NANOPHOTONICS
Purcell effect for active tuning of lightscattering from semiconductoroptical antennasAaron L. Holsteen,1 Søren Raza,1 Pengyu Fan,1 Pieter G. Kik,1,2 Mark L. Brongersma1*
Subwavelength, high–refractive index semiconductor nanostructures support opticalresonances that endow them with valuable antenna functions. Control over the intrinsicproperties, including their complex refractive index, size, and geometry, has beenused to manipulate fundamental light absorption, scattering, and emission processesin nanostructured optoelectronic devices. In this study, we harness the electric andmagnetic resonances of such antennas to achieve a very strong dependence ofthe optical properties on the external environment. Specifically, we illustrate howthe resonant scattering wavelength of single silicon nanowires is tunable across theentire visible spectrum by simply moving the height of the nanowires above a metallicmirror. We apply this concept by using a nanoelectromechanical platform todemonstrate active tuning.
High-index semiconductor nanostructuresdisplay a diverse set of optical resonancesthat can give rise to structural color (1) andfacilitate effective lightmanipulation at thenanoscale (2). The optical resonances are
tunable by manipulation of properties such asrefractive index, size, and geometry, akin to theadaptability ofmetallic nanoparticles that supportplasmonic resonances. A multipole analysis of thelight scattering process provides valuable insightsinto the resonances that give rise to specific op-tical functionalities (3–7). We demonstrate thatbringing these nanostructures into close proxim-ity of a reflective surface can markedly enhanceor suppress the interaction with selected multi-poles. This is reminiscent of the Purcell effect inquantum optics, which dictates that the internaldecay of an excited quantum emitter can bemod-ified by placing it near amirror or into a resonantcavity (8, 9). From studies on quantum objectsplaced in tailored environments, it is also knownthat surface selection rules can emerge that havea substantial effect on processes such as fluores-cent decay or Raman scattering (10). We illustratethese concepts for the lowest-order resonances ofjudiciously sized Si nanowires (NWs) and dem-onstrate active tuning of the structural color of aSi NW across the visible spectrum with a nano-electromechanical device.We first analyzed the white-light scattering
from Si NWs above an aluminum (Al) mirror atdifferent heights (Fig. 1A). Si NWs grown bychemical vapor deposition were deposited ona quartz substrate and then suspended abovean Al-coated plano-convex lens with a largeradius of curvature (rm = 10 mm). This con-figuration affords nanometer-scale control over
the NW height above the metal surface by slid-ing the quartz substrate in a plane normal to theoptical axis of the Almirror. A topographicmap ofthis mirror was created by charting the Newton’srings resulting from the interference of mono-chromatic light between the air-quartz interfaceand the mirror (Fig. 1B) (11). The volume be-tween the quartz slide and mirror was sub-sequently filled with an index-matching oil toproduce an optically homogeneous mediumaround the NW.In this configuration, the scattered light inten-
sity from a NW is no longer just a function of theintrinsic NW properties. It is also dependent onthe NWheight above the mirror, as it canmodifythe excitation of relevant NW modes and thesubsequent collection of the scattered fields by adetector. This can be seen by considering an exci-tation planewavewith an intensity I0 and awavevector of a magnitude 2p/l (l, wavelength) thatis incident on themirror at an off-normal anglef.Themirror reflection generates a standingwaveabove the mirror (Fig. 1C). On the basis of thespatial variations in the fieldmagnitudes, one canexpect concomitant variations in the excitationefficiency of the supported NW resonances. Weinitially consider an idealized scenario in whichthe mirror is taken as a perfect electrical conduc-tor (PEC) and the near-field interactions betweenthe NW and substrate are neglected. This servesas a valuable reference case, as a high-conductivityAlmirror approximates a PEC and the consideredNW height h in our experiments is typically suf-ficiently largeð2kh ≫ 1Þ to ensure aminimal effectof near-field interactions [supplementary text sec-tions S1 to S3 (12)]. For this case, a simple ex-pression can be written for enhancements inlocal electric and magnetic fields hEi
