optical antennas: resonators for local ﬁeld...

JOURNAL OF APPLIED PHYSICS VOLUME 94, NUMBER 7 1 OCTOBER 2003

Optical antennas: Resonators for local field enhancementK. B. Crozier,a) A. Sundaramurthy, G. S. Kino, and C. F. QuateE. L. Ginzton Laboratory, Stanford University, Stanford, California 94305

~Received 13 December 2002; accepted 26 June 2003; publisher error corrected 22 October2003!

Electromagnetic field enhancement in optical antenna arrays is studied by simulation andexperiment at midinfrared wavelengths. The optical antennas are designed to produce intense opticalfields confined to subwavelength spatial dimensions when illuminated at the resonant wavelength.Finite difference time domain~FDTD! method simulations are made of the current, charge, and fielddistributions in the antennas. The influence of antenna shape, length, and sharpness upon theintensity of the optical fields produced is found. Optical antennas arrays are fabricated ontransparent substrates by electron beam lithography. Far-field extinction spectroscopy carried out onthe antenna arrays shows the dependence of the resonant wavelength on the antenna length andmaterial. The FDTD calculated and experimentally measured extinction efficiencies of the opticalantennas are found to be in good agreement. ©2003 American Institute of Physics.@DOI: 10.1063/1.1602956#

thetiosot

arn

lincca

ani

omit

animp

m

sa

ernnru

dl

in-

-a-c-

os-y oftive-stop

das

redtal

er-eirld.c-o-nen-or is

tthethertors

ton

f

I. INTRODUCTION

Considerable interest currently exists for the study ofoptical properties of metal nanoparticles, largely due to thability to produce giant and highly localized electromagnefields. Important applications include microscopy, spectrcopy, and optoelectronic devices. In scanning near-fieldtical microscopy~SNOM!, the localized field enhancemenin the vicinity of a metal nanoparticle mounted on a nefield probe would allow nanoscale features in biological asolid-state systems to be selectively illuminated, enabspatial resolution better than the diffraction limit. In spetroscopy, metal nanoparticle arrays amplify the Raman stering cross sections of molecules adsorbed onto them,1 en-abling potentially important applications in biophysics.2 Inoptoelectronics, ordered arrays of closely spaced metal nparticles enable the guiding of electromagnetic energysubwavelength-sized devices.3

We present a study of field enhancement in arraysmetal nanoparticles, that we term optical antennas, by silations and experiments at midinfrared wavelengths. Findifference time domain~FDTD! method calculations areused to find the influence of antenna shape, length,sharpness upon field enhancement. The results of these slations are compared with far field extinction spectroscomeasurements on antennas fabricated by electron beathography on flat transparent substrates.

Field enhancement in optical antennas for applicationSNOM has been previously studied by numericsimulation.4–6 Matsumoto, Anzai, and Shimano4 studiedbow-tie antennas at visible wavelengths using finite diffence time domain simulations, although the effect of antedesign upon field enhancement was not addressed. KSanchez, and Xie5 simulated trigonal gold probes for fielenhancement. Kottmannet al.6 simulated two-dimensiona

a!Electronic mail: [email protected]

4630021-8979/2003/94(7)/4632/11/$20.00

Downloaded 09 Dec 2003 to 171.64.86.205. Redistribution subject to A

eirc-

p-

-dg-t-

o-n

fu-e

du-

yli-

inl

-ag,

silver nanowires of a triangular cross section, predictingtensity enhancements of up to;73105. Their small size~triangle has base;18 nm, height;36 nm! and very sharpcorners~0.25 nm rounding!, however, would make fabrication challenging. In this study, the results of FDTD simultions are directly compared with measured far-field extintion spectra.

In addition to field enhancement for Raman spectrcopy, metallic nanostructures have been used for a varietapplications. Dipole arrays, known as frequency-selecsurfaces, have been previously demonstrated as bandtransmission filters at mid-infrared wavelengths,7,8 an exten-sion from earlier demonstrations at far-infrarewavelengths.9 Triangular nanoparticles have been usedsensors for the refractive index of their surroundings.10 An-tennas have also been used to mix optical fields at infrawavelengths by coupling them to metal-oxide-mediodes.11–13

Optical antennas have considerable potential for aptureless scanning near-field optical microscopy, due to thability to produce large enhancements in the optical fieApertureless SNOM14 uses the local field enhancement ocurring in the vicinity of a sharp tip to improve optical reslution beyond the diffraction limit. There is no exploitatioof the antenna resonance effect in increasing the fieldhancement, however, and the intensity enhancement factestimated to be;16 times for a gold tip~radius of curvatureof 10 nm! illuminated atl5633 nm.15 This enhancemenfactor is about two orders of magnitude smaller thanwork presented here. It should be noted, however, that oworkers have predicted higher intensity enhancement facfor apertureless near-field microscopy, for example;3000times for a gold tip~tip radius of 5 nm! at l5800 nm.16

Applications of apertureless microscopy include two-phofluorescence imaging of photosynthetic membranes,17 infra-red spectroscopy of silicon carbide,18 and laser machining o;10 nm features in thin gold films.19

2 © 2003 American Institute of Physics

IP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

kcrozier

Rectangle

this

sgn

tesusofinteasedicica

a

aye

at,aao

atha-

ren

iuisthnenad

subetint tnntb

ho

on

fwn.

