Multiband Plasmonic Sierpinski Carpet FractalAntennas

Francesco De Nicola,∗,† Nikhil Santh Puthiya Purayil,† Davide Spirito,¶ MarioMiscuglio,¶ Francesco Tantussi,‖ Andrea Tomadin,† Francesco De Angelis,‖

Marco Polini,† Roman Krahne,¶ and Vittorio Pellegrini†

†Graphene Labs, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy‡Physics Department, Universita degli studi di Genova, Via Dodecaneso 33, 16146 Genova,

Italy¶Nanochemistry Department, Istituto Italiano di Tecnologia, Via Morego 30, 16163

Genova, Italy§Chemistry and Industrial Chemistry Department, Universita degli studi di Genova, Via

Dodecaneso 33, 16146 Genova, Italy‖Plasmon Nanotechnologies, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova,

Italy

E-mail: francesco.denicola@iit.it

Abstract

Deterministic fractal antennas are employedto realize multimodal plasmonic devices. Suchstructures show strongly enhanced localizedelectromagnetic fields typically in the infraredrange with a hierarchical spatial distribu-tion. Realization of engineered fractal an-tennas operating in the optical regime wouldenable nanoplasmonic platforms for applica-tions, such as energy harvesting, light sensing,and bio/chemical detection. Here, we intro-duce a novel plasmonic multiband metamaterialbased on the Sierpinski carpet (SC) space-fillingfractal, having a tunable and polarization-independent optical response, which exhibitsmultiple resonances from the visible to mid-infrared range. We investigate gold SCs fabri-cated by electron-beam lithography on CaF2

and Si/SiO2 substrates. Furthermore, wedemonstrate that such resonances originatefrom diffraction-mediated localized surfaceplasmons, which can be tailored in determin-istic fashion by tuning the shape, size, andposition of the fractal elements. Moreover, our

findings illustrate that SCs with high orderof complexity present a strong and hierarchi-cally distributed electromagnetic near-field ofthe plasmonic modes. Therefore, engineeredplasmonic SCs provide an efficient strategy forthe realization of compact active devices witha strong and broadband spectral response inthe visible/mid-infrared range. We take ad-vantage of such a technology by carrying outsurface enhanced Raman spectroscopy (SERS)on Brilliant Cresyl Blue molecules depositedonto plasmonic SCs. We achieve a broadbandSERS enhancement factor up to 104, therebyproviding a proof-of-concept application forchemical diagnostics.

Keywords

Au sierpinski carpet fractal; quasi-periodic pho-tonic crystal; surface enhanced Raman spec-troscopy; localized surface plasmon; chemicalsensor; antenna metamaterial

Over the past decade, there has been a strong

1

arX

iv:1

804.

0286

6v1

[ph

ysic

s.op

tics]

9 A

pr 2

018

and ongoing interest in developing the design offractal metamaterials for compact, multiband,and high-gain antennas intended for radio-frequency applications,1 THz resonators2–4 andlasers,5 and microwave devices.1,6 Also, in themid-infrared range plasmonic fractal structureshave been reported to act as frequency-selectivephotonic quasi-crystals.7–15 Besides a few at-tempts by Dal Negro et al.,16,17 research in thevisible range is still in an early stage. This isdue to the expensive and challenging fabrica-tion of nanofractals, resulting from the needof high-resolution electron- or ion-beam tech-niques.

In this regard, plasmonic deterministic frac-tals7 offer the effective control and reproducibil-ity of their optical properties, by adjusting theirsize, shape, and position. The scale-invarianceproperty of deterministic fractals may be ex-ploited to realize devices with a tailorable, self-similar, and multimodal spectral response. Fur-thermore, such fractals can provide a potentialplatform to study enhanced light-matter inter-actions. Moreover, the tunable plasmonic near-field enhancement may lead to the realizationof advanced optoelectronic devices, such as so-lar cells,18 photodetectors,14,19 and on-chip sen-sors of multiple bio/chemical assays (multiplex-ers).10,15,17,20

Here, we present the fabrication, optical char-acterization, and electromagnetic simulation ofAu plasmonic structures inspired by the Sier-pinski carpet (SC) deterministic fractal.21 Upto date, such SCs have been experimentallystudied mainly in the far-infrared range,12,13

while at optical frequencies only calculationshave been reported.18,22 We systematically in-vestigated both experimentally and theoreti-cally plasmonic SCs from the visible to mid-infrared (VIS-MIR) range. In particular, werealized for the first time a space-filling SCwith five orders of complexity. We show thatthe fractal acts as a photonic quasi-crystal,23

due to the self-similar and hierarchical arrange-ment of its elements, with a multiband spec-tral response over the full investigated range,which can be tuned by controlling the frac-tal size, thickness, and order. We demon-strate that the resonances observed in the ex-

tinction spectra are diffraction-mediated sur-face plasmons. Furthermore, we illustrate bymeans of surface enhanced Raman spectroscopy(SERS)24–27 that such plasmonic SCs are ableto confine strong electromagnetic fields downto the nanoscale (sub-diffraction focusing) andon a broadband range of the electromagneticspectrum, thereby providing a promising appli-cation for bio/chemical sensing.

