Reciprocal space engineering with hyperuniform gold metasurfaces

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by  Marta Castro-Lopez

Reciprocal space engineering with hyperuniform gold metasurfaces
Marta Castro-Lopez,1 Michele Gaio,1 Steven Sellers,2 George
Gkantzounis,2 Marian Florescu,2,∗ and Riccardo Sapienza1,†
1Department of Physics, King’s College London, Strand, London WCR 2LS, United Kingdom.
2Department of Physics, University of Surrey, Guildford, Surrey GU27XH, United Kingdom.
Hyperuniform geometries feature correlated disordered topologies which follow from a tailored
k-spacedesign. Herewestudygoldplasmonichyperuniformmetasurfacesandwereportevidenceof
theeffectivenessofk-spaceengineeringonbothlightscatteringandlightemissionexperiments. The
metasurfaces possess interesting directional emission properties which are revealed by momentum
spectroscopyasdiffractionandfluorescenceemissionringsatsize-specifick-vectors. Theopeningof
these rotational-symmetric patterns scales with the hyperuniform correlation length parameter as
7 predicted via the spectral function method.
1
0
2 Coherent control of optical waves by scattering from high-Q optical cavities and low-loss waveguides [30–32],

n 2Dnanostructuredsurfacesisrevolutionisingthewaywe and microwave photonic circuits [25]. HuD structures
a shape the wavefront of an incoming light beam, open- fabrication is improving quickly, reaching already the IR
J
ing new avenues for miniaturised optical components for range [24] but not yet the visible.

4 integrated optical circuits [1], flat display technology [2], Here, we report visible light scattering and light emis-
2
andenergyharvesting[3,4]. Metallicsurfacesareinpar- sionexperimentsfromHuDplasmonicgoldmetasurfaces.
] ticular attractive due to the strong light-matter interac- We find that scattering from the metasurfaces is princi-
s tion associated with surface plasmons, enabling diffrac- pally directed into an annular angular pattern indicat-
c
i tion control through plasmonic crystals [5, 6] and metal ing reciprocal space engineering. Moreover, we investi-
t
p nano-particle arrays [7, 8], broadband operation and in- gatedirectionalemissionfromnear-fieldcoupledemitters
o crease of the plasmon mode density [9], enhanced omni- which, as confirmed by theoretical modelling, is shaped
s. directionallight extractionandcoupling[10], broadband into a ring from the effective band folding into the light
c absorption [11], fluorescence enhancement [12] and las- cone by scattering processes.
i
s ing [13, 14], and more recently the realisation of ultra
Themetasurfacedesignisderivedfromastealthhyper-
y thin lenses [15] and metasurface holograms [16].
h uniform point pattern with χ = 0.49 comprising 4000
p Whereas periodic geometries suffer from limited ro- points[22]andgeneratedunderaperiodicboundarycon-
[ tational symmetries, aperiodic and disordered topolo- dition, for a given average inter-scatterer distance a. A

