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Nanofocusing radially-polarized beams for high-throughput funneling of optical energy to the near fi

Nanofocusing radially-polarized beams

for high-throughput funneling of optical

energy to the near?eld

Xue-Wen Chen,Vahid Sandoghdar,and Mario Agio?

Laboratory of Physical Chemistry,ETH Zurich,8093Zurich,Switzerland

*mario.agio@phys.chem.ethz.ch

Abstract:We theoretically show that a weakly-focused radially polar-

ized beam can excite surface-plasmon-polaritons in metal nanowires and

nanocones with ef?ciencies of the order of90%and large bandwidths.

The coupling mechanism relies on the formation of a standing wave on

the nanowire facet,which imposes a relationship between the operating

wavelength and the nanowire radius.An immediate application of this

?nding is nanofocusing of optical energy for implementations of ultra-fast

and high-throughput linear and nonlinear nanoscopies,optical nanolithogra-

phies,quantum nano-optics and photochemistry at the nanoscale.

?2010Optical Society of America

OCIS codes:(250.5403)Plasmonics;(260.6042)Singular optics;(180.4243)Near-?eld mi-

croscopy;(240.6695)Surface-enhanced Raman scattering;(320.7110)Ultrafast nonlinear op-

tics;(210.4245)Near-?eld optical recording.

References and links

1.L.Novotny,D.W.Pohl,and B.Hecht,“Scanning near-?eld optical probe with ultrasmall spot size,”Opt.Lett.

20,970–972(1995).

2.T.Kalkbrenner,M.Ramstein,J.Mlynek,and V.Sandoghdar,“A single gold particle as a probe for apertureless

scanning near-?eld optical microscopy,”J.Microsc.202,72–76(2001).

3.J.N.Farahani,D.W.Pohl,H.-J.Eisler,and B.Hecht,“Single quantum dot coupled to a scanning optical antenna:

A tunable superemitter,”Phys.Rev.Lett.95,017402(2005).

4.T.H.Taminiau,F.D.Stefani,and N.F.van Hulst,“Single emitters coupled to plasmonic nano-antennas:angular

emission and collection ef?ciency,”New J.Phys.10,105005(2008).

5. F.Keilmann,“Surface-polariton propagation for scanning near-?eld optical microscopy application,”J.Mi-

croscopy194,567–570(1999).

6. A.J.Babadjanyan,N.L.Margaryan,and K.V.Nerkararyan,“Superfocusing of surface polaritons in the conical

structure,”J.Appl.Phys.87,3785–3788(2000).

7.M.I.Stockman,“Nanofocusing of optical energy in tapered plasmonic waveguides,”Phys.Rev.Lett.93,137404

(2004).

8. E.J.S′a nchez,L.Novotny,and X.S.Xie,“Near-?eld?uorescence microscopy based on two-photon excitation

with metal tips,”Phys.Rev.Lett.82,4014–4017(1999).

9.T.Ichimura,N.Hayazawa,M.Hashimoto,Y.Inouye,and S.Kawata,“Tip-enhanced coherent anti-stokes raman

scattering for vibrational nanoimaging,”Phys.Rev.Lett.92,220801(2004).

10. A.Hartschuh,“Tip-enhanced near-?eld optical microscopy,”Angew.Chem.Int.Ed.47,8178–8191(2008).

11.S.Mackowski,S.W¨o rmke,A.J.Maier,T.H.P.Brotosudarmo,H.Harutyunyan,A.Hartschuh,https://www.wendangku.net/doc/9110787295.html,orov,

H.Scheer,and C.Br¨a uchle,“Metal-enhanced?uorescence of chlorophylls in single light-harvesting complexes,”

Nano Lett.8,558–564(2008).

12. D.E.Chang,A.S.S?rensen,P.R.Hemmer,and M.D.Lukin,“Quantum optics with surface plasmons,”Phys.

Rev.Lett.97,053002(2006).

13.G.Wysocki,J.Heitz,and D.B¨a uerle,“Near-?eld optical nanopatterning of crystalline silicon,”Appl.Phys.Lett.

84,2025–2027(2004).

14.X.-W.Chen,V.Sandoghdar,and M.Agio,“Highly ef?cient interfacing of guided plasmons and photons in

nanowires,”Nano Lett.9,3756–3761(2009).

