Broadband Antenna Sacs Nano

8/13/2019 Broadband Antenna Sacs Nano

1/8

NAVARRO-CIA AND MAIER VOL. 6 NO. 4 3537 3544 2012

www.acsnano.org

3537

March 19, 2012

C 2012 American Chemical Society

Broad-Band Near-Infrared PlasmonicNanoantennas for Higher HarmonicGenerationMiguel Navarro-Cia * and Stefan A. Maier

Experimental Solid State Group, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom

A ntennas1 are widely used at radio

and microwave frequencies to cou-ple/radiate energy from a source to

free space with a far- eld emission of re-duced angular divergence. Due to recipro-city, they also collect radiation efficientlyfrom de ned directions. These functional-ities are performed via the manipulation of

enhanced elds in subdiff raction volumes.With the advent of nanotechnology, anten-nas operating at optical/near-infrared fre-quencies havebecomeaccessible, 2 exceedingthe energy localization capabilities of tradi-tional optical elements such as mirrors andlenses.3 Optical antennas 2 can be advanta-geously used to either harvest or focus lightin nanoscale volumes not limited by di ff rac-tion. This results in a large electromagnetic

eld enhancement in the proximity of theantenna. Likewise, they tailor the excitationand emission processes of nearby uores-cent molecules or quantum dots. 4 6 Theseabilities hold signi cant promise for opticalemitters, photovoltaics, spectroscopy, andnonlinearities. 2,7 12

Most nanoantennas reported in the lit-erature so far (nanorods and nanodipoles)show a narrow-band response because of their dipolar nature. 1,7 However, it wouldbe highly desirable to have a nanoantennawith signi cant bandwidth of operation, forexample, more than an octave. Nanoanten-nas with such properties are expected to

make signi cant contributions,2

for in-stance, in the burgeoning areas of surface-enhanced linear/nonlinear vibrational spec-troscopy 13,14 and spontaneous two-photonemission,15,16 which are intrinsically multi-wavelength and broad-band in nature, andin higher harmonic generation. We willfocus on the latter in this article. Indeed, abroad-band plasmonic nanoantenna couldbe used for more speci c applications linkedto harmonic generation, such as perfectlensing via phase conjugation and time

reversal by enhancing thee fficiency of non-linear processes not only at the funda-mental 17 but also at the harmonic frequency.

In an eff ort to surpass the inherentlylimited narrow-band operation of infraredfrequencies, nanorods and the bow-tie to-

pology have been extensively explored.Nevertheless, their bandwidths of operationaresigni cantlybelow an octave. 11,15,16,18,19

Other attempts less explored involve theuse of fractal topologies, 20 multielementarrangements, 21 23 or the interaction withgrating modes. 24 However, theyalso experi-ence limitations. For instance, the fractalSierpinski nanocarpet 20 has strong eld en-hancement at several wavelengths, but thespatial position of thehot spot is wavelength-dependent; multi-nanodipoles of di ff erent

* Address correspondence [email protected].

Received for review February 7, 2012and accepted March 19, 2012.

Published online

10.1021/nn300565x

ABSTRACT

We propose a broad-band near-infrared trapezoidal plasmonic nanoantenna, analyze it

numerically using nite integration and diff erence time domain techniques, and explain

qualitatively its performance via a multidipolar scenario as well as a conformal transforma-

tion. The plasmonic nanoantenna reported here intercepts the incoming light as if it were of

cross-sectional area larger than double its actual physical size for a 1500 nm bandwidth

expanding from the near-infrared to the visible spectrum. Within this bandwidth, it also

con nes the incoming light to its center with more than 1 order of magnitude eld

enhancement. This wide-band operation is achieved due to the overlapping of the diff erent

dipole resonances excited across the nanoantenna. We further demonstrate that the broad-

band eld enhancement leads to efficient third harmonic generation in a simplied wire

trapezoidal geometry when a Kerr medium is introduced, due to the lightning rod eff ect at the

fundamental and the Purcell eff ect at the induced third harmonic.

KEYWORDS: broad-band . conformal transformation . nanoantenna .plasmonic . third harmonic generation

A R T I C L E
http://pubs.acs.org/action/showImage?doi=10.1021/nn300565x&iName=master.img-000.jpg&w=181&h=56


2/8

NAVARRO-CIA AND MAIER VOL. 6 NO. 4 3537 3544 2012www.acsnano.org

3538

lengths arranged radially 21,22 require circularly/ellipti-cally polarized light to excite the resonance of eachnanodipole, and the bandwidth is constrained to thenumber of diff erent nanodipoles that one can setradially; like fractal nanoantennas, thehot spot locationof an array of nanorods of diff erent length 23 is wave-length-dependent; nally, the grating-assisted multi-wavelength nanoantenna 24 requires several gratingsof diff erent periodicities, leading to impractical largestructures. For microwave frequencies, broad-bandantennas (with bandwidths up to 10:1, i.e., decade oreven higher) were introduced in the1950s via so-calledfrequency-independent antennas. 1,25 Similar to thehistory of the development of optical bow-tie andYagi-Uda dipolar antennas, 2,7 microwave designs of broad-band antennas arealso attractivestarting pointsfor broad-band optical nanoantennas. Indeed, one can

nd a compact advanced design such as the trapezoi-dal logperiodic antenna, 1,25 which displays a broad-

band single hot spot without the need for circularly/ elliptically polarized light.