e ðf; hÞ andhHie ðf; hÞ of the excitation standing wave [supple-
mentary text sections S2 and S3 (12)]. For off-normal incidence angles, field enhancements canbe seen in both the horizontal ð∥Þ plane and the
direction normal ð⊥Þ to the mirror surface, as de-noted by the label i.Similar height-dependent variations appear
in the process of collecting scattered light fromthe NW by a finite-sized detector. These varia-tions result from the interference between lightthat is directly scattered toward the detector andlight entering this detector after reflecting fromthe surface. The strength of this interference isagain dependent on h but also on the collectionangle q (13, 14). These additional height-dependentvariations in the measured intensity are under-stood from a reciprocity argument; that is, by an-alyzing the properties of a plane wave sent backfrom the location of the photodetector toward theNW and the mirror. If the resulting collectionstanding wave can effectively excite a NW reso-nance of interest, then conversely the resonantlyexcited NW can scatter light effectively towardthe detector. The collection efficiency can belinked to the field enhancements hEi
c ðq; hÞ andhHic ðq; hÞ for the collection standing wave. Asthe scattered intensity relies on an efficient ex-citation followed by an efficient collection, it willbe functionally dependent on products of fieldenhancements for the excitation and collectionplane waves in the form hHi
t ¼ hHie ðf; hÞhHi
c ðq; hÞand hEi
t ¼ hEie ðf; hÞhEi
c ðq; hÞ. Because the excita-tion and collection efficiencies have different spa-tial periodicities, the total efficiency contains abeating pattern that depends on f and q.For the experimentally relevant case that
a detector collects light normal to the surfaceðq ¼ pÞ, the far-field scattered intensity (Iff) canbe written in an intuitive form [supplementarytext sections S2 and S3 (12)]
I ffðr; fÞI0
¼ 2
pkr f hH∥t a0 � 2hE∥
t
X
m¼1;3;…
cosðmfÞam�����
þ 2hH∥t
X
m¼2;4;…
cosðmfÞamj2 TE
hE∥t b0 � 2hH∥
t
X
m¼1;3;…
cosðmfÞbm�����
þ 2hE∥t
X
m¼2;4;…
cosðmfÞbmj2 TM
wherem is an integer that labels the relevantMiecoefficients am and bm that quantify the excita-tion strength of the variousmultipolar resonancesof a cylindrical NW illuminated in free space (3)and r is the observation distance. Different reso-nances are excited for the transverse-magnetic(TM) and transverse-electric (TE) polarizationsthat feature incident electric and magnetic fieldsparallel to the SiNWaxis, respectively.When lightis collected in a direction normal to the metal sur-face, only enhancements in the electric andmag-netic fields in the horizontal plane are relevant, asthey candriveNWresonances capable of scatteringlightupward to thedetector. As such, thequantitieshH∥t andhE∥
t describe the relevant beating patternof the excitation and collection planewaves thatgovern the scattered intensity in this experimentalgeometry. Depending on the symmetry proper-ties of the relevantmultipoles, the resonances are
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Holsteen et al., Science 358, 1407–1410 (2017) 15 December 2017 1 of 4
1Geballe Laboratory for Advanced Materials, StanfordUniversity, Stanford, CA 94305, USA. 2CREOL, The Collegeof Optics and Photonics, University of Central Florida,Orlando, FL 32816, USA.*Corresponding author. Email: [email protected]
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most effectively excited at maximums in eitherthe electric or magnetic field.Figure 1E shows an example of a 50-nm–
diameter Si NW that is brought toward an Almirror. Dark-field images of this NW, usingunpolarized white light, show substantial colorchanges as its height above the mirror changesby only a few hundred nanometers. A Si NWwitha diameter this small supports only the lowest-order TM resonance with one electric field max-imum in the core. It serves as a linear electricdipole, with scattering intensity governed by theMie coefficient b0. When the NW is 20 mm fromthemirror, the NW appears white, as it features aspectrally broad resonance in the scattering ef-ficiency (Qsca). However, when theNW is closer tothe mirror, the peak wavelength for this reso-nance is modified and can be tuned across thevisible spectrum (Fig. 1F).To systematically study the selective excitation
of the first twoMie resonances for both polariza-tions at a range of heights, we used electron beamlithography and reactive ion etching to fabricatea 105-nm-wide and 100-mm-long Si NW (Fig. 2A).