15.M.Celebrano,P.Biagioni,M.Zavelani-Rossi,D.Polli,https://www.wendangku.net/doc/9110787295.html,bardi,M.Allegrini,M.Finazzi,L.Du`o,and

G.Cerullo,“Hollow-pyramid based scanning near-?eld optical microscope coupled to femtosecond pulses:A

tool for nonlinear optics at the nanoscale,”Rev.Sci.Instr.80,033704(2009).

16.R.Eckert,J.M.Freyland,H.Gersen,H.Heinzelmann,G.Sch¨u rmann,W.Noell,U.Staufer,and N.F.de Rooij,

“Near-?eld?uorescence imaging with32nm resolution based on microfabricated cantilevered probes,”Appl.

Phys.Lett.77,3695–3697(2000).

17.K.Tanaka,G.Burr,T.Grosjean,T.Maletzky,and U.Fischer,“Superfocussing in a metal-coated tetrahedral tip

by dimensional reduction of surface-to edge-plasmon modes,”Appl.Phys.B93,257–266(2008).

18. E.G.Bortchagovsky,S.Klein,and U.C.Fischer,“Surface plasmon mediated tip enhanced raman scattering,”

Appl.Phys.Lett.94,063118(2009).

19. A.Dechant,S.K.Dew,S.E.Irvine,and A.Y.Elezzabi,“High-transmission solid-immersion apertured optical

probes for near-?eld scanning optical microscopy,”Appl.Phys.Lett.86,013102(2005).

20. C.Ropers,C.C.Neacsu,T.Elsaesser,M.Albrecht,M.B.Raschke,and C.Lienau,“Grating-coupling of surface

plasmons onto metallic tips;a nanocon?ned light source,”Nano Lett.7,2784–2788(2007).

21. F.De Angelis,M.Patrini,G.Das,I.Maksymov,M.Galli,L.Businaro,L.C.Andreani,and E.Di Fabrizio,“A

hybrid plasmonic-photonic nanodevice for label-free detection of a few molecules,”Nano Lett.8,2321–2327 (2008).

22.S.Quabis,R.Dorn,M.Eberler,O.Gl¨o ckl,and G.Leuchs,“The focus of light theoretical calculation and

experimental tomographic reconstruction,”Appl.Phys.B72,109–113(2001).

23. E.Descrovi,L.Vaccaro,L.Aeschimann,W.Nakagawa,U.Staufer,and H.-P.Herzig,“Optical properties of

microfabricated fully-metal-coated near-?eld probes in collection mode,”J.Opt.Soc.Am.A22,1432–1441 (2005).

24.M.Fleischer,C.Stanciu,F.Stade,J.Stadler,K.Braun,A.Heeren,M.H¨a ffner,D.P.Kern,and A.J.Meixner,

“Three-dimensional optical antennas:Nanocones in an apertureless scanning near-?eld microscope,”Appl.Phys.

Lett.93,111114(2008).

25.T.J.Antosiewicz,P.Wr′o bel,and T.Szoplik,“Nanofocusing of radially polarized light with dielectric-metal-

dielectric probe,”Opt.Express17,9191–9196(2009).

26. F.I.Baida and A.Belkhir,“Superfocusing and light con?nement by surface plasmon excitation through radially

polarized beam,”Plasmonics4,51–59(2009).

27.M.Agio,X.-W.Chen,and V.Sandoghdar,“Nanofocusing radially-polarized beams for high-throughput funnel-

ing of optical energy,”(2010),US Patent Pending.

28.N.A.Issa and R.Guckenberger,“Optical nanofocusing on tapered metallic waveguides,”Plasmonics2,31–37

(2007).

29.M.W.V ogel and D.K.Gramotnev,“Adiabatic nano-focusing of plasmons by metallic tapered rods in the presence

of dissipation,”Phys.Lett.A363,507–511(2007).

30. A.V.Goncharenko,M.M.Dvoynenko,H.-C.Chang,and J.-K.Wang,“Electric?eld enhancement by a

nanometer-scaled conical metal tip in the context of scattering-type near-?eld optical microscopy,”Appl.Phys.

Lett.88,104101(2006).

31. A.V.Goncharenko,J.-K.Wang,and Y.-C.Chang,“Electric near-?eld enhancement of a sharp semi-in?nite

conical probe:Material and cone angle dependence,”Phys.Rev.B74,235442(2006).

32. A.Goncharenko,H.-C.Chang,and J.-K.Wang,“Electric near-?eld enhancing properties of a?nite-size metal

conical nano-tip,”Ultramicroscopy107,151–157(2007).