-

4633J. Appl. Phys., Vol. 94, No. 7, 1 October 2003 Crozier et al.

II. FIELD ENHANCEMENT IN OPTICALANTENNAS-THEORY

A. Current, charge, and field distributions

A computational approach is adopted for calculatingfield distribution in the vicinity of the optical antennas. This based on the finite difference time domain~FDTD!method20 in which Maxwell’s time dependent curl equationare solved over a three-dimensional grid. The grid spacinx, y, andz directions is 20 nm~;l/500!. The antennas are oa substrate~Si! with plane wave illumination introducedfrom the substrate side. The medium above the substrafree space. The dielectric constants of the antenna andstrate are from Paliket al.21 Periodic boundary conditionare used in thex andy directions to simulate the responsea periodic array of optical antennas, with spacing matchthat used in the experimental work. The results presenhere, therefore, apply for periodic arrays of optical antennrather than for isolated optical antennas. As will be discuslater, however, the results presented here are a good intion of the field enhancement expected for isolated optantennas. Perfectly matched layers are used at the topbottom boundaries of the propagation direction (z) to absorboutgoing waves from the computational domain.

FDTD simulation results for a gold optical antenna arrelement on a silicon substrate are shown as Fig. 1. Thements of the antenna array are spaced by 3mm in x and ydirections. The simulated structure is illustrated schemcally as Fig. 1~a!, with the direction of the electric fieldmagnetic field, and propagation vector shown. The antenn1.56mm long, 60 nm thick, and has a 15° included anglethe tip. The tip is modeled as a cylinder with a radiuscurvature of 120 nm. Figure 1~b! presents the FDTD-calculated̂ uEu2& intensity at the top surface of the antennFrom this figure, it may be seen that the peak intensity attip is ;3905 times that of the incident plane-wave illumintion. The illumination is from the bottom~i.e., substrate! sideat l510.375mm, and polarized in thex-direction. Figure1~c! shows an expanded view of the intensity in the tipgion, with the half-maximum intensity contour also showThe contour has an extension of;160 nm ~;l/66! in thex-direction and;280 nm ~;l/37! in the y-direction. Thecontour follows the curvature of the tip, which has a radof curvature of;l/86. The spatial confinement of the fielddue to the tip sharpness and may be a small fraction ofwavelength. Work currently being undertaken at visible anear-infrared wavelengths indicates a similar intensityhancement and spatial confinement with suitably scaledtennas. At these wavelengths, the fields are confined tomensions of the order of 10–20 nm.

The intense electric field at the antenna tip is the reof currents induced by the incident illumination. This mayunderstood by considering the case of a perfectly conducantenna, a good approximation for metals such as gold amidinfrared wavelengths under consideration. The curreare necessary to satisfy the requirement that the tangecomponent of the electric field at the conductor surfacezero. They generate a scattered electromagnetic field wtangential component at the antenna surface is equal and


e

in

isb-

gd

s,da-lnd

le-

i-

istf

.e

-.

s

ed-n-i-

lt

ghetsialese

op-

FIG. 1. ~a! Schematic of gold optical antenna array element on silicsubstrate simulated by the finite difference time domain~FDTD! method.The antennas are elements of an array withx andy interelement spacings o3 mm. Electric field, magnetic field, and propagation vectors are shoIllumination wavelengthl510.375mm. Antenna lengthL51.56mm, ~b!FDTD-calculated̂ uEu2& intensity at top surface of antenna, with illumination from bottom~substrate! side, and~c! zoom-in of^uEu2& intensity at tipof antenna. Half-maximum-intensity contour is shown.


kcrozier

Rectangle

e of

4634 J. Appl. Phys., Vol. 94, No. 7, 1 October 2003 Crozier et al.

FIG. 2. FDTD simulation of linear antenna array element. The antenna is an element of an array withx andy interelement spacings of 3mm. Antenna is gold~60 nm thick! on silicon substrate. Antenna length is 1.56mm. Illumination wavelengthl510.375mm. ~a! Simulated structure,~b! equivalent instantaneoussurface current~direction plot!, ~c! equivalent instantaneous surface current~perspective plot!, and~d! instantaneous surface charge density at top surfacantenna.

taot

nT

neile, tio

no

n

20in-

, in-ffi-alur-

en-

posite in magnitude to the incident electric field. The totangential electric field at the antenna surface is then zerrequired. The currents decrease in magnitude towardends of the antenna, leading to a net charge appearing oantenna surface, as required for charge conservation.surface charge density and therefore the normal compoof the electric field are maximized at the tip. Note that whthese arguments are for a perfectly conducting antennaFDTD calculations presented do not make this assumptinstead fully modeling the effects of conductor loss.