gies, with their richer symmetries and patterns, can section of the point pattern, decorated by discs of ra-
1
v lead to superior optical functionalities [8], as in om- dius 0.3a, is shown in Fig. 1A. The structure factor of
9 nidirectional absorption for solar applications [17, 18], thepointpatternisshowninFig.1B:thepointdistribu-
9 scattering-inducedlightlocalisation[19]andlightextrac- tion exhibits significant local structural correlations: the
7
tion from LED/OLED [20]. Moreover, disordered meta- typical exclusion region around k = 0 which character-
6
surfaces are expected to be more resilient against fab- izesstealthyhyperuniformpatternsandabroadisotropic
0
. rication imperfection and therefore more apt for tech- diffraction maximum peaked around ak/2π =1.03.
1
0 nological implementation. Given the vast possible de- Next, a Delaunay tessellation protocol [22] is per-
7 signs of non-periodic topologies, ranging from random formed, obtainingastrictlytrivalentcontinuousnetwork
1 to correlated-disordered, their full potential is still to be topology (Fig. 1C) with walls of thickness 0.35a. The
v: fully explored. structure factor of this network is presented in Fig. 1D.
Xi There exists a general class of disordered systems, Thestealthinessofthearchitecturehasbeensignificantly
called hyperuniform disordered (HuD) photonic struc- reduced: the diffraction spectrum (Fig. 1D, inset) ex-
r
a tures, which are of particular interest because they ex- hibits low intensity diffuse scattering around k = 0, in
hibit wide and isotropic photonic band gaps [21], ro- contrast to the sharp exclusion zone of the simple point
tational symmetry and broadband k-space control, and pattern(Fig.1B,inset). Nonetheless,thegeneralformof
can be systematically generated through a specific de- the point pattern structure factor dominated by a single
sign rule via universal tessellation protocol [22, 23]. Pio- broad and isotropic resonance around ak/2π = 1.09 is
neering experiments on photonic HuD systems have ex- reproduced by the network.
ploredIRlightdiffractionin3Ddielectricstructures[24], Gold metasurfaces were fabricated by electron beam
microwave band-gaps formation [25], polarization filter- lithography on a glass substrate for various size scaling
ing [26] and random quantum cascade lasers [27]. The- parameters a. The samples are of two kind: pillar-type
oretical proposals have been put forward for surface en- samples comprising isolated pentagonal, hexagonal and
hanced Raman scattering [28], transparency design [29], heptagonal gold pillars (sketched in Fig. 1E and SEM
2
A C recorded in the farfield by imaging the Fourier plane of
a microscope objective (oil immersion, NA=1.45). The
maximum observable momenta is overlaid as a coloured
dashedcircle. AllL 50−L 30samplesexhibitbroadand
p p
statisticallyisotropicscatteringringswhichresemblethe
primaryresonanceofthedesignedstructurefactorshown
in the inset of Fig. 1D. The momentum associated with
1 B D the scattering resonance peak increases with the down-
scaling of the sample; in L 25−L 20 the scattering ring
0.8 p p
crosses over the observable momentum limit. The bright
Smax0.6 spot at the centre of each farfield results from the spec-
)/kr0.4 ular reflection along the axis of incidence.
S(
Fig. 2C shows the azimuthally averaged farfield inten-
0.2
sity distributions. As the sample correlation length is
0
0 1 2 3 0 1 2 3 reduced in size, the momentum of the primary scatter-
ak/2π ak/2π
r r ing peak increases with a small intensity decrease. The
E F
structures L 50−L 35 are all characterised by a single
p p
scatteringpeakwithsomefinerstructurethatvariesfrom
sampletosample. Interestingly,theL 30sampleexhibits
p
adoublepeak,whileL 25onlyasecondarylowshoulder
p
peak. The linear scaling with the reciprocal of the corre-
lation length, shown in the insets of Figs. 2C, can be ex-
pectedbysimplediffractiontheory,whilethefinerstruc-
G H tures are captured by numerical finite-difference time-
domain (FDTD) simulations shown in Fig. 2D. In par-
ticular, FDTD predicts the multi-peak signature of the
L 30 sample, suggesting that this feature is a genuine
p
property of the sample. We attribute this finer structure
5 μm
totheinterplayofthesurfaceplasmonattheair/goldin-
terfacesustainedbyasinglepillarwiththelineardiffrac-
tion dispersion. In fact, the HuD structure comprises el-
FIG. 1. The initial HuD point pattern (panel A) with ements of different sizes, much larger than the plasmon
χ=0.49 presents a structure factor (panel B) with a typical wavelength, which present high-order resonances in the
zero around k = 0 and a broad isotropic diffraction maxi- visible range and an overall response close to that of a
mum(inset). TheHuDconnectednetwork(panelC)broadly surfaceplasmonresonanceofaninfinitefilmwhichpeaks
preserves the k space characteristics (panel D) of the point
around k/k =1.09.
0
pattern. SketchesandSEMimagesoftheresultingpillar-type
We performed also a broadband scattering character-
(panelEandG)andnetwork-type(panelFandH)metasur-
ization of the L 50 design. The sample was illumi-
faces. p
nated from below with white light, and the reflected and
scattered light was spectrally decomposed into its wave-
in Fig. 1G), and network-type designs (identical but in- length and momentum components (Fig. 3B) by spec-
verted)consistingofaconnectednetworkofgold(sketch trally imaging the Fourier plane of the sample. In this
in Fig. 1F and SEM in Fig. 1H). The samples are la- wayanenergy-wavevectordispersiondiagramcanbecon-
belled as L N for pillars and L N for networks, with structed as shown in Fig 3B (experiments) and Fig 3A
√p n
N = a× 4000: for example L 50 for a = 790nm has (FDTD calculations). Both images display a bold diag-
p
a side dimension of 50µm. Network designs larger or onal slash, from low-scattering angle to high-scattering
smallerthan40µmhavebeencroppedorperiodicallyre- angle, and the evolution, for increasing wavelengths, to-
peated, respectively, to cover a 40×40µm2 area. wards larger momenta of the primary scattering peak.
Fig. 2 presents light scattering experiments on the From this linear relationship we conclude that the light
pillar-typemetasurfaceswhoseSEMimagesareshownin diffraction follows the designed structure factor with a
Fig. 2A. Similar experiments performed on the network- single main peak (Fig. 1D).
typesamplesledtocomparableresultsandarenotshown So far, we have investigated the ability of our gold
here. Themeasuredfarfieldintensitydistributionofeach metasurfaces to mediate between incident and scat-
pillarmetasurfaceisshowninFig.2B.Thesampleswere tered light. We now seek to characterise the HuD
illuminatedthroughtheglasssubstratewithacollimated metasurface electromagnetic modes and their momen-
laser (λ =532 nm) while the back-scattered light was tum distribution. The metasurface modes are excited
3
A
Lp50 Lp45 Lp40 Lp35 Lp30 Lp25 Lp20
5 μm
B
k
y
k
x
C D
1.5 1.5
experiment theory
k0 k0
/max /max
k| k|
u.) |0 |0
(a. 2 a-1 (m-11) 5 2 a-1 (m-11) 5
y
nsit LLpp5405
e Lp40
nt Lp35
I L30
p
L25
p
L20
p
0.4 0.6 0.8 1 1.2 1.4 0.4 0.6 0.8 1 1.2 1.4
|k|/k |k|/k
0 0
FIG.2. SEMimagesofpillartypedesigns(panelA)togetherwiththeirfarfielddiffractionpatterns(panelB)whenilluminated
witha532nmlaser. Thenumericalaperturelimitsaremarkedascolouredrings. PanelCdisplaystheazimuthallyintegrated
farfieldsdistributionsasafunctionofin-planemomentum(normalizedtotheincidentwavevectork ),showingbroadscattering
0
resonances. PanelDshowsthesamecalculatedazimuthallyintegratedfarfieldswhichagreeswellwithexperiment. Theinsets
(panelC&D)plotsthescatteringpeakpositionasafunctionofthereciprocalscalingparameter(a−1)andtheexpectedlinear
dependence.
molecules which was spin coated on the samples (Fig. 4,
top panel). Figs. 4A and B present the theoretical and
experimental frequency-momentum distribution, or dis-
1.5A 0 persion plot, of the fluorescence light emitted from the
L 50structurewhenexcitedwithagreenlaseratawave-
p
0 lo length of 532 nm.
k g
k/ I The pair of intense emission bands just outside the