For both TE and TM polarizations (Fig. 2B), wemeasuredand calculated the scattering efficienciesof the Si NWwithout themirror (Fig. 2, C andD).The scattering calculations were performed usingMie theory for a Si cylinder in free space. Thecorresponding optical images of the NWs areshown next to the spectrums, displaying a uni-form color. The gray dotted line represents thesimulated spectrum of Qsca, whereas the blackdotted line denotes the partial scattering efficiencyobtained by integrating the differential scatteringefficiency over the collection solid angle of theobjective. We find that the latter matches theexperimental scattering spectra substantiallybetter than the total scattering efficiency, in-dicating the importance of accounting for theanisotropic scattering properties of these NWs[supplementary text section S4 (12)]. The peaksin the total scattering efficiency identify the spec-tral locations of the supported Mie resonances.The field maps for the resonances are shown asinsets and facilitate a classification accordingto their dipolar nature. The a1 and b0 Mie co-efficients are associated with electric dipole (ED)
resonances. Similarly, the a0 and b1 Mie coef-ficients can be linked to magnetic dipole (MD)resonances.Light scattering spectrawere taken for different
wire heights above the mirror in the range from0 to 2 mm and cascaded to create maps of thespectral and height dependent scattering proper-ties of the NWs (Fig. 2, E and F). Adjacent to thesemaps, one can see the dark-field white-light scat-tering images of the NWs. Strong scattering isobserved in the spectral region correspondingto the different Mie resonances, and the colorvaries substantially along the NW length. Thisis explained by the fact the scattering intensityat each resonance wavelength is modulated asthe NW height changes. To explore the validityof the proposed analytical model, we first cal-culated the composite standing field profiles (i.e.,hH∥t andhE∥
t ) [supplementary text section S3 (12)].Themaxima in the in-plane electric (black) andmagnetic (white) fields for f = 37° and q = 180°are overlaid on the map and seen to intersect ex-perimental maxima in the scattering intensity. Thestrong scattering from electric (magnetic) dipole
Holsteen et al., Science 358, 1407–1410 (2017) 15 December 2017 2 of 4
Distance from mirror center (µm)
Hei
ght (
µm)
0
1.0
2.0
3.0
4.0
0 50 100 150 200 250
Radial Intensity (a.u.)
0.1
0.2
0.3
0.4
0.5
.Ei kiHi
.rH rk
h
|E|2
0 1
hφ
mirror
p
|E|2
0 1
h
π − θ
mirror
λ(nm)450 550 650 750
0
0.5
1
420 nm340 nm230 nm
Inte
nsity
(a.
u.)
20 µm
420 nm
340 nm
230 nm
220 - 350 nm
Convex MirrorQuartz Coverslip
Quartz
Mirror Oil
SiNW
Quartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz CoverslipQuartz Coverslip
Fig. 1. Light scattering from Si NWs near a mirror. (A) Configurationof the suspended NWs. (B) Light intensity of Newton’s rings (inset)imaged at 500 nm (blue trace), showing that the minimums in theinterference pattern (red squares) map the parabolic mirror surface (blackdashed line). a.u., arbitrary units. (C and D) Standing wave intensityfrom an incident (C) and collected (D) TM-polarized plane wave. E, electric
field; h, NW height; Ei, incident electric field; ki, incident wave vector; Hi,incident magnetic field, Er, reflected electric field; kr, reflected wave vector; Hr,
reflected magnetic field; p→, dipolar scatterer; f, angle of the incident plane
wave; q, collection angle. (E) Optical images from a single silicon NW atvarious heights above the mirror shown in (A). Scale bar, 5 mm. (F) Dark-fieldscattering spectra from three heights shown in (E).