The FDTD-calculated current and charge distributiofor a thin linear gold antenna array element on a silicsubstrate are shown as Fig. 2. The interelementx andy spac-ings of the array are 3mm. The simulated structure is showas Fig. 2~a!, with the electric field (E), magnetic field (H),and propagation vector (k) of the plane wave illuminationshown. The illumination is from the bottom~i.e., substrate!


lashethehent

hen,

sn

side atl510.375mm. The simulated structure is 1.56mmlong ~x-direction!, 240 nm wide~y-direction!, and 60 nmthick ~z-direction!. The radius of curvature at the ends is 1nm. Because the antenna is not a perfect conductor, theduced currents are not confined to the antenna surfacestead flowing within the antenna. However, due to the diculty in displaying and interpreting a three-dimensioncurrent distribution, we instead present the equivalent sface current distribution as Figs. 2~b! and 2~c!. These areobtained by integration in thez-direction of the x- andy-directed volume current densities. The volume current dsitiesJ are calculated fromJ5sE, wheres is the conduc-tivity and E the electric field. The conductivitys is calcu-lated using

~N1 iK !25« r1s

iv«0, ~1!


kcrozier

Rectangle

nt

ntthetn

rothts

uri

th

roerodseu-fi

thatefs

ityve

is

i-

g

telyomar,is

snderon

nt

edsed.nsith

nna

ts ofnde.en-thet isnts

thean-

erstri-are

t o

as

of an

ted


where the value of the complex refractive indexN1 iK istaken from Paliket al.21 Note that thez-directed currents arenot shown, as these are much smaller than thex-andy-components. Figure 2~b! shows the instantaneous curredirection ~magnitude proportional to arrow length!. Clearly,the current is predominantly in thex-direction, as this is thepolarization of the input illumination. Note that the curreshown is the instantaneous distribution and oscillates atfrequency of the input illumination. The magnitude of thcurrent is shown as Fig. 2~c!. The currents are maximum ax50 and decrease smoothly toward the ends of the ante(1x and 2x directions! where they must be close to zesince there is very little charge storage at the ends ofantenna. From Fig. 2~c!, it may also be seen that the currenincrease toward the edges of the antenna (1y and 2ydirections!.22 The surface charge distribution on the top sface of the antenna resulting from the current distributionshown as Fig. 2~d!. The decreasing currents at the ends ofantenna result in increased surface charge.

B. Field enhancement and antenna geometry

The strength of the local optical field enhancement pvided by the optical antenna is particularly important in ctain applications. In Raman spectroscopy of single mecules, for example, local field enhancement is needecompensate for the very small Raman scattering crosstion. We therefore use FDTD simulations to find the inflence of antenna shape, length and sharpness upon theenhancement.

The optical antenna is a resonant structure, sincecurrents flowing in it are maximized when it is illuminatedthe resonance wavelength. The surface charge and therthe field enhancement factor are also maximized on renance. This is illustrated in Fig. 3, in which the intens(E2) enhancement factor is plotted as a function of walength~mm!. As shown in the schematic~inset of Fig. 3!, thisgold antenna~1.56 mm long, 60 nm thick! has a triangular

FIG. 3. Intensity (̂ uEu2&) enhancement vs wavelength~mm! for gold opticalantenna array element on a silicon substrate. The antenna is an elemenarray withx andy interelement spacings of 3mm. Schematic of simulatedstructure shown. Vertical dotted line is wavelength corresponding to antenna length ofL5l/(2n), wheren is refractive index of substrate. Radiuof curvature at tip is 140 nm.


e

na

e

-se

--l-toc-

eld

e

oreo-

-

~isosceles, 30° included angle! cross section. The antennaan element in an antenna array withx and y spacings of 3mm. The antenna array is on a silicon substrate, with illumnation from the substrate side atl510.375mm. The positionof the wavelengthl corresponding to the antenna havinlengthL equal tol/(2n), wheren is the substrate refractiveindex, is also shown. This is expected to be approximathe resonant wavelength of the antenna. It is known frantenna theory that the input impedance of a thin, linecenter-fed antenna is purely real when the total lengthslightly less thanl/2.23 At this length, the induced current imaximized and the antenna resonates. The antennas uconsideration have a more complex geometry and aresubstrates, but the resonant length is still close toL5l/(2n). From Fig. 3, it may be seen that the resonawavelengthl is slightly less than would be given by theL5l/(2n) approximation.