33.Z.Li,F.Hao,Y.Huang,Y.Fang,P.Nordlander,and H.Xu,“Directional light emission from propagating surface

plasmons of silver nanowires,”Nano Lett.9,4383–4386(2009).

34.R.Gordon,“Re?ection of cylindrical surface waves,”Opt.Express17,18621–18629(2009).

35. D.R.Lide,ed.,CRC Handbook of Chemistry and Physics(CRC Press,Boca Raton,FL,2006),87th ed.

36. B.Richards and E.Wolf,“Electromagnetic diffraction in optical systems.ii.structure of the image?eld in an

aplanatic system,”Proc.R.Soc.A253,358–379(1959).

37.N.M.Mojarad and M.Agio,“Tailoring the excitation of localized surface plasmon-polariton resonances by

focusing radially-polarized beams,”Opt.Express17,117–122(2009).

38.H.Ling and S.-W.Lee,“Focusing of electromagnetic waves through a dielectric interface,”J.Opt.Soc.Am.A

1,965–973(1984).

39.I.M.Bassett,“Limit to concentration by focusing,”J.Mod.Opt.33,279–286(1986).

40. E.Verhagen,M.Spasenovi′c,A.Polman,and L.Kuipers,“Nanowire plasmon excitation by adiabatic mode

transformation,”Phys.Rev.Lett.102,203904(2009).

41. F.De Angelis,G.Das,P.Candeloro,M.Patrini,M.Galli,A.Bek,https://www.wendangku.net/doc/9110787295.html,zzarino,I.Maksymov,C.Liberale,L.C.

Andreani,and E.Di Fabrizio,“Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,”Nat.Nano.5,67–72(2010).

42.M.Zavelani-Rossi,M.Celebrano,P.Biagioni,D.Polli,M.Finazzi,L.Du`o,G.Cerullo,https://www.wendangku.net/doc/9110787295.html,bardi,M.Allegrini,

J.Grand,and P.-M.Adam,“Near-?eld second-harmonic generation in single gold nanoparticles,”Appl.Phys. #123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010 (C) 2010 OSA10 May 2010 / Vol. 18, No. 10 / OPTICS EXPRESS 10879

Lett.92,093119(2008).

43. A.Ta?ove and S.C.Hagness,Computational Electrodynamics:The Finite-Difference Time-Domain Method

(Artech House,Norwood,MA,2005),3rd ed.

44.J.D.Jackson,Classical Electrodynamics(John Wiley&Sons,New York,1999),3rd ed.

1.Introduction

Since its birth in the mid-1980s,scanning near-?eld optical microscopy(SNOM)has suffered from the small fraction of optical energy that can be concentrated near the tip apex.For high-resolution probes,this factor is at most of the order of10?3but usually much less,depending on the probe parameters[1].Optical antennas can perform better,but their implementation in a scanning device is still restricted by dif?culties associated with the high-throughput fabrication or attachment of a well-de?ned metal nanoparticle to the end of a tapered?ber[2,3].Further-more,these probes exhibit a nearly-dipolar radiation pattern,which requires high numerical-aperture(NA)optics to obtain large coupling ef?ciencies[4].

An emerging approach to concentrate light into a subwavelength spot size relies on the so-called nanofocusing of surface plasmon-polaritons(SPPs)[5–7].Nanofocusing could in-deed revolutionize SNOM by largely improving?uorescence,Raman and other nonlinear nanoscopies[8–10].Furthermore,the possibility of feeding optical energy into a nanoscale volume has also immediate implications for photochemistry[11],quantum optics[12]and nanolithography[13].However,practical exploitations of this concept require a rapid and ef-fective conversion of SPPs into photons,especially in the visible and UV spectral range,where absorption losses by real metals lead to very small propagation lengths.

We recently demonstrated that guided photons of a dielectric nano?ber are converted into SPPs in metal nanowires(NWs)and vice versa with close to100%ef?ciency.Based on these ?ndings,we suggested that a high-throughput SNOM could be realized by butt-coupling a metal cone with a tapered?ber[14].Since SNOMs based on cantilevers are gaining interest due to their reliability and performances[15],it is relevant to know whether SPPs in metal nanocones attached to cantilevers can be ef?ciently excited by focused beams.