The article is structured as follows: rst, the trape-zoidal logperiodic nanoantenna is presentedand char-acterized in terms of cross sections and eld en-hancement at the gap and vertexes. Second, theunderlying physics of the nanoantenna is qualitativelydescribed from a simplemultidipolar scenario andby aconformal transformation approach. This study willallow us to subsequently propose a simpli ed designgeometry, which would alleviate demands on themanufacturing process while retaining all features

associated with the broad-band trapezoidal nanoan-tenna. Finally, third harmonic generation is demon-strated via a Kerr medium placed at the gap betweenthe arms of the simpli ed nanoantenna. All numericalcalculations assume, for simplicity, that the singlenanoantenna is surrounded by free space.

RESULTS AND DISCUSSION

Extinction, Scattering, and Absorption Cross Sections. Atrapezoidal nanoantenna is displayed in Figure 1a,where the geometrical parameters are defined asfollows: Ri 1 / Ri = R0.5 with i = 1, 2...5, R1 = 1000 nm,and R , which controls the width of the teeth, variablefrom 0.39 to 0.74 in 0.05 steps; inner and outer angle i = 30 and o = 60 , respectively; metal thicknesst = 60 nm; separation between top and bottom armsg = 50 nm. For the finite integration time domainsimulations,26 the metal is assumed to be silver, witha permittivity following the Drude model Ag = 0( (p2 / ( i )), with = 4.039, plasma frequencyp = 1.39077 1016 rad/s, and damping constant = 1.23955 1015 rad/s. Notice that has beenoverestimated compared to Johnson and Christy 27 toaccount for imperfections in a real situation and toreduce computational time. For accurate calculation of

the scattering properties and the field distributionclose to the metal, several precautions were taken,which are detailed in Methods.

Initially, thedependence of thecross section on theteeth number is investigated for a nanoantenna withR = 0.49, as seen in Figure 2a. As expected from themicrowave counterpart of the nanoantenna, 1,25 theinclusion of additional teeth increases the nanoanten-na's bandwidth. Thus, this design allows for a systema-tic wideningof thewavelength bandwidthconstrainedonly by space limitations. In Figure2a, one can identifythree peaks in theextinction cross section fora 4-toothnanoantenna, whereas ve peaks emerge for a 6-toothnanoantenna. This suggests that the number of peaksfor the extinction cross section is N 1, where N is the

number of teeth. The origin of this relation is eluci-dated below.

Unlikedipoleandbow-tie antennas, thefundamen-tal operation of the trapezoidal tooth nanoantenna isinduced by a normal-incident plane-wave polarized perpendicular to the axis aligned with the two arms of the nanoantenna. 1,25,28 For more information, thereader is referred to the Supporting Information. Onthe left-hand side of Figure 2b, the charge densitydistribution at the plane of the middle cross section of the nanoantenna is plotted for all resonance peaksshown in panel a. In addition, the perspective view of the eld enhancement ( i.e., |E |/|E incident |) at the middlecross section of the nanoantenna is displayed on theright-hand side. An inspection of these charge densi-ties shows that twooppositeneighboringteeth of eacharm of the nanoantenna are active at each resonancein a dipole fashion. These local dipoles at each arm arein phase with each other and mainly oriented in theu-direction. Otherwise, they would notbe induced by au-polarized plane-wave. Likewise, the charge densitiescon rm that a local vertical dipole between arms isinduced for each resonance at the center gap. Never-theless, this dipole is not induced directly by the coup-ling to the incident eld given their cross-polarization

Figure 1. Schematic geometry of the solid (a) and wire (b)trapezoidal nanonantenna. The nanoantennas are illumi-nated by a u -polarized plane-wave propagating in the w -direction.

A R T I C L E


3/8


3539

but by the currents excited in the nanoantenna bythe teeth-based dipoles. These charge densities alongwith the eld enhancement put also in evidencethat the active region shifts from the ends of the

nanoantenna toward its center as the wavelength

decreases, leading to larger eld localization. Finally,the eld enhancements highlight that the gap be-tween arms is indeed a broad-band hot spot since italways shows thelargest eld enhancement across thenanoantenna for all resonant peaks. Further informa-tion about the elddistribution and induced current atthe middle cross section of the nanoantenna can befound in the Supporting Information. Notice that theabsolute value of the eld enhancement should betaken with precautions since it depends on the meshgrid, and ideal in nitely small grid mapping perfectlyall sharp features would lead to larger eld enhance-ments than those reported here. Nevertheless, in thereal experiment, blunt nanoantennas are measured,and thus, the results should be closer to the simulationwith a mesh grid like the one used here (mesh cellresolution up to 1 nm 1 nm 5 nm in the zonebetween arms) ratherthan an ideal in nitely smallgrid.