Results and discussion

Deterministic fractals21 are self-similar ob-jects generated by geometrical rules, havinga non-integer (Hausdorff-Besicovitch) dimen-sion. Sierpinski carpets can be generated bya recursive geometrical algorithm employinga Lindenmayer system implementation28 (seeSupporting Information 1). Practically, our AuSCs are designed starting from a unit cell ofside L0 = 10 µm that is divided into a 3 × 3array of sub-cells of lateral size L1 = L03

−1,with an Au square placed in the central sub-cell. By iteratively applying the same rule tothe generated sub-cells of size Lt = L03

−t, it ispossible to obtain fractals for higher orders tof complexity. At each iteration the side of thesub-cells is reduced by a factor L = 3. Since thenumber of empty sub-cells in the SC increasesby a factor N = 8 at every iteration, the fractaldimension is dH = logN / logL ≈ 1.89, whilethe topological dimension of such a discretesystem is zero.

By employing electron-beam lithography,metal evaporation, and lift-off techniques (seeMethods), we fabricated the first five orders ofan Au SC on CaF2 and Si/SiO2 substrates(Supporting Information 2). The nominalthickness of the Au squares ranged from 25± 3nm to 45± 3 nm, while their lateral sizes wereL1 = 3.38 ± 0.05 µm, L2 = 1.12 ± 0.01 µm,L3 = 390 ± 17 nm, L4 = 130 ± 7 nm, andL5 = 44 ± 3 nm. The representative scanningelectron microscopy (SEM) micrograph of thesample for t = 5 in Figure 1 show the excel-lent homogeneity and uniformity of the fractalstructure. In addition, we realized periodicarrays of Au squares with lateral size Lt, as

2

Figure 1: Plasmonic Au SC. a, Scanning electron micrograph of a 35±3 nm thick Au SC depositedon a Si/SiO2 substrate for fractal order t = 5. b, A 35± 3 nm thick Au periodic array with squaresize L5, as a comparison. Fast Fourier transform of the SEM micrographs for the SC at t = 5 (c)and the periodic array (d). The ∆ = ΓX and Σ = ΓM direction in the fractal reciprocal latticeare marked along with the first pseudo-Brillouin zones [−π/at, π/at]2 of the different orders.

a reference. A periodic array with size L5 isreported in Figure 1b.

Our fractal structure can be regarded as ametallo-dielectric photonic crystal. However,the quasi-periodic23 and self-similar arrange-ment of the square elements forming the SCcrystalline lattice breaks, due to its long-rangeorder, the translational invariance propertytypical of periodic photonic crystals,29 whileretaining a scale invariance. Therefore, fractalshave also self-similar and non-discrete recip-rocal lattices.7 In Figure 1c,d a comparisonbetween the singular-continuous7 reciprocal

lattice of the SC for t = 5 and the discretesquare reciprocal lattice of the periodic arraywith square size L5 is provided, respectively, bycomputing the Fourier transform of their SEMmicrographs. As confirmed by the box-countingmethod (see Supporting Information 3), the re-ciprocal lattice of the SC is self-similar. Also,the SC has a larger number of points in thereciprocal space than the periodic array, sinceits fractal reciprocal lattice is a superpositionof five periodic lattices with different constantsat = 3Lt, under the periodic approximation.7,30

Starting from the origin, each point of the SC

3

reciprocal lattice in Figure 1c is defined by a re-

ciprocal lattice vector∣∣∣G(t)

ij

∣∣∣ = 2π√i2 + j2/at.

It is worth mentioning that also Gij is scale-

invariant as G(t)ij = 3t−1G

(1)ij , thereby realiz-

ing a hierarchy of first pseudo-Brillouin zones[−π/at, π/at]2. It follows that the diffractionpatterns and the related optical spectra of suchfractals are themselves self-similar,7,23,31 with alarger number of allowed optical states than inperiodic arrays (Figure 1d). All these featuresmake fractals, such as the SC, an intriguinggeometry for the realization of a novel class ofphotonic quasi-crystals.7

Surface plasmons are collective charge os-cillations at the interface between a dielectricand a thin metal surface, which can be excitedby light, for instance.32 When the conductorsize is much smaller than the wavelength of theincident light (L < λ/10), surface plasmonstend to be spatially localized around the struc-ture.33

In the case of periodic and quasi-periodicphotonic crystals, when the wavelength of alocalized surface plasmon (LSP) resonance isslightly larger than the lattice constant, thephotonic mode, due to the optical diffractionassociated with the lattice, couples to the plas-monic mode of each particle to produce a hy-brid mode7,12,13,16,34–39 (Wood anomaly). Inparticular, when the wavelength of the incidentlight is larger than the lattice spacing (Rayleighcutoff), all the diffracted waves other than thezeroth order are evanescent and all the particlesare radiating in phase by dipolar coupling inthe plane of the grating. This results fromthe momentum-matching condition16,35,36,38

q = k sin θ ± gij, where q = k√εeff is the

diffracted beam wavevector, εeff is the effectivedielectric constant of the lattice, |k| = 2π/λis the wavevector of the incident light, θ is itsangle of incidence with respect to the latticesurface normal, and gij are the lattice wavevec-tors. Herein, gij are the SC reciprocal vectors

G(t)ij . At normal incidence, diffraction-mediated

LSPs can be excited when k(t)√εeff = ±G(t)ij .

