For this purpose, we consider the FT, expressed in polar coordinates F(k,φ),at a radius k = 2π/
√3a corresponding to the distance of the lattice nodes, and we define the
function A(φ) =< F(2π/√
3a,α)F(2π/√
3a,α +φ)>. This function shows a transition fromthe ordered to the isotropic situations. For the 20x20 μm2 portion, on the one hand, the plotexhibits a single 60o-periodicity corresponding to the hexagonal order. For the 60x60 μm2 por-tion, on the other hand, the quasi-isotropic nature of the sample is evidenced by the almostconstant autocorrelation function. A weak 15o-periodicity is also observed, which indicates thepresence of several monodomains tilted by multiples of 15o from each other.
The conclusion of this section is that the periodicity of our structure is maintained overtypical distances of 20 μm, larger than the SPP propagation length (3 μm at 600 nm for a flatgold surface [36]) : this sample constitutes indeed a plasmonic crystal. On the other hand, dueto the presence of multiple domains of random orientations, the behavior of this sample atmillimetric scale is isotropic : there is no preferred azimuthal orientation (as opposed to one-dimensional metallic gratings for instance).
4. Optical characterization
In this section, we characterize the SPP modes of the plasmonic samples by optical polarization-resolved reflectometry.
A collimated white-light beam was passed through a 1-mm diaphragm and a polarizer anddirected onto the sample with an incident angle θ . The reflected beam was passed through a2 mm diaphragm (chosen larger than the former diaphragm because of the slight beam diver-gence) in order to separate reflection from low-angle scattering, collected by an optical fiber andanalyzed by a spectrometer. All spectra were normalized by the spectrum of the illuminationlamp (measured with the 2-mm diaphragm and fiber facing the incident beam).
Figure 3 shows the reflection spectra for incident angles θ from 20 to 80 o for the same plas-monic crystal sample. We also plot in dashed lines the reflection spectra (at 20 and 70o) of aplane gold surface, deposited under the same conditions. The plane gold reflectivity decreasesbelow 500 nm due to bulk gold absorption by interband transitions. The same effect is ob-served for the plasmonic crystal. At high wavelengths, the reflectivity of the plasmonic crystalis maximum, but lower than the reflectivity of the plane gold surface, which we attribute to thescattering by the surface roughness.
The p-polarized spectra show a dip moving to longer wavelengths as θ increases (from 560nm at 20 to 650 nm at 80), while the s-polarized spectra show a fainter dip around 570 nm. Bothdips indicate the absorption of the incoming light by plasmonic modes of the sample, which arethen dissipated or re-radiated in different directions.
As SPP modes are transverse-magnetic, the s-polarized incident beam should not be coupledto these modes. Moreover, the position of the dip in s-polarization shows little dependence onthe incidence angle θ . We thus attribute this dip to a LSP mode, introduced by the sharpnessof the sample structure. For metallic nanovoids, such non-dispersive modes were also observedand attributed to LSP modes, which was confirmed by numerical modeling [24] .
The p-polarized dip, on the other hand, corresponds to the SPP modes, as evidenced by itsstrong position dependence in the incidence angle. The reflectivity at the bottom of this dipis only a few percent, as compared to typically 40 % above 700 nm. We conclude that, at theSPP wavelength, about 95 % of the incoming beam is absorbed by the plasmonic sample. Thisdemonstrates the excellent coupling of the SPP modes with light.
The same measurement was performed for samples with different groove depths h. The re-sults are summarized in Fig. 4(a) which plots the SPP-dip wavelength λ as a function of θ(circles), along with the theoretical SPP-coupling wavelength (full line), calculated at the zero-
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24429
400 500 600 700 8000
0.1
0.2
0.3
0.4
0.5
0.6
400 500 600 700 8000
0.1
0.2
0.3
0.4
0.5
P polarization
S polarization
Wavelength (nm)
Refle
ctio
n s
pec
tru
mRe
flect
ion
sp
ectr
um
θ = 20, 40, 60, 80°
θ = 80 °
θ = 20 °θ = 40 °θ = 60 °
θ θ
θ θ
Fig. 3. Full lines : p- and s-polarized reflection spectra, at incidence angles θ ranging from20 to 80 o, with steps of 10o, of a plasmonic sample with groove depth h = 90 nm. Dashedlines : p- and s-polarized reflection spectra of a plane gold surface for θ = 20 (black) and70 o (grey) (divided by 2 for clarity because the reflectivity of the plane sample is larger).
th order in h as explained in the next section. As expected, the experimental curves convergetowards the theoretical one as h is decreased, which confirms our attribution of the reflectiondip to SPP modes and validates the model.