light lines (white dashed lines indicating k/k =±1) re-
0
0 -7.5
sults from the characteristic radiation profile of a dipole
1.5B 0
near the glass-air interface [33]. Inside the light cone, we
observe annular features which describe the decomposi-
k0 lo
/ g tion of the metasurface slab modes into their in-plane
k I momentum components. These may be viewed as the
generalised dispersion relation ω(k) of the slab modes.
0 -6
SimilardispersiondiagramsweremeasuredfortheL 50,
390 910 p
λ (nm)
L 45, L 40, L 35 and L 30 metasurfaces.
p p p p
InordertofurtheranalysethedispersionplotsofFigs.
FIG. 3. Theoretical (A) and experimental (B) white light
4, we convert the emission wavelength and in-slab mo-
scatteringbytheL 50metasurface. Boththeoryandexperi-
p
ment match well and show that the scattering peak momen- mentum to the dimensionless quantities a/λ and ka/2π
tum increases linearly with wavelength. respectively. The experimental dispersion diagrams can
then be stacked into a single image to illustrate the dis-
persion over a large normalized frequency range (Fig. 5,
by a 50 nm layer of Poly(methyl methacrylate) polymer left panel). It shows that the fluorescent light is emit-
highly doped with fluorescent 4-(Dicyanomethylene)-2- ted isotropically from the HuD surface, into a cone with
methyl-6-(4-dimethylaminostyryl)-4H-pyran (DCM) dye varying opening angle, which depends on the emission
4
1.42
experiment theory
A max
1
k0 lo
/0 g
k I a/λ

-1
min 0.9 max
B max
1
k0 lo
/0 g min
k I 0.63
-1 1.5 0 1.5
min ka/2π
550 λ (nm) 730
FIG. 5. Left, experimental dispersion relations for samples
L 50, L 45, L 40, L 35 and L 30 are stacked together as
FIG. 4. Generalised dispersion relation ω(k) of L 50 slab p p p p p
p
a function of a/λ. Right panel, FDTD simulations which
modes calculated summing incoherently the farfields of 48
confirm the crossing at a/λ = 0.9 where the light is emitted
randomly oriented dipole (panel A) and measured by fluo-
normal to the metasurface plane.
rescence emission (panel B).
ACKNOWLEDGEMENTS
wavelength to correlation length ratio. As the frequency
increases from a/λ = 0.63, the dominant momentum of
TheworkwassupportedbytheEngineeringandPhys-
the slab modes first decreases, reaching a zero in the re-
ical Sciences Research Council (EPSRC EP/M027961/1
gion of a/λ = 0.9, at which point light is emitted nor-
andEP/M013812/1),theLeverhulmeTrust(RPG-2014-
maltotheslabplane,beforegraduallyopeningbackout.
238) and the Royal Society (RG140457).
The experiments are in good agreement with FDTD cal-
culations (Fig. 5, right panel) obtained with the spectral
function method [32]. Specifically, decomposition of a
slab’s eigenmodes into a plane wave basis can directly
predictthefarfieldangularprofileofitsdirectionalemis- ∗ m.fl[email protected]
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