We predict a set of four-fold degenerate LSPresonances, due to the square lattice symme-try, emerging in the Au SC optical spectra at

self-similar wavelengths (critical modes7)

λ(t)n =a08

−n/dH√i2 + j2

√εeff , (1)

where n ∈ [1, t] is the n-th resonance at thet-th fractal order.

In Figure 2a, we observed the zeroth-order(the incident and detected light are collinear)extinction (1−T ) spectra of the Au SCs exhibit-ing multiple resonances in the VIS-MIR range.The extinction efficiency (i.e., the extinctiondivided by the total area of the fractal) of theresonances is up to 185%, thus showing an ex-traordinary extinction.40 From the comparisonwith the extinction spectra of the periodic ar-rays (Figure 2b), it is possible to infer that theposition of the SC resonances scales linearlywith the lattice constant a (Figure 2b). TheSC resonances are blue-shifted with respect tothose of the periodic arrays, due to the couplingbetween the squares belonging to the differentfractal orders. As depicted in Figure 2c, theposition of the resonances in the SC extinctioncorrespond to the first reciprocal lattice vectorG

(t)10 of each fractal order. However, such modes

occur at slightly smaller wavenumbers than theFourier peaks in the ΓX and ΓM directionsobtained from Figure 1c (i.e., at wavelengthsslightly larger than the lattice constants at),thus confirming that the origin of such res-onances in the Au SC extinction spectra isnot due to a diffraction mechanism, but todiffraction-mediated LSPs.

Furthermore, Au SCs are insensitive to thelinear and diagonal polarization of the incidentlight, having a centrosymmetric geometry (seeSupporting Information 4). This is an impor-tant feature in order to realize polarization-independent devices, since other fractal ge-ometries2,7,10,11,41 and conventional plasmonicstructures33,34 usually depend strongly on lightpolarization.

On the other hand, SCs do depend on thethickness of the metal squares, since they mustbe optically thick to achieve a large extinc-tion. This implies that the thickness must beseveral times the skin depth of the metal.34

Typical skin depths are on the order of 30-170

4

Figure 2: Optical properties of plasmonic Au SCs. a, Experimental extinction and extinctionefficiency spectra of 35± 3 nm thick SCs for t = 1-5 orders. Extinction peaks λ

(5)n are marked. b,

Experimental (solid curves) and calculated (dash-dot curves) normalized extinction of 35 ± 3 nmthick Au periodic arrays with lattice constants at. Dashed lines indicate the array LSPs. Curvesin a and b are offset by 0.15. c, Experimental normalized extinction spectrum of the SC at t = 5(magenta solid curve) and normalized intensity of the points in the SC fast Fourier transform inFigure 1c, along the ∆ = ΓX (red solid curve) and Σ = ΓM (blue solid curve) directions. Curvesare offset by 1.5. Note that the SC Fourier spectra were converted into photon energy units by~ω = ~kc. Extinction peaks λ

(5)n and reciprocal lattice vectors G

(t)10 are marked. d, Experimental

extinction spectra of SCs for t = 5 with thicknesses 25±3 nm (blue solid curve), 35±3 nm (magentasolid curve), and 45 ± 3 nm (black solid curve). Inset, FWHM of the LSP modes as a function ofthe aspect ratio w in log-log scale.

nm for Au in the VIS-MIR range. As illus-trated in Figure 2d for an Au SC at t = 5, theextinction spectrum changes qualitatively formetal thicknesses ranging from 25 ± 3 nm to45 ± 3 nm displaying sharp Fano resonances42

in place of broad peaks (see Supporting Infor-

mation 5). This suggests that the full-width-half-maximum (FWHM) of the LSPs dependson the aspect ratio (i.e., lateral size to thick-ness) wt = Lt/h.36 Indeed, the inset in Figure2d shows that the closer the aspect ratio tounity, the sharper and the shorter in wavelength

5

Figure 3: Scaling of the Au SC plasmons. a,Experimental LSP resonances λ

(t)n as a function

of their index n. The black solid line is the bestfit of the experimental data given by Equation1, which is in agreement with electromagneticsimulations for λ

(5)n (orange star). The fit gives

a fractal dimension value dH = 1.92 ± 0.04.b, Experimental and calculated (black curve)LSP resonances as a function of LSP wavevec-tor kp = π/Lt. The red line represents the free-space dispersion of light ~ω = ~kc.

the resonance (see Supporting Information 6).Therefore, the sharpest resonance occurs whenthe structures are isotropic (cubic), and thebroadest when they are oblate.The SC optical spectrum at a given fractalorder t exhibits n = t resonances with wave-

length λ(t)n corresponding mainly to the first

order of diffraction (i, j) ≡ (1, 0). Of such res-onances, n − 1 refer to the SC at order t − 1,although shifted by a factor ∝ a−1

t owing tothe far-field diffraction coupling among the in-creased number of squares.33 In Figure 3a thewavelengths λ

(t)n of the peaks in the extinction

measurement for each fractal order are plot-ted, along with the calculated data for λ

(5)n .