The optimum shape of optical antennas for maximizlocal field enhancement has not been previously addresIn order to determine the optimum shape, FDTD simulatioare carried out on antennas of triangular cross section wthe included angle varied. In these simulations, the antelength~1.56mm! and the radius of curvature~120 nm! at theend of the tip are kept constant. The antennas are elemenan array withx andy spacings of 3mm. The antennas are oa silicon substrate, with illumination from the substrate siThe results are shown as Fig. 4, which is a plot of the intsity enhancement as a function of the included angle attip. From this figure, it may be seen that the enhancemenmaximized for an included angle of zero, which represethe linear antenna shown as Fig. 2~a!. The current and sur-face charge densities are higher for this antenna than forwider-angled antennas, leading to stronger fields at thetenna tip.

To understand why the intensity enhancement is lowfor the wider-angled antennas, the current and charge dibutions for the antenna with an included angle of 75°

f an

n-

FIG. 4. Intensity (̂ uEu2&) enhancement vs tip angle~°! for gold opticalantenna array element on silicon substrate. The antenna is an elementarray with x and y interelement spacings of 3mm. Antenna lengthL51.56mm. Radius of curvature at tip is 120 nm. Schematic of simulastructure is shown.


kcrozier

Rectangle

with

at


FIG. 5. FDTD simulations of triangular antenna array element. Antenna is gold~60 nm thick! on silicon substrate. The antenna is an element of an arrayx and y interelement spacings of 3mm. Antenna length is 1.56mm. Illumination wavelengthl510.375mm. ~a! Simulated structure,~b! equivalentinstantaneous surface current~direction plot!, ~c! equivalent instantaneous surface current~perspective plot!, and~d! instantaneous surface charge densitytop surface of antenna.

teed

t-

g-

ges.

-ear

d the

plotted. The antenna is an element of an array withx andyspacing of 3mm. The antennas are on a silicon substrawith illumination from the substrate side. The simulatstructure is shown as Fig. 5~a!, with the electric field (E),magnetic field (H), and propagation vector (k) of the planewave illumination shown. The illumination is from the botom ~i.e., substrate! side atl510.375mm. The simulatedstructure is 1.56mm long ~x-direction! and 60 nm thick~z-direction!. The radius of curvature at the tip is 120 nm. Fi


,ure 5~b! shows the instantaneous current direction~magni-tude proportional to arrow length!. The currents vary indirection from beingx-directed at the center (y50) of theantenna to flowing parallel to the edges at the antenna edThe magnitude of the current is shown as Fig. 5~c!. Similarto the linear antenna of Fig. 2~c!, the currents increase toward the edges of the antenna. The current is maximum nthe center of the antenna and decreases smoothly towarends of the antenna (1x and 2x directions!. However, the


kcrozier

Rectangle

sueis

a

crgerrn

ichta

he

wn

indtnth

w

ate

o

ol

aysts ofdre

byly.

it-

odicatusheiveeo bede-

d

a-call-

ury-to

l


peak current density is 0.16448mA/mm, which is less thanthe value of 0.29471mA/mm for the linear antenna. Thiresults in surface charge distribution with a lower peak valas shown in Fig. 5~d!. The resultant intensity enhancementtherefore lower for this antenna than for the linear antennFig. 2.

The field at the antenna tip is a result of the high surfacharge density there. It may be expected that a sharpewill lead to a higher surface charge density, since charappearing on the antenna surface due to decreasing cudistribution will be confined to a smaller area. This is cofirmed by the FDTD calculations presented in Fig. 6, whshows the intensity enhancement as a function of theradius of the curvature for triangular gold optical antenn~included angle 30°! at a wavelength ofl510.375mm. Asthe radius of curvature is varied from 220 to 60 nm, tintensity enhancement increases from;1960 to ;6230times. As before, the antennas are elements of an arrayx and y spacings of 3mm. The antennas are on a silicosubstrate, with illumination from the substrate side.

III. RESONANCES OF OPTICALANTENNAS-EXPERIMENT

Optical antennas of different shapes operating at midfrared wavelengths~;2–10 mm! are fabricated and testeusing far-field extinction measurements. Good agreemenfound between experiment and theory. Triangular antenare fabricated with a range of sizes, demonstrating thatantenna resonance wavelength may be tuned over arange.

A. Antenna fabrication and testing

The optical antennas are fabricated on silicon substrusing the lift-off process. Electron-beam lithography is usto expose bi-layer PMMA ~polymethyl methacrylate!electron-beam resist. This is followed by evaporation

FIG. 6. Intensity (̂ uEu2&) enhancement vs tip radius of curvature~nm! forgold optical antenna array elements~60 nm thick! on silicon substrate. Theantenna is an element of an array withx and y interelement spacings of 3mm. Antenna lengthL51.56mm. Tip angle is 30°. Schematic of simulatestructure is shown.


,

of

etips

ent-

ips

ith

-

isase

ide

esd

f

chrome~5 nm, for adhesion! and gold~60 nm! layers. ThePMMA is then dissolved in acetone, followed by methanand isopropyl alcohol.