Several designs of cantilever-based SNOMs are found in the literature.For example,a Gaus-sian beam focused into an aperture SNOM[16]or a fully metal coated dielectric tip[17,18], and an aperture probe combined with a microsphere[19].Other schemes used a grating etched on the side of the nanocone[20]or a photonic-crystal cavity[21]to improve the cou-pling ef?ciency.On the other hand,the polarization and pro?le of TM0SPPs suggest that a promising candidate for their ef?cient excitation in a nanofocusing device could be a focused radially-polarized beam(FRB)[22].Indeed,radially-polarized light has already been applied to nanocones[23–26],but the conversion ef?ciency of photons into SPPs did not exhibit a large improvement in comparison to the other arrangements.Furthermore,when light is focused on to the tip apex it gives rise to a strong background illumination.

Here,we show that the conversion mechanism of our?ber-based high-throughput SNOM, namely the molding of SPPs at the cone base[14],holds also for free-space coupling.When a weakly-focused radially-polarized beam is incident on the nanocone base,the conversion of photons into SPPs can reach90%ef?ciency.Moreover,since the tip apex is out of focus, background noise due to direct illumination is further suppressed[27].

2.Results and Discussion

The primary processes that we need to consider in a high-throughput SNOM are nanofocusing of SPPs and conversion of SPPs into photons.Since there exists much literature on nanofocus-ing[5–7,28–32],we direct our attention only to the coupling between photons and SPPs in the collection and illumination modes.To this end,in Sec.2.1we?rst analyze the re?ection and #123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010 (C) 2010 OSA10 May 2010 / Vol. 18, No. 10 / OPTICS EXPRESS 10880

scattering of SPPs at the end of a metal NW [33,34]in the presence of a semi-in?nite dielectric that accounts for the cantilever.In Sec.2.2,we consider the far-?eld pattern and compare it to the ?eld pro?le of FRBs.In Sec.2.3,we study the conversion of photons into SPPs by illumi-nating the NW end with FRBs.Finally,in Sec.2.4we combine our ?ndings with nanofocusing to assess ?eld enhancement and spatial resolution.

2.1.Re?ection and Directional Emission

We ?rst considered the re?ection and radiation properties of TM 0SPPs when they reach the end of a semi-in?nite metal NW.In contrary to butt-coupling with a dielectric nano?ber [14]and free-space coupling [33,34],here we placed a semi-in?nite dielectric at the NW termination.Besides holding the NW,the substrate changes re?ection and radiation of SPPs.Figure 1(a)sketches the situation for a gold [35]NW on a glass substrate (refractive index n =1.5)together with the simulation layout.Our calculations were carried out using the body-of-revolution (BOR)?nite-difference time-domain (FDTD)method,whose details and advantages are brie?y explained in the Appendix.Throughout this work we chose a working wavelength of λ=633nm,keeping in mind that these results are generally valid over a broad spectral range if the NW radius (r )is properly scaled [14,34].0100200300400

500Nanowire Radius (nm)010********R e f l e c t i o n (%)Au - n =1.5Au - n =2.0Ag - n

=1.5

Nanowire Semi-infinite Substrate PML Source

Air

ρ20060010001400180022002006001000

1400

200600

1000

1400

z (nm)

ρ (n m )20060010001400180022002006001000

1400

200

600

10001400

z (nm)ρ (n m )(a)(b)(c)(d)

Fig.1.(a)Layout of a semi-in?nite gold NW in air on a glass substrate.The dashed lines

delimit the computational domain of BOR-FDTD.(b)Re?ection as a function of the NW

radius for different metals and substrates.(c)and (d)Time-averaged magnetic ?eld for a

gold NW on glass (n =1.5)with r =160nm and r =340nm,respectively.In (b)–(d)the

vacuum wavelength is 633nm.In (a),(c)and (d)the solid red lines indicate the source

position.

#123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010

A TM 0SPP is launched on the gold NW and when it reaches the NW end it can be re?ected into the same SPP mode,into free space,and scattered in the forward direction.Figure 1(b)displays the amount of re?ection back into the SPP as a function of the NW radius for different metals and substrates,showing that it is minimized for some values of r .Figures 1(c)and 1(d)plot the time-averaged magnetic ?eld at two re?ection minima corresponding to a gold NW on glass with respectively r =160nm and r =340nm.It turns out that the NW facet supports a standing wave [14],which leads to a directional radiation pattern with a pro?le determined by the ?eld near the NW facet.There is no radiated power along the z -axis,a result that simply stems from the spatial symmetry and polarization of TM 0SPPs.Figure 1(b)also shows that when gold NWs are replaced by silver [35]NWs re?ection and emission are almost the same.We then investigated the effect of changing the dielectric substrate.For example,when the refractive index is set to n =2,re?ections increase and the minima shift towards shorter NW radii.This is a further indication that the standing wave on the NW facet plays an important role in lowering re?ection,as we found for the case of butt-coupling with a dielectric nano?ber [14].We have also considered the amount of re?ection that is not channeled into SPPs and found that it can be negligible.