The best fit of the experimental data, whichis in excellent agreement with the numericalsimulations, is given by Equation 1 (where dHis treated as the fitting parameter), setting(i, j) ≡ (1, 0). The fit returns a fractal dimen-sion dH = 1.92± 0.04. As predicted, such LSPresonances are self-similar as their wavelengthhas the same scale-invariance law (Lt = 8−t/dH )as the SC, depending on the fractal dimensionas an exponential law. From data in Figure 2a,we can draw in Figure 3b the dispersion rela-tion of diffraction-mediated LSP modes. Here,kp = π/Lt = 3π/at is the LSP wavevector ofthe SC, as shown in Figure 4. It follows thatalso kp is self-similar.

In order to investigate the electromagnetic be-havior of the plasmonic SCs, we computed theirelectromagnetic near-field spatial distributionsby finite element method analysis. In Figure 4,the calculated electric near-field enhancementEz/E0 is depicted for the fractal orders t = 1-4at their LSP resonances. Our calculations showa resonant excitation of coupled dipolar anten-nas centered on the elements constituting thefractal. On the other hand, by increasing thefractal order, the system exhibits highly local-ized electromagnetic fields (hot spots) locatedon a sub-wavelength scale, resulting in addi-tional plasmonic modes at shorter wavelengths.This mechanism provides a hierarchical multi-scale of hot spots that transfer the excitationstowards progressively smaller length scales, ex-hibiting large values of electric near-field en-hancement. As a consequence of the SC fractalscaling the hot spot distribution of the resonantmodes is self-similar. Two main phenomena canbe distinguished. On one hand, a red-shift ata given LSP wavelength along with a decreaseof its electric near-field intensity. As alreadystated for the far-field optical spectra, this is

6

Figure 4: Finite element method simulations of plasmonic Au SCs. Simulated electric near-fieldenhancement (Ez/E0) distribution of SCs for orders t = 1−4 (from left to right) at their resonances

λ(t)1 (a-d), λ

(t)2 (e-g), λ

(t)3 (h-i), λ

(t)4 (j). The incident electric field E0 is polarized vertically and the

phase is set to π/4 in order to maximize the field intensity. Each distribution is normalized to itsmaximum value. Inset, a sketch of the modeled Au SC deposited on a CaF2 substrate.

attributed to the coupling among structural el-ements of different size, with the difference thatnear-fields couple by dipolar interactions. Onthe other hand, new LSP modes arise at shorterwavelengths with higher intensity. Analogousconsiderations can be drawn for the magneticfield enhancement (see Supporting Information7).

Another experimental evidence that LSPscan strongly couple by diffraction-mediated far-field interactions is presented in Figure 5. Themicrographs, which refer to dark-field scat-tering maps of SCs illuminated using whitelight, illustrate characteristic localized spatial

distributions with peculiar colors,16 which crit-ically depend on the fractal order and on thedistance between the squares. Hence, the in-terplay between short-range dipolar coupling(sub-wavelength near-field localization) andlong-range far-field coupling (radiative multiplescattering) produces a variation of the near-field intensity and spatial distribution (Figure4), and a wavelength shift of the LSP reso-nances along with a change in their intensity(Figure 2a) and far-field spatial distribution(Figure 5).

In order to experimentally confirm the com-putational model, we investigated the SC

7

Figure 5: Dark-field images of the SCs at different fractal orders t = 1-5. Note that since themicroscope halogen lamp is a white source, it does not emit at mid-infrared wavelengths. Thus,the first and second fractal orders diffract the incident light (λ << Lt).