Far-field measurements are carried out on periodic arrof antennas using the set-up shown as Fig. 7. This consisa Fourier transform infrared~FTIR! spectrometer connecteto an infrared microscope.24 Transmission measurements amade over the wavelength range of 2 to 16mm. The lightfrom the FTIR spectrometer is polarized and then focuseda reflection objective lens to illuminate the sample uniformA reflection objective lens~NA 0.4! collects the transmittedlight onto the mercury cadmium telluride~MCT! infrareddetector. An adjustable iris allows for collection of transmted light only from the 200mm3200mm region comprisingthe periodic array of antennas.

B. Experimental results

Transmission measurements are made on the periarrays of optical antennas using the experimental apparof Fig. 7. The antenna array is uniformly illuminated and ttransmitted light within the acceptance angle of the objectlens ~NA 0.4! is collected onto the MCT detector. Thesmeasurements allow the antenna resonant wavelength tdetermined, since the power received at the detector

FIG. 7. Infrared microscope with illumination from Fourier transform infrred ~FTIR! spectrometer for far-field extinction measurements on optiantenna arrays (l52 to 16mm!. Lenses are reflection-type objectives. Colection objective numerical aperture is 0.4. Photodetector is merccadmium-telluride~MCT! detector. An aperture in the image plane is usedcollect light only from the 200mm3200mm region comprising the opticaantenna array.


kcrozier

Rectangle

sn

ncleth

n

-

iefl

te

ongov.

nay

f

i

s-io

tnh

n

toth

ceiteeccio

nts


creases on resonance due to increased scattering and abtion. Absorption due to ohmic losses in the metal antenincreases with the stronger currents that flow on resonareducing the power received at the detector. Scattered etric and magnetic fields are produced by reradiation fromcurrents in the antenna. The received powerU at the detectoris the power in the incident beam less that removed fromby absorption in the antenna and scattering in all directioIt is given by25

U5U inc2Wabs2Ws , ~2!

whereU inc is the incident power~i.e., the power at the detector in the absence of the antenna!. Wabs is the power re-moved from the incident beam by absorption due to ohmlosses in the antenna.Ws is the power removed from thincident beam by scattering, equal to the scattered powerintegrated over all directions.

The received power at the detector may be also writas25

U5U inc2Si3Cext ~3!

whereSi is the power density~W mm22! of the incident il-lumination andCext is the extinction cross section~mm2!.Cext is also known as the area of the ‘‘geometric shadow’’the antenna, since the rate at which energy would impiupon this area is equal to the actual rate of energy remfrom the incident beam due to scattering and absorption

Scanning electron micrographs~SEMs! of gold opticalantenna array elements on silicon substrates are showFig. 8. The optical antennas are elements of periodic arrwith x and y spacings of 3mm. Figure 8~a! shows a linearantenna,;1.55 mm long, ;60 nm thick, and;0.23 mmwide. Figure 8~b! shows a triangular optical antenna,;1.56mm long,;60 nm thick, with an included angle at the tip o;30°. The tip radius of curvature is;140 nm. Figure 8~c!shows a triangular optical antenna,;1.56mm long,;60 nmthick, with an equilateral shape. The tip radius of curvature;190 nm. A circular optical antenna is shown as Fig. 8~d!.The width~x-direction! is ;1.70mm, the height~y-direction!is ;1.50mm and the thickness is;60 nm.

The experimental and FDTD calculated extinction crosectionsCext and efficienciesQext of the optical antenna array elements of Fig. 8 are plotted as Fig. 9. The extinctefficiencyQext is the ratio of the extinction cross sectionCext

to the antenna area. It should be noted that according todefinition of extinction efficiency, the detector must subtean infinitesimally small solid angle so that none of the ligscattered into a direction other than forward is collected.25 Inpractice, the detector has a finite acceptance angle givethe numerical aperture of the collection lens~0.4!. However,almost all of the scattered light is excluded from the detecas most of the power radiated by the antennas is intosubstrate~i.e., back toward the source! or at angles notwithin the collection angle of the lens. Therefore, the extintion efficiency measured in this way is accurate. Furthmore, the FDTD calculations model the effect of the finacceptance angle of the collection lens, allowing a dircomparison between theory and experiment. The periodi~square lattice, 3mm spacing! of the antenna array is als


orp-ae,c-e

its.

c

ux

n

feal

ass,

s

s

n

hedt

by

re

-r-

tty

FIG. 8. Scanning electron micrographs~SEMs! of gold optical antenna ar-ray elements~60 nm thick! on silicon substrates. The antennas are elemeof an array withx andy interelement spacings of 3mm. ~a! Linear antenna,~b! triangular antenna~;30° included angle!, ~c! triangular antenna~equi-lateral, i.e.,;60° included angle!, and~d! circular antenna.


kcrozier

Rectangle


FIG. 9. Experimental and FDTD-calculated extinction efficiencies Qext vs wavelength~mm! for ~a! linear @see Fig. 8~a!#, ~b! triangular@;30° included angle,see Fig. 8~b!#, ~c! triangular@60° included angle, see Fig. 8~c!#, ~d! circular @see Fig. 8~d!# optical antennas. The antennas are elements of an array withx andy interelement spacings of 3mm.

u-,

heajewi-titioterlluhon

oss

an-cur-

ance

raystel-

is at34e-

taken into account in the FDTD calculations. Figures 9~a!,9~b!, 9~c!, and 9~d! present the results for the linear, trianglar ~30° included angle!, triangular~60° included angle, i.e.equilateral! and circular antennas, respectively.