From the local dipole picture, we can foresee a redshift of the bandwidthof operation as theparameter Rincreases (i.e., thinner teeth) because, then, the dis-tance between the charges of di ff erent sign in eachlocal dipole are larger. In addition, in general, thelarger/longer the physical area/length of the nanoan-tenna, the larger the scattering. 1 Figure 3a shows clear

Figure 2. (a) Extinction (solid), scattering (dashed), andabsorption cross section (dash-dot) for a 4- (dark red) and

6-tooth trapezoidal nanoantenna (red) with R = 0.49 whenthe structure is illuminated by a u -polarized plane-wave.The numbers account for the peak order. (b) From top tobottom: rst, second, third, fourth, and fth resonanceaccording to panel a. Static charge density at the middlecross section of the nanoantenna (left) and eld enhance-ment at the cross-sectional plane of the nanoantenna(right). The and symbols superimposed underline theassociated charge distribution. Notice that each eld en-hancement plot has its own scale bar.

Figure 3. (a) From top to bottom, extinction, absorption, andscatteringcrosssection ofa 6-tooth trapezoidalnanonantennawithvarying R parameter, i.e. , tooth width.Notice the di ff erentscale of the absorption cross section. (b) Field enhancementwith respect to the incident eld, |E |/|E incident |, at the center of the nanonantenna as a function of the R parameter.

A R T I C L E
http://pubs.acs.org/action/showImage?doi=10.1021/nn300565x&iName=master.img-003.jpg&w=198&h=294http://pubs.acs.org/action/showImage?doi=10.1021/nn300565x&iName=master.img-002.jpg&w=198&h=502


4/8


3540

evidence of thetwo trendsdescribed above,wheretheextinction, absorption, and scattering cross sectionsare plotted for various values of the R parameter at arange of wavelengths.

Currently, nanoantennas can nd extremely usefulapplications by incorporating nonlinear media or im-mobilizing/retaining a biological recognition elementat the spatial location of maximum eld enhancement(hot spot).2,7,8,12 14,17 For that reason, the e ff ect thatthe parameter R has on the eld enhancement (withrespect to the incident eld) at the center gap of thenanoantenna is shown in Figure 3b. In passing, noticethat the largest eldenhancement does nothappenatthe center but at the central vertexes of the arms; seeFigure 2b and Figure S3. According to our simulations,the eld is expected to be enhanced 15 times at thelowest resonant wavelength and is kept 10 timeshigher than the incident eld for a wide wavelengthrange for the chosen gap of 50 nm. Although these

valuesdo notoutperform those of othernanoantennas(e.g., dipole and bow-tie nanoantennas) already re-ported in the literature, the nanoantenna proposedin this article has the outstanding advantage to main-tain large extinction cross sections and high eldenhancements at a single position, the center, at atruly broad-band spectrum.

Conformal Transformation Explanation. The broad-bandperformance of the trapezoidal nanoantenna and anumber of its key physical properties can also beunderstood using coordinate transformation, in a si-milar fashion to touching plasmonic elements. 29,30

Since the proposed system is admittedly far morecomplex than previous examples because the quasi-static limit approximation is no longer valid and it is athree-dimensional finite system, the analysis pre-sented below is only qualitative.

Let us consider an in nite two-dimensional systemthat inherently has a broad-band response: a linedipole aligned along the y -axis at x = betweentwo semi-in nite metal strips lined up along x ; seeFigure 4a. If the strips represent a perfect electricconductor, thiscon guration is thewell-knownparallelplate waveguide, which has a broad-band responsewith twostraightlinesof slope 45 passing through the

origin of the k 0 diagram representing either for-ward- or backward-traveling waves. 25 Thus, the spec-trum is continuous and broad-band. If now corru-gations with period p are applied to the semi-in nitemetal strips, the dispersion relation becomes a typicalperiodic stop- and pass-band; 25 see Figure 4b.

Let us now apply the following conformal transfor-mation on the above structure: 28,31

z 0 e z (1)

where both z and z 0 are complex numbers with theconvenient form z = x i y and z 0 = u iv = Feij .