electric near-field spatial distributions bySERS measurements on a thin layer (12 ± 2nm) of Brilliant Cresyl Blue (BCB) dye[(C17H20ClN3O)2ZnCl2], as a probe depositedon the Au SCs. Average Raman spectra of thesamples acquired at λex = 633 nm are plottedin Figure 6a for fractal orders t = 1-5 and foran unpatterned Au film, as a reference. Theexcitation wavelength is resonant with the dye(Figure 6b). The Raman spectra show a seriesof vibrational bands, arising from the molecule,with an increasing intensity as a function of thefractal order. The enhancement of the Ramansignal attributed to the SCs at higher ordersis much stronger than that of the referenceAu film, thus confirming the presence of hotspots. We selected the strongest BCB vibra-tional mode ω? = 1655 cm−1, correspondingto the coupling of NH2 scissor mode with theasymmetric stretch mode of C rings,43 in orderto evaluate the maximum SERS enhancementfactor EFsers (see Supporting Information 8).The EFsers at λex = 633 nm as a function ofthe lattice constant at of the fractals is reportedin Figure 6c, while for the fractal at t = 5 as afunction of the incident wavelength is reportedin Figure 6d. We found that EFsers increaseswith the fractal order as a power law. DespiteBCB is resonant at λex = 633 nm, for orderst = 1-3 the enhancement factor is very small asno LSP mode is in resonance (Figure 6b). Fororders t = 4-5, EFsers is highest as the excita-tion wavelength is not only resonant with thedye, but also with a LSP resonance of the SC.The resonant EFsers obtained at λex = 633 nmis about 104, while in the non-resonant case, for

instance at λex = 785 nm, is about 103 (Figure6d). It means that a maximum electric fieldenhancement factor of about 10 is provided inthe resonant case, while of about 5 in the non-resonant case. In particular, the latter factoris not affected by the dye fluorescence, thus ispurely a surface-enhanced electromagnetic ef-fect. We infer that the plasmonic fractal has abroadband EFsers, which is about twice higherin absolute value than an equivalent periodicarray (Figure 6d), and such a structure couldbe used for multiplexing experiments with sev-eral assays absorbing in different ranges of theelectromagnetic spectrum.

In Figure 6e, the spatial distributions of elec-tric field enhancement E/E0, obtained fromthe the experimental Raman intensity maps ofω? at λex = 633 nm normalized to the signalof the reference Au film, are reported for frac-tal orders t = 1-5. The contour plots presenta maximum of contrast localized over the el-ements constituting the fractals for t = 1-3orders. Differently, for t = 4-5 a large enhance-ment of the electric field is shown in betweenthe structures of the previous orders, respec-tively in correspondence of the squares withsize L4 and L5. Note that since the area of thelaser spot is 0.785 µm2, the instrument aver-ages out over the structures L4 and L5. Forinstance, the intensity profile across the map att = 5 changes by a factor ≈ 10 from the centralsquare L1 to the surrounding smaller squares(see Supporting Information 8). Therefore, thesmaller the element size, the larger the electricfield localization occurring on it due to LSPssupported by the Au structures, which decay

8

Figure 6: Surface enhanced Raman spectroscopy on plasmonic Au SCs. a, Raman spectra atλex = 633 nm of BCB deposited on the SC for t = 1-5 orders and on a reference Au film. Curvesare offset by 0.20. The band at 800-1000 cm−1 is due to the Si/SiO2 substrate on which SCswere patterned. b, Normalized extinction spectra of BCB (blue solid curve), SC at t = 5 (blacksolid curve), and periodic array at L5 (red solid curve). Curves are offset by 0.20. Dotted linesrepresent Raman excitation wavelengths λex. c, SERS enhancement of the BCB vibrational modeω? = 1655 cm−1 at λex = 633 nm as a function of the SC lattice constant at, in log-log scale. d,SERS enhancement of the BCB vibrational mode ω? = 1655 cm−1 as a function of λex for the SCat t = 5 (black dots) and periodic array at L5 (red squares). Dashed lines are guides for the eyes.Experimental electric field enhancement E/E0 maps of ω? at λex = 633 nm for t = 1-5 orders ofthe SC (e) and electromagnetic simulations of E/E0 (f). Each map is normalized to its maximumvalue.

9

rapidly outside the squares. Our results are ingood agreement with those obtained by elec-tromagnetic simulations shown in Figure 6f,and with the work by Hsu et al.20 Notably, thecomputed map for t = 5 has a maximum valueof the electric field enhancement E/E0 ≈ 13on L5 squares at λex = 633 nm, which is com-parable with the experimental value obtainedEF

1/4sers ≈ 10.

In conclusion, we have demonstrated bothexperimentally and theoretically a novel multi-band plasmonic antenna based on the com-pact design of a gold-based Sierpinski carpetfractal yielding multiresonant modes from thevisible to mid-infrared range. This class of en-gineered devices offer promising applicationsfor bio-chemical detection. As an example,we have carried out surface enhanced Ramanspectroscopy on Brilliant Cresyl Blue moleculesdeposited onto a plasmonic Sierpinski carpetachieving a broadband enhancement factor upto 104. The exploitation of such plasmonicfractal antennas to improve the versatility ofRaman spectroscopy in the routine applicationto biology and chemistry.