At short wavelengths, the extinction efficiencies of tlinear, triangular, and circular antenna array elementsproach 2. In general, the extinction cross section of an obmuch greater in size than the wavelength approaches tits cross sectional area.26 The flux impinging on the geometric cross section is either scattered or absorbed, contribua value equal to the cross sectional area to the extinccross section. The fields on the opposite side of the objecthe illumination are zero, so that the scattered field thmust be equal in magnitude and opposite in sign to the imination field. This scattered flux then contributes to textinction cross section a value equal to the cross secti


p-ctce

ngntoe-

eal

area. The total extinction cross section is then twice the crsectional area.

On resonance, the extinction cross sections of thetenna array elements peak, since the increased antennarents result in greater scattering and absorption. Resonfor the linear antenna array element occurs atl59.60mm,where the extinction cross section is 4.98mm2 and the ex-tinction efficiency is 14.70. For the triangular antenna arelement~30° included angle!, the measured extinction crossection is 5.96mm2 and the extinction efficiency is 6.39 al59.93mm. For the equilateral triangular antenna arrayement, the measured extinction cross section is 7.05mm2 andthe extinction efficiency is 4.27 atl510.08mm. The mea-sured resonance of the circular antenna array elementl510.07mm, where the extinction cross section is 7.mm2 and the extinction efficiency is 3.48. At short wav


kcrozier

Rectangle

lu

gttha

ayi

th

hte

ieThg

thtd

throanpe-

ha

ria,roofg

regt, tthl6

tesfttednlda

th

isnt

teala

tioum

that

oldd bydues ofingmicthetedhasen

ceves

-arees.onun-hfor

f a

e is

gestumetal,ithces,sil-heare

l ap-


lengths, the extinction efficiency approaches a limiting vaof 2.

At wavelengths longer than the resonance wavelenthe extinction efficiency steadily decreases. This is due tosmaller currents induced in the antenna, leading to lesssorption and scattering. At very long wavelengths the Rleigh scattering limit would be approached, however thisnot applicable here, since it occurs when the radius ofscatterer is less than;0.05l.25

The FDTD calculatedQext are in good agreement witexperiment. Differences are attributed to losses in the annas due to edge and surface roughness~not modeled in theFDTD calculations! and differences between the geometrof the actual antennas and those of the FDTD model.circular and equilateral triangle antennas have a simplerometry, without the small radius of curvature corners oflinear and triangular~30° included angle! antennas, so thathe geometry used for these antennas in the FDTD mobetter matches that of the actual antennas. Furthermore,are smaller differences between elements of the electbeam-fabricated antenna array for the larger circularequilateral triangle antennas. For these reasons the exmental and FDTD calculatedQext spectra are in better agreement for the circular and equilateral triangle antennas tfor the linear and triangular~30° included angle! antennas.

In order to study the effect of antenna size and mateupon the position and strength of the antenna resonanceangular antennas with a range of sizes are fabricated fgold, silver, and aluminum. The antennas are elementsperiodic array and are on silicon substrates. The triangleometry is kept constant as the size is varied~i.e., the trianglesare similar!, although the smaller triangles display morounding at their corners as a fraction of the triangle lenthan do the larger triangles. As the antenna size is variedx and y interelement spacings are scaled linearly. Forsmallest antenna elements~design length 433 nm, actualength 409 nm!, thex andy spacings are 1039 nm and 110nm, respectively. For the largest array elements~designlength 1126 nm, actual length 1084 nm!, thex andy spacingsare 2702 nm and 2876 nm, respectively. It should be nothat the orientation of successive antenna array elementternates in thex direction between the tip being on the leside, and the tip being on the right side~as shown in the inseof Fig. 10!. This is different from the other arrays discussin this article, in which all array elements are oriented idetically. This is expected to have little effect upon the fieenhancement. The experimental results obtained for thetenna arrays are shown as Fig. 10. The approximationthe resonant length isL5l/(2n), wheren is the substraterefractive index, is also plotted. As the triangle lengthvaried from ;0.4 to 1.1 mm, the gold antenna resonawavelength increases from;2.5 to;7.3 mm. The variationof resonant wavelength with antenna length is approximalinear and the resonant wavelength is close to the hwavelength approximation. In general, the actual resonwavelength is less than the half-wavelength approximafor all the metals studied. This may be due to the mediabove the antenna being free space, withn51.0, so that the


e

h,eb--

se

n-

see-e

eleren-dri-

n

ltri-ma

e-

hhee

dal-

-

n-at

lyf-ntn

effective refractive index seen by the antenna is less thanof the substrate.