Obviously, all points at x = in z translate to theorigin in z 0, and vertical and horizontal lines in the z -plane are converted to circles and radial lines in the z 0-plane. Hence, theresulting structure is a smoothandtooth bow-tie for the smooth and corrugated parallelplate waveguide, respectively. Likewise the line dipolesource in z translates to a point dipole at the origin in z 0 aligned along the v -axis. Hence, if the bow-tiestructure of in nite extend is fed at the vertex, it showsa broad-band naturesincethe originaland transformedstructure have the same spectral response. 29 31

Indeed, from antenna theory and microwave designs,we know that the bow-tie response is broad-band. 1

Similarly, if the tooth bow-tie is fed at the vertex, its

Figure 4. From left to right: two metallic slabs ( z -plane),dispersion diagram, and transformed structures ( z 0-plane):semi-in nite (a) and truncated slabs (b f). The dipolesource at x = is transformed into a dipole at the vertex.If the metallic slabs are either in nitely long (a) or areterminated in a matched (nonre ecting) load, only thosebranches of the dispersion curve which have positive slopeare applicable. Hence, the nonexcited backward-travelingmode is displayed as a dashed line in panel a. When atermination is present as it is the case for the rest, thebranches with negative slope are also valid.

A R T I C L E


5/8


3541

response is periodic. 1,25,28 Notice that a truncation in z ,which means that our parallel plate waveguide doesnot extend to in nity, leads to a truncation in z 0; seeFigures 4b f. However, the broad-band characterremains as long as standing waves are not excited. Intermsof the z -plane, this can beensured if the re ectedtraveling wave is negligible by, for instance, a lossy (i.e.,the metal is no longer a perfect electric conductor buthas certain, yet high, conductivity) waveguide longenough for the forward-traveling waveto decay beforereachingthe endor by placing an absorbingmaterial atthe end. This undesired backward-traveling mode ex-citation via the nite lengthof thestructure is known asthe end e ff ect in microwave antennaengineering. 1,25,28

Finally and more interesting is the situation when thearms of the bow-tie do not touch at a single point, buttheyare moved apart a certain distance, as it is the casein reality; see Figure 4f. This modi cation maps inthe z -plane as an adiabatic truncation of the slabsbefore reaching x = , and the hypothetical linedipole connecting arms in the z 0-plane transforms toa line dipole connectedto both stripsat theendof them. These alterations are not expected to cause any sig-ni cant change in the electromagnetic response of theparallel waveguide and, thus, of the bow-tie antenna,either smooth or tooth kind.

For a real metal represented via a Drude function,the previous qualitative discussion is completely valid.However, the dispersion diagram for the smooth bow-tie does not extend in nitely following the light line asit would happen in an ideal perfect electric conductorparallel plate waveguide, but it bends over approach-

ing an asymptotic limit corresponding to the surfaceplasmon frequency. 32 Given that this limit happens atnear-infrared, one can still consider the system broad-band (it operates from DC to near-infrared). 29 For thetooth bow-tie, on the contrary, the dispersion relationexhibits qualitatively the same induced periodicity asthat of the perfect electric conductor case.

Wire Trapezoidal Nanoantenna: Harmonic Generation with aNonlinear Kerr Medium. Given the fact that the mechan-ism of this nanoantenna can be understood as origi-nating from a collection of individual dipole antennasresonating at different wavelengths (Figure 2b andFigureS2), onecould suggest replacing thetrapezoidalnanoantenna with an array of dipole nanoantennas. This simplification preserves the broad-band scatteringcharacteristics,but at theexpenseof havingseveral hotspots rather than a single hot spot for the wholefrequency bandwidth (see Figure 2b and SupportingInformation for more details), which is crucial for theharmonic generation scheme proposed below. Never-theless, onecanenvision a similarsimplification, whichpreserves the broad-band scattering as well as single-spot features: the trapezoidal nanoantenna can betransformed to a winding wire nanoantenna; seeFigure 1b, with wire width s = 30 nm in the case

discussed here. The extinction cross section and fieldenhancement at the center are plotted in Figure 5 andcompared with the case of a solid trapezoidal antenna

with outer angle o = 90 . As it is apparent, the wireantenna performs very closely to thesolidone. Thetwomost distinctive consequences of the simplified wiredesign are as follows: the response experiences a redshift, and additional resonant peaks or shouldersemerge. These features stem from the fact that, now,the nanoantenna can be understood as an array of sixhorizontal nanorods (connected) inducing at least sixresonances rather than five. The upper-most nanorod,which is indeed the extra resonant element comparedto thesolid trapezoidal nanoatenna, admits an induceddipole with larger distance between charges thananyone excited in the solid trapezoidal nanoantenna. Therefore, it resonates at longer wavelengths.