Methods

Sample fabrication

Sierpinski carpets were patterned by electron-beam lithography (Raith 150-Two) on CaF2

and Si/SiO2 substrates. A layer of ap-proximately 160 nm of 950K poly-methyl-methacrylate (PMMA A2 1:1, 1% in anisole)was deposited by spincoating on the substratespreviously cleaned by O2 plasma, then post-baked for 7 min on a hot plate at 180◦ C. Inorder to prevent charge accumulation due tothe electron beam, a 10 nm thick Al conduc-tive layer was deposited on CaF2 substratesat a rate of 0.2 A/s by thermal evaporation(Kurt J. Lesker) at an operating pressure of10−6 mbar. The electron beam was operatedat 20 kV with a current of 35 pA. The SCpatterns were exposed with a varying dose in-versely proportional to the size of the squaresof the fractal. The conductive layer was re-

moved by washing it in KOH (1 M) for 10seconds, followed by rinsing in deionized wa-ter. The resist was developed for 30 s in a cold(8◦ C) 1:3 mixture of MIBK:IPA. A 5/X nm(where X is 25-45 nm) thick Ti/Au film wasdeposited on the substrates at a rate of 0.2 A/sby electron-beam evaporation (Kenosistec) atan operating pressure of 10−6 mbar. Lift-offwas then performed by hot acetone. For Ra-man measurements, SCs were dip-coated for 1h in 1 mM BCB aqueous solution, then rinsedin deionized water to wash the excess moleculesin order to form a thin layer about 10 nm thick,and finally dried in nitrogen flow.

Sample characterization

Scanning electron microscopy micrographs ofSC samples deposited on Si/SiO2 were ac-quired by FEI Helios NanoLab DualBeam 650.Atomic force microscopy height profiles of thesamples deposited on Si/SiO2 were measuredin tapping mode by Bruker Innova in combi-nation with V-type cantilever and SiN tips.Optical spectroscopy in transmission modewas performed with unpolarized and polarizedlight on SCs deposited on CaF2 substrates,by Thermo Fisher FTIR spectrometer andThermo Scientific Nicolet Continuµm micro-scope equipped with NO2-cooled MCT and Sidetectors, KBr and quartz beamsplitters, and a15× (0.58 N.A.) Cassegrain objective. Surfaceenhanced Raman spectroscopy was carried outby Renishaw inVia micro-Raman microscopeequipped with a 150× (0.95 N.A.) objective andλex = 514 nm, λex = 532 nm, λex = 633 nm,and λex = 785 nm laser sources at a power 0.5mW and integration time 10 s. All spectra werecalibrated with respect to the first-order siliconLO phonon peak at 520 cm−1 and recordedin backscattering geometry at room tempera-ture. Raman measurements were performed onBCB adsorbed on SCs and as a reference on a35±3 nm thick (3 nm root-mean-square rough-ness) Au film deposited on the same Si/SiO2

substrate of the fractals. Raman maps of theBCB ω? = 1655 cm−1 vibrational mode werescanned at 0.3 µm steps in both the directionsin the plane of the sample. Renishaw WiRE

10

3.0 software was used to analyze the collectedspectra, whose baseline was corrected to thethird-order polynomial. Dark-field images ofthe SC samples were recorded by Nikon Eclipseupright microscope. Samples were illuminatedwith unpolarized white light by a 50 W halo-gen lamp in transmission mode. The lightscattered by the SCs was collected with a 100×(0.96 N.A.) objective and imaged by a digitalcamera.

Acknowledgement This work was supported

by the European Unions Horizon 2020 researchand innovation programme under Grant Agree-ment No. 696656 Graphene Flagship – Core1.The authors declare no competing financialinterests.Supporting Information. Detailed informa-tion on the generating algorithm of the fractals,additional experimental data, fractal analysis,optical response with polarized light, fitting ofthe extinction resonances, scaling of the plas-mons, magnetic near-field simulations of thefractal, details on SERS measurements.

References

(1) Werner, D. H.; Ganguly, S. An Overviewof Fractal Antenna Engineering Research.IEEE Antennas Propag. Mag. 2003, 45,38–57.

(2) Miyamaru, F.; Saito, Y.; Takeda, M. W.;Hou, B.; Liu, L.; Wen, W.; ; Sheng, P. Ter-ahertz Electric Response of Fractal Meta-material Structures. Phys. Rev. B 2008,77, 0451241–0451246.

(3) Maraghechi, P.; Elezzabi, A. Y. EnhancedTHz Radiation Emission from PlasmonicComplementary Sierpinski Fractal Emit-ters. Opt. Express 2010, 18, 27336–27345.

(4) Agrawal, A.; Matsui, T.; Zhu, W.; Na-hata, A.; Vardeny, Z. V. Terahertz Spec-troscopy of Plasmonic Fractals. Phys. Rev.Lett. 2009, 102, 1139011–1139014.

(5) Mahler, L.; Tredicucci, A.; Beltram, F.;Walther, C.; Faist, J.; Beere, H. E.;

Ritchie, D. A.; Wiersma, D. S. Quasi-Periodic Distributed Feedback Laser. Na-ture Photonics 2010, 4, 165–169.

(6) Wen, W.; Zhou, L.; Hou, B.; Chan, C. T.;Sheng, P. Resonant Transmission of Mi-crowaves through Subwavelength FractalSlits in a Metallic Plate. Phys. Rev. B2005, 72, 1534061–1534064.