From Fig. 10, it may be seen that in general the gantennas have the longest resonant wavelengths, followethe silver and then aluminum antennas. This variation isto material differences, as the geometry of the antennathe same length is identical for the different metals, bedefined in the same electron beam lithography step. Ohconduction losses in the metals may be responsible fordifferences in resonant wavelength, which may be expecto be shortened by increased loss. Loss increases the pconstantb, which is the imaginary part of the propagatioconstant g (g5a1 i * b) and determines the resonanwavelength. This may be understood by considering wapropagating along one dimension in a lossy medium~e.g.,lossy transmission line27!. In this model, the antenna is considered a thin center-fed antenna, the two halves of whichapproximated as a pair of open circuited transmission linNote that this simplified model does not predict radiatifrom the antenna, but allows the resonance effect to bederstood. When each~lossless! transmission line has a lengtof l/4, the input reactance is zero, which is the conditionresonance. The total length of the antenna is thenl/2. Nowconsider the effect of loss upon the phase constantb. Thetransmission line loss may be modeled by the addition oseries resistance termR to the series inductanceL and shuntcapacitanceC terms. This increases the phase factorb,27 sofor the same transmission line length, the input reactanczero at a shorter wavelength.

As discussed, gold antennas have in general the lonresonant wavelengths, followed by the silver and aluminantennas. This suggests that aluminum is the lossiest mfollowed by silver and gold. This trend is in agreement wthe peak extinction efficiencies at the antenna resonanwhich are measured to be greatest for gold, followed byver, and then aluminum. From Ref. 28, it is known that tantenna currents, and therefore the extinction efficiency,

FIG. 10. Resonant wavelength~mm! vs antenna length~mm! for gold, silver,and aluminum antenna arrays on silicon substrates. Line is theoreticaproximation that the antenna resonant length isL5l/(2* n), wheren is therefractive index of the substrate.


kcrozier

Rectangle

ol,toid

tio

initnnre

thfo

nachathtetu

spe

in

is

y

encf

in

s

u

. TceTeca

enc

r-b

nm

re

hog-onea-

ereso-ingrialer-

nt

el-rdel toia

el-ssorro-

an

B.

s.:

sc.

ys.

s,

at


reduced as the metal losses are increased. It should be nthat in addition to the intrinsic conductivity of the metalosses are in general influenced by sample-specific facsuch as surface roughness, the presence of surface oxgrain size, grain orientation, and residual gas incorporainto the film.

In this study, periodic arrays of optical antennas arevestigated for experimental considerations, namely, thatnot possible to make measurements on isolated antewith the infrared microscope used in this study. Furthermothe boundary conditions in the FDTD software used20 areinherently periodic. Nevertheless, it may be expected thatcurrent distributions and field enhancements calculatedthe optical antennas in this study are a good indicationwhat would occur for the case of a single optical antenCurrent in an antenna is induced by the incident field whifor the case of an isolated antenna, consists of a plane wFor an antenna in an array, in addition to the plane wave,incident field consists of electromagnetic waves reradiaby the currents in other antennas in the array. The muimpedance concept from antenna theory29 may be used toestimate the effect of this coupling upon the antenna renance. Resonance is obtained when the sum of self imance of the antenna and mutual impedance between thetenna and other antennas in the array is purely real.7 Basedon the self- and mutual-impedances of infinitesimally thhalf-wave dipole antennas,29 a good approximation for theantennas in this study, the resonant wavelengths of anlated antenna and an antenna in an array~with 3 mm inter-element spacing! are predicted to be very close, differing bless than;2%. In order to verify this experimentally withthe antennas used in this study, measurements are madsamples with different interelement spacings. The differebetween the longest and shortest resonant wavelengths olinear antenna arrays fabricated with interelement spacbetween 3 and 10mm is less than;5%. For triangular an-tenna arrays~30° included angle! with spacings between 3and 10mm, the difference between resonance wavelengthless than 7%. For triangular antenna arrays~60° includedangle! with spacings between 3 and 9mm, the differencebetween resonance wavelengths is less than 7%. For circantenna arrays with spacings between 3 and 6mm, the dif-ference between resonance wavelengths is less than 7%relatively small variation in resonant wavelength with spaing suggests that similar current distributions and hence fienhancements may be expected for isolated antennas.suggests that optical antennas could be fabricated at theof atomic force microscope tips and used as probes for sning near-field optical microscopy.