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resonances occurs when theNW is located at oneof the electric (magnetic) fieldmaxima. The com-plete solution for this experimental configura-tion, including real material parameters andnear-field interactions, was also solved analyti-cally using the method described in (13), and thefar-field scattered intensities are shown in Fig. 2,G and H.The presence of the mirror results in enhance-
ments in light scattering that are reminiscent ofthe changes in Raman scattering and fluorescentemissionwhenmolecules are placed near amirror(8, 9, 15). When the total scattered power with the
mirror present is normalized by the total scatteredpower in free space, enhancements are observedfor each mode orderm
F TEm¼0 ≅ ½1þ J0ð2khÞ�jhHe ðfÞj2 ð2Þ
F TEm¼�1;1 ≅ ½1þ J2ð2khÞ�jhEe ðfÞj2 ð3Þ
F TMm¼0 ≅ ½1� J0ð2khÞ�jhEe ðfÞj2 ð4Þ
FTMm¼�1;1 ≅ ½1� J2ð2khÞ�jhHe ðfÞj2 ð5Þ
where Jm is the Bessel function of the first kind[supplementary text sections S6 and S7 (12)]. Inthese products, the first terms with the Besselfunction describe the radiative decay rate enhance-ment, and the second terms (jhEe ðfÞj2 or jhHe ðfÞj2)quantify the excitation efficiency enhancementsseen in the presence of a mirror. The decay rateenhancements are analogous to the Purcell ef-fect and are directly connected to the local den-sity of optical states (LDOS) [supplementary text
Holsteen et al., Science 358, 1407–1410 (2017) 15 December 2017 3 of 4
Fig. 2. Dipolar modescontributing to lightscattering from aSi NW near a mirror.(A) Experimentalconfiguration for theresults shown in (E) to(H). f is the angle ofthe incident plane wave.(B) The polarizationconvention for thiswork. (C and D) Finite-difference time-domain(FDTD) simulation of thetotal scattering crosssection collected at allangles (gray dottedlines), with the electricand magnetic fieldprofiles on resonance(insets) for bothpolarizations. Theexperimentally collectedscattering spectrum(solid lines) and thecorresponding FDTDsimulated differentialscattering efficiencycollected within a0.7–numerical apertureobjective through thequartz handle wafer(black dotted lines).The insets show thefield magnitude mapsfor each resonancelabeled as eitherelectric dipole–like(ED) or magneticdipole–like (MD).Qsca, scatteringefficiency; TE,transverse-electricpolarization; TM,transverse-magneticpolarization. (E andF) Experimentally collected light scattering spectra at heightsranging from 0 to 2000 nm for TE and TM polarization with a scaleof arbitrary units. Dark-field images of the NW vertically scaledto compensate for the parabolic shape of the mirror are shownto the right of each plot. The simulated electric (black) and magnetic(white) field maxima are overlaid, with the width of the lines
corresponding to the magnitude of the field maxima. (G and H) Analyticmodel of far-field diffracted light scattered from a Si NW abovean Al mirror for both polarizations, showing the ratio of the intensityof the scattered light (Iff) to the incident intensity (I0) collectednormal to the mirror plane where the observation distance isr = 2/(pk).
0
500
1000
1500
Hei
ght
(nm
)
x
Ei
kiHi
mirror
TE
.Ei ki
Hi
mirror
TM
0
500
1000
1500
Hei
ght
(nm
) Q
sca
0
4
8 TM11
TM 01
No Mirror
6x6x
ED
MD
0
0.5
1|E|2
Qsc
a
0
1
2
3
TE11 TE01
No Mirror
3x
3x
EDMD
0
0.5
1|H|2
400 500 600 700 8000
500
1000
1500
2000
5
10
15
20
25
λ (nm)
Hei
ght
(nm
)
o/ Ι
ff Ι T
M (θ
= 1
80 )o
400 500 600 700 8000
500
1000
1500
2000
5
10
15
Ι T
E (θ
= 1
80 )
λ (nm)
Hei
ght
(nm
)
ffo
/ Ιo
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section S7 (12)]. LDOS highlights the classicalnature of this effect, with the magnitude of thescattering efficiency determined by optical inter-ference. Similarly, the Purcell effect has also beenobserved for Rayleigh scattering from moleculesin a cavity (16). For selected heights, a mirror canenhance the total scattered power more thanfive times for m = 0 and more than twice form = ±1 modes, as compared with the free-spacecondition for both polarizations. This enhance-ment in the scattering efficiency from the NWnear the mirror takes into account the scat-tering to all directions. When only one specificfar-field scattering direction is chosen, even fur-ther enhancement values can be observed. Fornormally incident excitation and collection fromaNW, a 16-fold enhancement over the free-spacescattered light intensity can be expected as theexcitation and collection efficiencies are enhancedby a factor of 4.We developed a nanoelectromechanical system
(NEMS) platform to actively tune the scatteringintensity and spectral properties of a NW. Re-configurable nanomechanical structures have re-cently received considerable interest from thenanophotonics community for their low-powerand high-frequency operation (17). We fabricateda 50-nm-wide Si NW with a square cross sectionwithin an underetched frame patterned into asilicon-on-insulator wafer (12). Such a small NWsupports only the lowest-order TM resonance.The dark-field scattering shows a uniform coloralong its length, indicating that the NW widthand height are constant (Fig. 3B). For voltagesfrom 0 to 2.75 V, we were able to tune the singlescattering peak across a large part of the visible
spectrum from 700 to 520 nm (Fig. 3, C andD), inagreement with simulations (fig. S10). As long asnonreversible pull-in is avoided, the device canbe reversibly tuned for more than 2 billion cycleswithout degradation with a maximum modula-tion near the fundamental mechanical resonancemode at 1 MHz (Fig. 3, E and F). For single-wavelength operation, this device can act as anintensity modulator. If we choose a spectral loca-tion such as 800 nmon the shoulder of one of theresonances, an intensitymodulation ratio as largeas 10 dB is achieved.We have demonstrated how the presence of a
mirror can substantially modify the excitationand collection of scattered light fromNWs, evenfor wavelength-scale separations. These modifi-cations are very different for the electrical andmagnetic dipole resonances supported by theNWs. As a result, both the light scattering in-tensity and the spectral properties of suspendedNWs are altered substantially. We made a rigor-ous link to the enhancements and suppressionsassociated with the Purcell effect observed forquantum objects. Looking forward, we envisionthat these NW devices will be used as buildingblocks for a range of active, integrated opto-electronic functionalities.