(7) Dal Negro, L.; Boriskina, S. V. Determin-istic Aperiodic Nanostructures for Pho-tonics and Plasmonics Applications. LaserPhotonics Rev. 2012, 6, 178–218.

(8) Hou, B.; Liao, X. Q.; Poon, J. K. S. Res-onant Infrared Transmission and EffectiveMedium Response of Subwavelength H-Fractal Apertures. Opt. Express 2010, 18,3946–3951.

(9) Huang, X.; Xiao, S.; Ye, D.; Huangfu, J.;Wang, Z.; Ran, L.; Zhou, L. Fractal Plas-monic Metamaterials for SubwavelengthImaging. Opt. Express 2010, 18, 10377–10387.

(10) Aslan, E.; Aslan, E.; Wang, R.;Hong, M. K.; Erramilli, S.; Turkmen, M.;Saracoglu, O. G.; Negro, L. D. Multi-spectral Cesaro-Type Fractal PlasmonicNanoantennas. ACS Photonics 2016, 3,2102–2111.

(11) Gottheim, S.; Zhang, H.; Govorov, A. O.;Halas, N. J. Fractal Nanoparticle Plas-monics: The Cayley Tree. ACS Nano2015, 9, 3284–3292.

(12) Bao, Y.-J.; Zhang, B.; Wu, Z.; Si, J.-W.; Wang, M.; Peng, R.-W.; Lu, X.;Shao, J.; Li, Z.-F.; Hao, X.-P.; Ming, N.-B.Surface-Plasmon-Enhanced Transmissionthrough Metallic Film Perforated withFractal-Featured Aperture Array. Appl.Phys. Lett. 2007, 90, 2519141–2519143.

(13) Bao, Y.-J.; Li, H.-M.; Chen, X.-C.;Peng, R.-W.; Wang, M.; Lu, X.; Shao, J.;Ming, N.-B. Tailoring the Resonancesof Surface Plasmas on Fractal-Featured

11

Metal Film by Adjusting Aperture Con-figuration. Appl. Phys. Lett. 2008, 92,1519021–1519023.

(14) Aygar, A. M.; Balci, O.; Cakmakya-pan, S.; Kocabas, C.; Caglayan, H.;Ozbay, E. Comparison of Back and TopGating Schemes with Tunable GrapheneFractal Metasurfaces. ACS Photonics2016, 3, 2303–2307.

(15) Aouani, H.; Rahmani, M.; Sıpova, H.;Torres, V.; Hegnerova, K.; Beruete, M.;Homola, J.; Hong, M.; Navarro-Cıa, M.;Maier, S. A. Plasmonic Nanoantennas forMultispectral Surface-Enhanced Spectro-scopies. J. Phys. Chem. C 2013, 117,18620–18626.

(16) Gopinath, A.; Boriskina, S. V.; Feng, N.-N.; Reinhard, B. M.; Negro, L. D.Photonic-Plasmonic Scattering Res-onances in Deterministic AperiodicStructures. Nano Lett. 2008, 8, 2423–2431.

(17) Lee, S. Y.; Amsden, J. J.; Boriskina, S. V.;Gopinath, A.; Mitropolous, A.; Ka-plan, D. L.; Omenetto, F. G.; Negro, L. D.Spatial and Spectral Detection of Pro-tein Monolayers with Deterministic Aperi-odic Arrays of Metal Nanoparticles. PNAS2010, 107, 12086–12090.

(18) Zhu, L.-H.; Shao, M.-R.; Peng, R.-W.;Fan, R.-H.; Huang, X.-R.; Wang, M.Broadband Absorption and Efficiency En-hancement of an Ultra-thin Silicon SolarCell with a Plasmonic Fractal. Opt. Ex-press 2013, 21, 313–323.

(19) Fang, J.; Wang, D.; DeVault, C. T.;Chung, T.-F.; Chen, Y. P.; Boltas-seva, A.; Shalaev, V. M.; Kildishev, A. V.Enhanced Graphene Photodetector withFractal Metasurface. Nano Lett. 2017, 17,57–62.

(20) Hsu, K. H.; Back, J. H.; Fung, K.-H.; Fer-reira, P. M.; Shim, M.; Fang, N. X. SERSEM Field Enhancement Study through

Fast Raman mapping of Sierpinski Car-pet Arrays. J. Raman Spectrosc. 2010, 41,1124–1130.

(21) Mandelbrot, B. The Fractal Geometry ofNature; W. H. Freeman and Co.: NewYork, 1982.

(22) Volpe, G.; Volpe, G.; Quidant, R. FractalPlasmonics: Subdiffraction Focusing andBroadband Spectral Response by a Sier-pinski Nanocarpet. Opt. Express 2011,19, 3612–3618.

(23) Janot, C. Quasicrystals - A Primer ;Clarendon Press: Oxford, 1994.