The difference between the calculations and the experimental data is larger for lower θ . Wesuggest that this occurs because h is then not negligible as compared to the SPP skin depth in airδ . In order to verify this, we plot in Fig. 4(b) the relative difference between the experimentaland theoretical λ , as a function of the ratio h/δ (δ being obtained from the experimental valuesof λ and θ , without any assumption on the SPP dispersion relation [37]). We find an excellentcorrelation between these two quantities, demonstrating that h/δ is indeed the parameter whichdetermines to which extent the zero-th order model is valid. This model remains valid within a
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24430
5 % margin as long as h/δ remains below 0.6. It is the case at θ > 40o for h = 90 nm, and forall data points for h = 55 nm.
0.2 0.4 0.6 0.8 1500
520
540
560
580
600
620
640
660
680
h = 150 nm
130 nm100 nm
90 nm
75 nm55 nm
Coup
led
SPP
wav
elen
gth
(nm
)
sin(θ)
a ) b )
0 1 2
0
0.05
0.1
0.15
0.2
0.25
0.3
Rela
tive
diffe
renc
e :
(λex
p - λ
theo
)/λt
heo
ratio h / δ
Fig. 4. (a) Dots : experimental wavelengths λ of the p-polarized reflection dip as a functionof θ for six samples with different groove depths h. Full line : theoretical position of thedip, as calculated in the last section for at the zero-th order in h. (b) Relative difference(λexp.−λtheo.)/λtheo. between the measured and theoretical wavelengths, as a function ofthe ratio of the groove depth h over the SPP skin depth in air δ . The colors correspond tothe same values of h as indicated in (a).
We finally develop a model for the calculation of the SPP-coupling relation λ (θ). The results,which were discussed above for comparison with the experimental data of Fig. 4(a), will hereuncover further characteristics of our samples.
At the zero-th order in h, the coupling conditions are given analytically by the SPP dispersionrelation of a flat gold surface and by the phase-matching condition of the triangular lattice.
The dispersion relation for a flat gold surface is kSPP(ω) = k0(ω)√
ε ′mεd/(ε ′m + εd), where,εm(ω) = ε ′m+ iε ′′m, εd and k0(ω) =ω/c are respectively the gold and air dielectric constants andthe wave vector of light in vacuum. For a given frequency ω , the norm of the SPP wave vector�kSPP is always larger than the norm k// = k0 sinθ of the in-plane component of the incomingbeam wave vector, forbidding any interaction with propagating fields. The phase matching isprovided by the vectors of the reciprocal lattice. The six first of these vectors, of norm 4π/
√3a,
are defined in the inset of Fig. 5 and labelled �Gi. For an azimuthal angle φ between the latticex-axis and the incoming beam, the phase-matching condition writes [11] :
kSPP =√(k//cos(φ)+Gix)
2 +(k//sin(φ)+Giy)2 (1)
We plot in Fig. 5(a) the corresponding calculated λ (θ) for a lattice parameter a = 390 nm,the gold dispersion εm(ω) being measured by ellipsometry on a plane gold surface. We limitourselves to values of φ from 0 to 30o because of the symmetries of the system, and to the �G4
and �G5 vectors because the other bands are below 500 nm, where gold absorption is dominant.The incident beam diameter is about 1 mm, so that, following the discussion of section 2,
it probes an isotropic distribution of monodomain orientations φ . By calculating the curves
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24431
φ = 0°φ = 10°φ = 20°
φ = 30°
φ = 20°
φ = 10°φ = 0°
Wav
elen
gth
(nm
)
sin(θ)
a ) b )
Γ
G3
k//
kSPPφ
x
y
ρ(θ,λ)0 0.2 0.4 0.6 0.8 1
450
500
550
600
650
700
θ = 30°
θ = 70°
0 0.02 0.04450
500
550
600
650
700
θ = 30°
θ = 70°
gold absorption gold abs.