REFERENCES AND NOTES
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ACKNOWLEDGMENTS
This research was supported by the U.S. Air Force Office ofScientific Research (grant FA9550-14-1-0389) and the Samsungcorporation. A.L.H. acknowledges a National Defense Scienceand Engineering Graduate Fellowship. S.R. acknowledgessupport by a grant (VKR023371) from VILLUM FONDEN. Wethank R. Zia for valuable discussions. M.L.B. and A.L.H. areinventors on patent application 62/486742 held and submittedby Stanford University that covers NEMS actuated high-indexoptical antennas for light manipulation and control.
SUPPLEMENTARY MATERIALS
www.sciencemag.org/content/358/6369/1407/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S11References (18–20)
31 July 2017; accepted 15 November 201710.1126/science.aao5371
Holsteen et al., Science 358, 1407–1410 (2017) 15 December 2017 4 of 4
0.00 V
1.00 V
1.50 V
2.00 V
2.25 V
2.50 V
2.75 Vλ (nm)
500 600 700 800 9000
0.5
1
1.5
2
2.5
0.00 V1.00 V1.50 V
2.00 V2.25 V2.50 V2.75 V
Inte
nsity
(a.
u.)
λ (nm)
Time (s)
0
1
2
3
900800700600500050
100
0.00 V2.75 V
Inte
nsity
(a.
u.)
Time (s)0 50 100
0
4
Mo
du
latio
n r
atio
(d
B)
0
5
0
10
530 nm
700 nm
800 nmFig. 3. Active tuning of light scattering with a nanoelectromechanicaldevice. (A) Scanning electron micrograph of a fabricated device with asuspended Si NW of ~60 nm in width. Scale bars, 2 mm (main panel);100 nm (inset) (B) Dark-field scattering image of the device shown in(A). (C) Dark-field scattering spectra confocally collected from the Si NWunder applied bias and TM polarization. (D) Dark-field images of the NW ateach bias shown in (C). Scale bar, 2 mm. (E) Dark-field scattering shownover time as the bias is turned on and off for 10 cycles at 6-s switchingintervals. (F) Modulation in the intensity for selected wavelengths overthe 10 switching cycles, showing repeatable and consistent amplitudecontrol for applied biases of 0 and 2.75 V.
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Purcell effect for active tuning of light scattering from semiconductor optical antennasAaron L. Holsteen, Søren Raza, Pengyu Fan, Pieter G. Kik and Mark L. Brongersma
DOI: 10.1126/science.aao5371 (6369), 1407-1410.358Science
, this issue p. 1407Sciencenano-electromechanical system illustrates the potential for developing active optical platforms.across the entire visible spectrum simply by adjusting the height of the nanowire above a metallic mirror. This
tuned the resonant scattering wavelength of silicon nanowireset al.properties under an external stimulus. Holsteen scale. Most devices developed to date have been passive structures or have shown only modest changes in optical
The development of nanophotonic technology relies on the ability to control and manipulate light at the nanometerTuning the scattering of light
ARTICLE TOOLS http://science.sciencemag.org/content/358/6369/1407
MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2017/12/13/358.6369.1407.DC1
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