Finally, we investigate harmonic generation withthe wire trapezoidal nanoantenna. Second- and third-order susceptibilities in optical nonlinear media are, ingeneral, several orders of magnitude smaller than the

rst-order linear susceptibility. 33 It has been shownthat nonlinear processes can be enhanced, however,via the use of plasmonic nanoantennas, whose collec-tive oscillation of electrons at their surface enhancesthe local eld intensity by several orders of magni-tude. 2,7,8,12 16,18,32,34 As a further re nement of thisscheme, two independent narrow-band nanoantennas

Figure 5. (a) Extinction cross sections of the two-arm solid(red) and wire trapezoidal nanonantenna (dark green) andfour-arm wire trapezoidal nanoantenna (dark gray) for 0 =60 (solid) and90 (dashed) and R = 0.49. (b) Field enhance-ment with respect to the incident eld at the center of thenanonantenna.

A R T I C L E


6/8


3542

aligned orthogonally have been recently suggested tobe used in second harmonic generation. 35 With thisapproach, four optimal processes work together toincrease the e fficiency of the harmonic generation:

rst, one of the two nanoantennas captures the in-cident eld at the fundamental frequency; second, viathe so-called lightning rod e ff ect, the local eld inten-sity is greatly enhanced at the gap between armswhere the nonlinear medium is smartly placed; third,the nonlinearity generates the corresponding harmo-nic dipole; fourth, the radiation of this harmonic dipoleis increased by the second nanonantenna workingspeci cally at such frequency via the Purcell eff ect.

It can be intuitively understood that a broad-bandnanoantenna would be able to enhance the harmonicgeneration of any order ( i.e., second, third, etc.) of anyfundamental frequency falling within its bandwidth of operation. Furthermore, by employing an additionalbroad-band nanoantennaorthogonally to the rstone,a polarization-independent scheme is easily envi-saged. This assumption is con rmed in Figure5, wherea four-arm wire trapezoidal nanoantenna displays al-most identical extinction cross section and eld en-hancement to our two-arm wire trapezoidal nano-antenna regardless of the incident polarization.

To study this proposal, nite diff erence time do-main calculations 36 were performed where the Drudeparameters of the silver have been tted to Johnsonand Christy.27 The Kerr medium is assumed to bechalcogenide glass 33 As2Se3 with n0 = 2.53 (r =6.4009) and (3) = 6.8 10 18 m2 /V 2 and lls a volumebetween arms of 100 nm 100 nm 60 nm; see

Figure 1b. To reduce computing resources, the total-eld scattered technique has been used. For more

details of the simulations, the reader is referred toMethods at the end of the article.

The extinction cross section for the wire trapezoidalnanoantenna loaded with a linear dielectric with thesame relative permittivity as the As 2Se3 and excited bya narrowtemporal pulse with amplitudeof 1 107 V/mis plotted in Figure 6. This peak amplitude has beenchosen to ful ll the condition (3) |E (t)|2 , r; see the

eld intensity (in logarithm scale) in the inset of Figure 6. The results are in agreement with thosepreviously shown in Figure 5. When the isolated Kerrmedium is illuminated by a Gaussian wave packetcentered at = 3 m (the largest resonant wavelengthof the loaded nanoantenna according to the previouscurve) and spectral width of 0.088 m, no signi cantthird harmonic generation is observed; see dotted linein Figure 6. However, when the nanoantenna is intro-duced, for the same long-standing pulse (narrow infrequency), a noticeable signal is radiated by ournanoantenna at the third harmonic. Indeed, the inten-sity of the third harmonic is 9 orders of magnitudehigher than without the nanoantenna. In addition,note the 6 orders of magnitude di ff erence between

the peak intensity and the noise oor. Finally, if thecentral wavelength of the Gaussian wave packet ischanged to 2.55 nm,the intensityof thethirdharmonicsignal is still several orders of magnitude higher thanthat without a nanoantenna as well as the peak-to-noise ratio, which proves all of our assumptions andshows the potential of introducing broad-band na-noantennas in the eld of nonlinearities.

CONCLUSIONS

In conclusion, a broad-band nanoantenna has been

shown andanalyzed via nite integration time domainsimulations. For an antenna with a physical crosssection of 8.45 105 nm 2 , the scattering cross sectionpeaks at 7.0 106 nm 2 for the longest wavelengthresonance and is kept at 2.2 106 nm 2 for a 1500 nmbandwidth expanding from the near-infrared to thevisible spectrum. Up to 15- and 14-fold eld enhance-ment at the center and up to 50.7 and 41.9 at thevertexes of the plasmonic nanoantenna is obtained atthe peak and in the spectrally at regime, respectively. The underlying physics has been captured in a simpleyetpowerful wayby identifying its multidipolarnature.Also, concomitant with this viewpoint, the conformaltransformation has beenbroughtaboutto shedfurtherlight in the mechanism of the nanoantenna. Theseinterpretations have allowed us to simplify the nano-structure without causing any penalty on its responsein terms of extinction cross section and eld enhance-ment at the hop spot, that is, the vertex of thenanoantenna. Finally, bene ted by the wide-bandresponse of the simpli ed wire trapezoidal nanoan-tenna, a compact and exible third harmonic genera-tion scheme is proposed and validated via nitediff erence time domain simulations. The results shownin this article are a signi cant step forward toward

Figure 6. Extinction cross section (dark green) when thenanoantenna is loaded by a linear dielectric with r = 6.4009and third harmonic radiated power with (solid black) andwithout nanoantenna (dotted black) for the nonlinear casewhen the excitation is a quasi-monochromatic plane-wavepolarized along u with central wavelength of = 2.55 and3 m. Top inset: eld intensity | E |2 (logarithm scale) at the

middle cross section of the loaded nanoantenna for =3 m.