In summary,when SPPs reach the NW end they radiate in the forward direction with a very high ef?ciency if,for a given wavelength,the NW radius is appropriately chosen.Furthermore,the radius can be reduced by increasing the refractive index of the supporting substrate,but at the cost of increasing re?ection.

2.2.Optimizing the Beam Parameters

Here we are interested in the conversion of focused beams into SPPs of metal NWs.Reci-procity tells us that if the out-coupling ef?ciency is high,the same holds for the opposite di-rection.However,one has to clarify what beam pro?le should be used to perform this task.We thus considered the near ?eld obtained from the BOR-FDTD calculations and transformed it to the far ?eld using an algorithm described in the Appendix.In the far region the ?eld is a spherical transverse wave polarized along θsince the ?component must be zero by symmetry considerations.

In the spherical coordinates (r,θ,?)we de?ne a Gaussian reference sphere (GRS)to inter-face the NW with the optical focusing system,as sketched in Fig.2(a).The polarization and spatial properties of the electric ?eld on the GRS suggest that a good candidate for coupling optical energy in the NW would be a radially-polarized beam [22].Its electric-?eld pro?le at the beam waist reads

E (ρ)=?ρ

E o exp (?ρ2/(2w 2))ρ/w ,(1)where E o is the ?eld amplitude,w the beam waist,ρthe radial coordinate,and ?ρ

its unit vector.Fig.2(a)depicts how this enters the optical system to reach the GRS with a transformed ?eld E (a ,θ)=E o exp (?a 2sin 2θ/2)a sin θ√cos θ?θ,(2)where a =f /w ,?θ

is the unit vector,and √cos θis the apodization function for an aplanatic system [36].f is the lens focal length,which corresponds to the radius of the GRS,and w is the beam waist.The idea is to optimize the beam parameter a such that the FRB matches the SPPs radiation pattern,whose far ?eld is given by Eq.(4)in the Appendix.

Figures 2(b)–2(e)illustrate the calculated far ?eld for different NWs and substrates at λ=633nm.In Fig.2(b)the ?eld of a gold NW on glass is maximum at about θ=18o when r =160nm,showing that the FRB does not need to be tightly focused.Indeed,good overlap between the two ?elds is empirically obtained by setting a =3.1,a value that leads to moderate focusing even with high-NA lenses [22].Interestingly,the radiation pattern does not depend very much on the refractive index of the substrate if one tunes the NW radius to minimize re?ections,as #123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010

02040

60800.00.2

0.40.6

θ (deg)E (a .u .)Au - r =340nm

a =4.8 - n =1.5020406080

θ (deg)Ag - r =160nm a =3.6 - n =1.5Au - r =110nm a =3.1 - n =2.00.0

0.2

0.4

0.6

E (a .u .)Au - r =160nm

a =3.1 - n =1.5FRB NW (b)(c)

(d)

(e)

z θα

w lens

(a)

RB GRS

reference

plane

Fig.2.(a)Matching the NW radiation pattern with a FRB.A radially-polarized beam (RB)

is focused by an aplanatic lens onto the NW.The ?lled red curves sketch the intensity

pro?le of a RB and the reference plane represents the integration domain used for the near-

to-far-?eld transformation of the ?eld radiated by the SPPs.(b)–(e)The electric ?eld E of

the FRB on the Gaussian reference sphere (GRS)can match that radiated from the NW if

the RB is adjusted by varying a =f /w ,where f is the lens focal length and w is the beam

waist.E of the FRB (black solid curves)and the NW (red dots)on the GRS are displayed

for different parameters.The vacuum wavelength is λ=633nm,f =1.8mm and α=90o .

evident in the comparison of Fig.2(b)with Fig.2(c).An intuitive explanation is found if the NW is considered as an aperture of radius r .A larger n increases the wavevector in the forward

direction k z = (2π/λ)2n 2?k 2ρ

,but a smaller aperture increases the span of the transverse wavevector k ρ∈[0,2π/r ].These effects compensate each others and lead to a small change in the radiation pattern.