(24) De Angelis, F. et al. Breaking the Diffu-sion Limit with Super-Hydrophobic Deliv-ery of Molecules to Plasmonic Nanofocus-ing SERS Structures. Nat. Photon. 2011,5, 682–687.

(25) Kneipp, K.; Wang, Y.; Kneipp, H.; Perel-man, L. T.; Itzkan, I.; Dasari, R. R.;Feld, M. S. Single Molecule Detection Us-ing Surface-Enhanced Raman Scattering(SERS). Phys. Rev. Lett. 1997, 78, 1667–1670.

(26) Chirumamilla, M.; Toma, A.; Gopalakr-ishnan, A.; Das, G.; Zaccaria, R. P.;Krahne, R.; Rondanina, E.; Leoncini, M.;Liberale, C.; De Angelis, F.; Di Fab-rizio, E. Plasmonic Nanostructures: 3DNanostar Dimers with a Sub-10-nmGap for Single-/Few-Molecule Surface-Enhanced Raman Scattering. Adv. Mater.2014, 26, 2353–2358.

(27) Gopalakrishnan, A.; Chirumamilla, M.;De Angelis, F.; Toma, A.; Proietti Za-ccaria, R.; Krahne, R. Bimetallic 3DNanostar Dimers in Ring Cavities: Recy-clable and Robust Surface-Enhanced Ra-man Scattering Substrates for Signal De-tection from Few Molecules. ACS Nano2014, 8, 7986–7994.

(28) Lindenmayer, A.; Prusinkiewicz, P. TheAlgorithmic Beauty of Plants ; Springer:New York, 1990.

12

(29) Sakoda, K. Optical Properties of PhotonicCrystals ; Springer: New York, 2005.

(30) Gambaudo, J.-M.; Vignolo, P. BrillouinZone Labelling for Quasicrystals. NewJournal of Physics 2014, 16, 1–11.

(31) Allain, C.; Cloitre, M. Optical Diffractionon Fractals. Phys. Rev. B 1986, 33, 3566–3569.

(32) Kittel, C. Introduction to Solid StatePhysics ; John Wiley & Sons: New York,2005.

(33) Maier, S. A. Plasmonics: Fundamentalsand Applications ; Springer: New York,2007.

(34) Genet, C.; Ebbesen, T. W. Light in TinyHoles. Nature 2007, 445, 39–46.

(35) Ghaemi, H. F.; Thio, T.; Grupp, D. E.;Ebbesen, T. W.; Lezec, H. J. SurfacePlasmons Enhance Optical Transmissionthrough Subwavelength Holes. Phys. Rev.B 1998, 58, 6779–6782.

(36) Ebbesen, T. W.; Lezec, H. J.;Ghaemi, H. F.; Thio, T.; Wolff, P. A.Extraordinary Optical Transmissionthrough Sub-Wavelength Hole Arrays.Nature 1998, 391, 667–669.

(37) Matsui, T.; Agrawal, A.; Nahata, A.;Vardeny, Z. V. Transmission Resonancesthrough Aperiodic Arrays of Subwave-length apertures. Nature 2007, 446, 517–521.

(38) Kravets, V. G.; Schedin, F.; Grig-orenko, A. N. Extremely Narrow PlasmonResonances Based on Diffraction Couplingof Localized Plasmons in Arrays of Metal-lic Nanoparticles. Phys. Rev. Lett. 2008,101, 0874031–0874034.

(39) Auguie, B.; Barnes, W. L. Collective Reso-nances in Gold Nanoparticle Arrays. Phys.Rev. Lett. 2008, 101, 1439021–1439024.

(40) Lochbihler, H. Surface Polaritons on Gold-Wire Gratings. Phys. Rev. B 1994, 50,4795–4801.

(41) Chirumamilla, M.; Chirumamilla, A.;Roberts, A. S.; Proietti Zaccaria, R.;De Angelis, F.; Kristensen, P. K.;Krahne, R.; Bozhevolnyi, S. I.; Ped-ersen, K.; Toma, A. Hot-Spot Engi-neering in 3D Multi-Branched Nanos-tructures: Ultrasensitive Substrates forSurface-Enhanced Raman Spectroscopy.Adv. Optical Mater. 2017, 5, 1600836–1600836.

(42) Luk’yanchuk, B.; Zheludev, N. I.;Maier, S. A.; Halas, N. J.; Nordlander, P.;Giessen, H.; Chong, C. T. The FanoResonance in Plasmonic Nanostructuresand Metamaterials. Nat. Mater. 2010, 9,707–715.

(43) Nieckarz, R. J.; Oomens, J.; Berden, G.;Sagulenkoa, P.; Zenobi, R. Infrared Mul-tiple Photon Dissociation (IRMPD) Spec-troscopy of Oxazine Dyes. Phys. Chem.Chem. Phys. 2013, 15, 5049–5056.

13

Graphical TOC Entry

Artisticillustration of an Au Sierpinski carpet.

14