A R T I C L E


7/8


3543

wide-band or multiwavelength, exible, and compactplasmonic devices for general purposes and, in parti-cular, for surface-enhanced spectroscopy and non-linear processes. The breadth and utility of these

applications in biosensing and generating extremeultraviolet radiation laser pulses suggests that broad-band antennas at thenanoscale mayplay a large role indriving the basic research as well as technology.

METHODS

Finite Integration Time Domain Method: Linear Analysis. Extinction,scattering, and absorption cross sections as well as near-fielddistribution are calculated using the commercial full-wavethree-dimensional software CST Microwave Studio.26 The di-electric response of silver is modeled as a Drude function of theform Ag = 0( (p2 / ( i )), with = 4.039, plasmafrequency p = 1.39077 1016 rad/s, anddampingconstant =1.23955 1015 rad/s. For accurate calculation of the scatteringproperties and the field distribution close to the metal, severalprecautions are taken. We make sure thatthe distance betweenthe structure and the perfectly matched layers defining thesimulation volume is at least of half wavelength size; subgrid-ding techniques are used to have a mesh cell resolution up to1 nm 1 nm 5 nm inthe zone between arms,and theresidualenergy in the calculation volume is 1 10 8 of its peak value. The time stepping stability factor is set to 1, which correspondstoa time step, t , of around0.0023fs. Thesolveris automaticallyrestarted twice with a reduced time step after an instabilityabort. The maximum simulation time addressed by the refer-ence excitation signal is set to 45 fs. Therefore, all of oursimulations have an excess of around 19 300 time steps. Thenanoantenna in a uniform dielectric medium ( n = 1) is illumi-nated with a u-polarized plane-wave propagating along w . Theextinction, ext , scattering, scatt , and absorption cross section, abs , are calculated with the solver defined script. To computethe scattering cross section, the radar cross section, that is, thefar-field scattered light intensity as a function of angle, is firstobtained by integrating the outward power flow over thecomputationalboundarieswith an appropriate near- to far-fieldtransform. Then,the scatteringcross section,definedas thesumof radar cross section of all angles, is computed. The absorption

cross section is obtained by integrating the net power flowinginward over thecomputational boundaries. Oncethe scatteringand absorption cross sections are known, the extinction crosssection is straightforwardly calculated by ext = scatt abs .

Notice thatthese nite integration timedomain simulationshave been double-checked with nite diff erence time domaincalculations with similar setup parameters as described belowin the nonlinear analysis.

Finite Difference Time Domain Method: Nonlinear Analysis. All spec-tra and field distributions in the section devoted to harmonicgeneration are calculated using the commercial software Lu-merical FDTD Solutions 7.5.36 The dielectric response of silver ismodeled using a 3 Drude-Lorentzian term fit to the experimen-tallymeasuredpermittivity. 27 We characterize thechalcogenideglass33 As2Se3 with n0 = 2.53 (r = 6.4009) and (3) = 6.8 10 18

m2 /V 2 and fills a volume between arms of 100 nm 100 nm60 nm. To reduce computing resources,the total-field scatteredtechnique is used. As for the linear analysis, we make sure thatthe distance between the structure and the perfectly matchedlayers defining the simulation volume is at least of half wave-length size. Convergence testing is done by starting the firstcalculation with a coarse grid and then reducing the grid sizeinsequential simulations and comparing their results. This itera-tive process is stopped when the results of the calculationclosely match those of the previous one. The final cubic grid issetto6nm 4 nm 5 nm, exceptfortheAs 2Se3,where1nm1 nm 5 nm cubic grid is applied. The time stepping stabilityfactor is set to 0.95. When the gap is filled by a linear dielectricand excited by a narrow temporal pulse, this stability factorcorresponds to a time step t = 0.0022 fs. When the gap isexcited by a long-standing pulse centered at = 3 nm or =2.55 nm, it leads to t = 0.0043 fs. The maximum simulationtime is set to 200 and 2000 fs for the narrow temporal and

long-standing pulse simulation, respectively. This leads to oursimulations havingan excessof around90 000and465000 timesteps for the narrow temporal and long-standing pulse simula-tion, respectively. Additionally, at the end of the simulation, allfield components are checked to see if they decay to zero, thusindicating that thesimulationhas runfor a sufficientlylong timefor the CW information obtained by Fourier transformations tobe valid. The residual energy in the calculation volume is 1 10 5 of its peak value. The nanoantenna in a uniform dielectricmedium (n = 1) is illuminated with a u-polarized plane-wavepropagating along w . The scattering cross section is thenobtained via the integration of the power flowing outwardthrough a box of monitors located outside of the source, that is,in the scattered field region, whereas the absorption crosssection is obtained via integration of the net power flowinginward through the monitors placed inside of the total field

scattered field source box, that is, in the total field region. Theextinction cross section is calculated by the sum of the scatter-ing and absorption cross sections.