θ = 50°
θ = 50°
G2
G1G4
G5 G6
G4
G5
Fig. 5. (a) Calculated values of the SPP-coupled wavelength as a function of the incidenceangle θ , for the phase-matching vectors �G4 and �G5, for a = 390 nm and for various gratingorientations φ . The line φ = 30o is a symmetry axis : λG4(60−φ) = λG5(φ). (b) Densityof coupled SPP modes for three angles θ , calculated as explained in text.
λ (θ) for Nφ =175 values of φ equally spaced from 0 to 30o and counting the number Nλ ,θof these curves which pass through a [λ ,λ + dλ ] interval, we can define a density of coupledmodes ρ(λ ,θ) = Nλ ,θ/(dλ .Nφ ). We then convolve it by a gaussian distribution of values ofa centered on 390 nm and of width 10 nm, and we plot the obtained ρ(λ ,θ) in Fig. 5(b) forthree values of θ . We check that
∫ρ(λ )dλ = 2 : two modes (coupled to �G4 and �G5) are above
500 nm.These densities of coupled SPP modes exhibit two peaks at lower and higher wavelengths
and a continuum of coupled modes at intermediate wavelengths.The peak at lower wavelength is close to 500 nm and could not be observed experimen-
tally. The higher-wavelength peak is attributed to the experimental reflectivity dip, with a goodagreement in the peak position and dependence on θ , as was already plotted and discussed inFig. 4(a). The width of the experimental dip (about 50-70 nm) is similar to the width of thecalculated peak, and it also increases with θ . It is much broader, for instance, than the SPPabsorption dip measured on one-dimensional gratings [38].
We note in the p-polarized experimental spectra of Fig. 3 that, in the spectral interval be-tween the bulk absorption at 500 nm and the dip, the reflectivity is much lower than in thespectral region above the dip - for the s-polarization, the short-wavelength side of the dip isalso lower, but only because of its proximity to the bulk absorption edge. This interval of lowerp-polarized reflectivity may be attributed to the continuum of SPP-coupled modes in Fig. 5(b).This continuum at intermediate wavelengths constitutes a large portion (two thirds for θ = 50o)of the total coupled SPP modes, and extends down to 500 nm. Absorption by SPP-couplingshould thus occur over a very broad range of the visible spectrum, opening new opportunitiesfor applications where broadband light coupling is required, such as multiplexed bioimaging orsolar cells [7].
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24432
6. Conclusion
In this article, we described the fabrication of self-assembled plasmonic crystals of centimetricscale. The depth h of the profile, measured by AFM, ranged between 55 and 150 nm and wastuned by changing the gold and silica thicknesses. SEM images showed that, due to the presenceof monodomains of random orientation, the microscopic crystalline order was averaged at themacroscopic scale so that the sample properties are isotropic. Under p-polarized illumination,a strong broadband absorption was measured, which was attributed to the coupling of lightto the SPP modes of the plasmonic crystal. We detailed calculations at the zero-th order in hand showed that they were sufficient as long as h was lower than the SPP skin depth. Thesecalculations showed that, due to the random orientation of the crystalline monodomains, SPP-assisted absorption occurs on a very broad continuum of the visible spectrum. Future work willfocus on taking advantage of this isotropic broadband absorption in hybrid structures includinga dielectric waveguide or an active medium.
Acknowledgments
This work was funded by the Centre de Competence NanoSciences Ile-de-France (C’Nano IdF).We thank A. Redkin and A. Gruzintsev (IMTHPM, Russia) for providing the opal samples, S.Chenot, E. Lacaze and D. Demaille (INSP) for the gold deposition and AFM and SEM charac-terizations, and J.-M. Frigerio, P. Benalloul and C. Barthou (INSP) for fruitful discussions.
#156040 - $15.00 USD Received 6 Oct 2011; revised 21 Oct 2011; accepted 24 Oct 2011; published 14 Nov 2011(C) 2011 OSA 21 November 2011 / Vol. 19, No. 24 / OPTICS EXPRESS 24433