IV. CONCLUSIONS

Optical antennas have been studied for local fieldhancement by simulation and experiment. Finite differentime domain~FDTD! method calculations allowed the curent, charge, and field distributions in the antennas tofound. FDTD calculations allowed the influence of antenshape, length, and sharpness upon the intensity enhance~;3 orders of magnitude! to be found. Optical antennas we


ted

rses,n

-isas,

eorf.,

ve.edal

o-d-

an-

o-

onethegs

is

lar

he-ldhisndsn-

-e

eaent

fabricated on transparent substrates by electron beam litraphy. Far-field extinction spectroscopy was carried outthe antennas. The FDTD calculated and experimentally msured extinction efficiencies of the optical antennas wfound to be in good agreement. It was shown that the renant wavelength of the antenna could be tuned by varythe antenna length. The influence of the antenna mateupon the resonant wavelength was also found, with diffences attributed to ohmic losses.

ACKNOWLEDGMENTS

This work was supported by the Army, the Departmeof Energy ~DOE!, and Advanced Micro Devices~AMD !.K.B.C. acknowledges support from a Leland T. Edwards Flowship. Fabrication work was carried out in the StanfoNanofabrication Facility, which is partially funded by thNational Science Foundation. The authors are gratefuProfessor Andrew Neureuther of the University of Californat Berkeley for use of the TEMPEST FDTD software devoped by his group. The authors are also grateful to ProfeTodd Smith for use of the FTIR spectrometer and micscope. The authors thank a reviewer for comments onearlier version of this article.

1N. Felidj, J. Aubard, G. Levi, J. R. Krenn, M. Salerno, G. Schider,Lamprecht, A. Leitner, and F. R. Aussenegg, Phys. Rev. B65, 075 419~2002!.

2K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, J. PhyCondens. Matter14, R597~2002!.

3S. A. Maier, P. G. Kik, and H. A. Atwater, Appl. Phys. Lett.81, 1714~2002!.

4T. Matsumoto, Y. Anzai, and T. Shimano,International Symposium onOptical Memory 2001, Toyama, Japan, November 2001.

5J. T. Krug, E. J. Sanchez, and X. S. Xie, J. Chem. Phys.116, 10 895~2002!.

6J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, J. Micro202, 60 ~2001!.

7I. Puscasu, D. Spencer, and G. D. Boreman, Appl. Opt.39, 1570~2000!.8T. Schimert, M. E. Koch, and C. H. Chan, J. Opt. Soc. Am. A7, 1539~1990!.

9R. Ulrich, Infrared Phys.7, 37 ~1967!.10C. L. Haynes and R. P. Van Duyne, J. Phys. Chem. B105, 5599~2001!.11V. Daneu, D. Sokoloff, A. Sanchez, and A. Javan, Appl. Phys. Lett.15,

398 ~1969!.12S. Wang, Appl. Phys. Lett.28, 303 ~1976!.13A. Sanchez, C. F. Davis, K. C. Liu, and A. Javan, J. Appl. Phys.49, 5270

~1978!.14F. Zenhausern, Y. Martin, and H. K. Wickramasinghe, Science269, 1083

~1995!.15Y. C. Martin, H. F. Hamann, and H. K. Wickramasinghe, J. Appl. Ph

89, 5774~2001!.16L. Novotny, R. X. Bian, and X. S. Xie, Phys. Rev. Lett.79, 645 ~1997!.17E. J. Sanchez, L. Novotny, and X. S. Xie, Phys. Rev. Lett.82, 4014

~1999!.18R. Hillenbrand, T. Taubner, and F. Keilmann, Nature~London! 418, 159

~2002!.19A. Chimmalgi, T. Y. Choi, C. P. Grigoropoulos, and K. Komvopoulo

Appl. Phys. Lett.82, 1146~2003!.20TEMPEST 6.0, Electronics Research Laboratory, University of California

Berkeley, Berkeley, California.21Handbook of Optical Constants of Solids, edited by E. D. Palik~Academic

Press, Orlando, Florida, 1985!.22Frequency Selective Surface and Grid Array, edited by T. K. Wu~Wiley,

New York, 1995!.23W. L. Stutzman and G. A. Thiele,Antenna Theory and Design~Wiley,

New York, 1981!.24FTIR is Bruker IFS 66v/s. Infrared microscope is Bruker IRScope II.


kcrozier

Rectangle

er

-


25C. F. Bohren and D. R. Huffman,Absorption and Scattering of Light bySmall Particles~Wiley, New York, 1998!.

26A. Ishimaru,Electromagnetic Wave Propagation, Radiation, and Scatting ~Prentice Hall, 1991!

27S. Ramo, J. R. Whinnery, T. Van Duzer,Fields and Waves in Communi


-

cation Electronics~Wiley, New York, 1994!, pp. 245–247.28T. A. Cwik and R. Mittra, IEEE Trans. Antennas Propag.AP-35, 1226

~1987!.29C. A. Balanis,Antenna Theory: Analysis and Design~Wiley, New York,

1997!.


kcrozier

Rectangle

optical antennas: resonators for local ﬁeld...

Documents