Conict of Interest: The authors declare no competingnancial interest.

Acknowledgment. The authors thank A. Liu from LumericalSolutions, Inc. for her technical support regarding the nitediff erence time domain simulations. E ff ort sponsored by Lever-hulme Trust, the U.S. Army International Technology Cen-tre Atlantic (USAITC-A) and the Office of Naval Research(ONR and ONR Global).

Supporting Information Available: When the solid logperio-dic nanoantenna is energized at the vertex: radiated poweras afunction of wavelength and radiation patterns for each reso-nant peak. For the solid logperiodic nanoantenna illuminated

by a u-polarized plane-wave as the main body of this paper:static charge density, induced current, eld distribution, and vw view of the total eld enhancement at the uv middle cross-section plane. This material is available free of charge via theInternet at http://pubs.acs.org.

REFERENCES AND NOTES

1. Balanis, C. A. Antenna Theory: Analysis and Design ; Wiley-Interscience: Hoboken, NJ, 2005.

2. Novotny, L.; van Hulst, N. Antennas for Light. Nat. Photo-nics 2011 , 5, 83 90.

3. Born, M.; Wolf, E. Principles of Optics: ElectromagneticTheory of Propagation, Interference and Diffraction of Light ;Cambridge University Press: Cambridge, UK, 1999.

4. Giannini, V.; Fernndez-Domnguez, A. I.; Heck, S. C.; Maier,S. A. Plasmonic Nanoantennas: Fundamentals and Their

Use in Controlling the Radiative Properties of Nanoemit-ters. Chem. Rev. 2011 , 111 , 3888 3912.

5. Pfeiff er, M.; Lindfors, K.; Wolpert, C.; Atkinson, P.; Benyoucef,M.; Rastelli, A.; Schmidt, O. G.; Giessen, H.; Lippit, M.Enhancing the Optical Excitation Efficiency of a Single Self-Assembled Quantum Dot with a Plasmonic Nanoantenna.Nano Lett. 2010 , 10, 4555 4558.

6. Kim,M. S.; Park, D.H.; Cho,E. H.;Kim, K.H.; Park, Q.-H.;Song,H.;Kim, D.-C.;Kim, J.;Joo, J. Complex Nanoparticleof Light-Emitting MEH-PPV with Au: Enhanced Luminescence. ACSNano 2009 , 6, 1329 1334.

7. Bharadwaj, P.; Deutsch, B.; Novotny, L. Optical Antennas. Adv. Opt. Photonics 2009 , 1, 438 483.

8. Schuller, J. A.; Barnard, E.; Cai, W.; Jun, Y. C.; White, J.;Brongersma, M. L. Plasmonics for Extreme Light Concen-tration and Manipulation. Nat. Mater. 2010 , 9, 193 204.

A R T I C L E


8/8


3544

9. Atwater, H. A.; Polman, A. Plasmonics for Improved Photo-voltaic Devices. Nat. Mater. 2010 , 9, 205 213.

10. Knight, M. W.; Sobhani, H.; Nordlander, P.; Halas, N. J.Photodetection with Active Optical Antenna. Science2011 , 332, 702 704.

11. Shegai, T.; Miljkovic, V. D.; Bao, K.; Xu, H.; Nordlander, P.;Johansson, P.; Kll, M. Unidirectional Broadband LightEmission from Supported Plasmonic Nanowire. Nano Lett.2011 , 11, 706 711.

12. Liu, N.; Tang, M. L.; Hentschel, M.; Giessen, H.; Alivisatos,A. P. Nanoantenna-Enhanced Gas Sensing in a Single Tailored Nanofocus. Nat. Mater. 2011 , 10, 631 636.

13. Schumacher, T.; Kratzer, K.; Molnar, D.; Hentschel, M.;Giessen, H.; Lippitz, M. Nanoantenna-Enhanced UltrafastNonlinear Spectroscopy of a Single Gold Nanoparticle.Nat. Commun. 2011 , 2, 333.

14. Le, F.; Brandl, D. W.; Urzhumov, Y. A.; Wang, H.; Kundu, J.;Halas, N. J.; Aizpurua, J.; Nordlander, P. Metallic Nanopar-ticle Arrays: A Common Substrate for Both Surface-Enhanced Raman Scattering and Surface-Enhanced Infra-red Absorption. ACS Nano 2008 , 2, 707 718.

15. Nevet,A.; Berkovitch, N.;Hayat, A.;Ginzburg, P.;Ginzach,S.;Sorias, O.; Orenstein, M. Plasmonic Nanoantennas forBroad-Band Enhancement of Two-Photon Emission fromSemiconductors. Nano Lett. 2010 , 10, 1848 1852.

16. Ko, K.D.; Kumar,A.; Fung, K.H.; Ambekar,R.; Liu,G. L.; Fang,N. X.; Toussaint, K. C., Jr. Nonlinear Optical Response fromArrays of Au Bowtie Nanoantennas. Nano Lett. 2011 , 11,61 65.

17. Chen, P.-Y.; Al, A. Subwavelength Imaging Using Phase-Conjugating Nonlinear Nanoantenna Arrays. Nano Lett.2011 , 11, 5514 5518.

18. Zuloaga, J.; Prodan, E.; Nordlander, P. Quantum Plasmon-ics:Optical Properties andTunabilityof Metallic Nanorods. ACS Nano 2010 , 4, 5269 5276.

19. Fromm, D. P.; Sundaramurthy, A.; Schuck, P. J.; Kino, G.;Moerne, W. E. Gap-Dependent Optical Coupling of Single Bowtie Nanoantennas Resonant in theVisible. Nano Lett.2004 , 4, 957 961.

20. Volpe, G.; Volpe, G; Quidant, R. Fractal Plasmonics: Sub-diff raction Focusing and Broadband Spectral Response bya SierpinskiNanocarpet. Opt.Express 2011 ,19, 3612 3618.

21. Unl, E. S.; Tok, R. U.; S- endur, K. Broadband PlasmonicNanoantenna with an Adjustable Spectral Response. Opt.Express 2011 , 19, 1000 1006.

22. Tok, R. U.; Ow-Yang, C.; S- endur, K. Unidirectional Broad-band Radiation of Honeycomb Plasmonic Antenna Arraywith Broken Symmetry. Opt. Express 2011 , 19, 2273122742.

23. Miroshnichenko, A. E.; Maksymov, I. S.; Davoyan, A. R.;Simovski, C.; Belov, P.; Kivshar, Y. S. An Arrayed Nanoan-tenna for Broadband Light Emission and Detection. Phys.Status Solidi RRL 2011 , 5, 347 349.

24. Boriskina, S. V.; Dal Negro, L. Multiple-Wavelength Plas-monic Nanoantennas. Opt. Lett. 2010 , 35, 538 540.

25. Collin, R. E.; Zucker, F. J. Antenna Theory ; McGraw-Hill: NewYork, 1969.

26. CST Microwave Studio, http://www.cst.com.27. Johnson, P.B.; Christy, R.W. Optical Constantsof theNoble

Metals. Phys. Rev. B 1972

, 6, 4370

4379.28. DuHamel, R. H.; Isbell, D. E. Broadband LogarithmicallyPeriodic Antenna Structures. IRE Int. Conv. Rec. 1957 , 5,119 128.

29. Aubry,A.;Lei,D.-Y.;Fernndez-Domnguez,A. I.;Sonnfraud, Y;Maier, S. A.; Pendry, J. B. PlasmonicLight-HarverstingDevicesover the Whole Visible Spectrum. Nano Lett. 2010 , 10 ,2574 2579.

30. Fernndez-Domnguez, A. I.; Maier, S. A.; Pendry, J. B.Collection and Concentration of Light by TouchingSpheres: A Transformation Optics Approach. Phys. Rev.Lett. 2010 , 105, 266807.

31. Luo, Yu; Pendry, J. B.; Aubry, A. Surface Plasmons andSingularities. Nano Lett. 2010 , 10, 4186 4191.

32. Maier, S. A. Plasmonics: Fundamentals and Applications ;Springer: New York, 2007.

33. Zakery, A.; Elliott, S. R. Optical Nonlinearities in Chalcogen-ide Glasses and Their Applications ; Springer: Berlin, 2007.

34. Kim, S.; Jin, J.; Kim, Y.-J.; Park, I.-Y.; Kim, Y.; Kim, S. W. High-Harmonic Generation by Resonant Plasmon Field En-hancement. Nature 2008 , 453, 757 760.

35. Chettiar, U. K.; Engheta, N. Pairs of Optical Nanoantennasfor Enhancing Second-Harmonic Generation. In Frontiersin Optics, OSA Technical Digest CD; Optical Society of America, 2010; paper FThR5.

36. Lumerical http://www.lumerical.com.

A R T I C L E

Documents

Broadband Antenna Sacs Nano