As shown in Fig.2(d),more directionality can be obtained by working with higher-order standing waves [see Fig.1(d)].The peak of the radiation pattern is now close to θ=12o ,and its width is signi?cantly narrower.However,besides the existence of wide secondary lobe,the main drawback is the larger NW radius,which for the same tapering angle implies a longer path for nanofocusing.Thus,higher-order patterns are interesting only for applications in a spectral range where propagation lengths are much greater than the nanocone dimensions [29].

As one last representative case,Fig.2(e)displays the SPPs radiation pattern for a silver NW on glass for r =160nm.The curve is very close to that of Fig.2(b),as expected if one notes that the re?ection minima in Fig.1(b)occur for nearly the same NW radii.Therefore,the advantage of using silver in place of gold NWs is only in the longer propagation length of SPPs due to #123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010

lower absorption losses [35].While in Fig.2(b)the beam parameter a is set to overlap the NW and the FRB electric ?elds for both small and large angles,in Fig.2(e)the optimization targets only small angles.In the next section we will investigate how this affects the excitation of SPP in the NW.

2.3.Ef?cient Excitation of SPP in Nanowires

Having found that a FRB can match the radiation pattern of SPPs in semi-in?nite metal NWs,we assessed the coupling ef?ciency in a more quantitative manner.To this end,we computed the electromagnetic ?eld of a FRB in the focal region [37]and used it as a source for the BOR-FDTD simulations.

Figure 3(a)shows the time-averaged magnetic ?eld of a FRB in an in?nite glass background for a =3.1and full NA=n sin α,with α=90o .Next,we performed BOR-FDTD simulations for gold and silver NWs on glass,varying a and the position of the focal spot with respect to the NW facet.The conversion ef?ciency was calculated by taking the ratio of the power coupled in the TM 0SPP and the power in the incident FRB.Selected data are shown in Fig.3(b).For both gold and silver NWs the ef?ciency is about 90%if the NW end is close to the focal spot and it remains larger than 60%even 400nm away from the optimal position.The maximum does not occur exactly when the NW facet is in focus because the glass-air interface changes the properties of a focused beam [38].Figure 3(c)con?rms that NW radius and operating wavelength are not independent from each others since the coupling ef?ciency drops when the r departs from the value that minimizes re?ections [see Fig.1(b)].

20060010001400

20060010001400ρ (n m )z (nm)200600

10001400-500-10030070020060010001400ρ (n m )z (nm)

Nanowire Position Relative to Focus (nm)C o u p l i n g E f f i c i e n c y (%)

(d)Radius (nm)C o u p l i n g E f f i c i e n c y (%)(a)Fig.3.(a)Time-averaged magnetic ?eld for a FRB in an in?nite glass background (a =3.1,

n =1.5).(b)Coupling ef?ciency as a function of the NW position with respect to the focal

spot.(c)Coupling ef?ciency as a function of the NW radius,when the NW position is 100

nm.(d)BOR-FDTD simulation for a FRB incident on a gold NW on glass with r =160

nm.The beam parameter is a =3.1and the focal spot is 100nm before the NW facet.The

white lines sketch the position of the substrate and the NW for the coupling problem.In (a)

and (d)the z coordinate is with respect to the focal spot and the vertical red lines indicate

the source position.

Figure 3(b)shows that choosing a =3.6yields similar performances to the case for a =3.1,suggesting that the FRB should be foremost optimized in the peak region.Therefore,lenses with a lower NA should not affect these results.For example,in Fig.2(d)the ?eld amplitude of #123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010

the FRB at θ=45o is about 10%of the maximum (1%for the intensity),meaning that an NA of 0.7in air would be enough to couple most of the beam energy into the SPP.

To give more insight on the conversion process,Fig.3(d)displays the time-averaged mag-netic ?eld for the case of a FRB impinging on a gold NW on glass when r =160nm,a =3.1,and the focal spot is 100nm before the NW end facet.The beam is partially re?ected,but the color scale shows that most of the energy is coupled into the SPP mode.Moreover,the ?eld pattern con?rms that the excitation of a standing wave on the NW facet plays a very important role in the conversion of photons into SPPs.

2.4.Nanofocusing and Spatial Resolution

The ef?cient excitation of SPPs in NWs can be immediately transferred to nanocones,pro-vided that the tapering angle of the nanocone is not large (adiabatic focusing)[5–7].Figure 4(a)sketches a possible implementation of a cantilever-based high-throughput SNOM.The radially-polarized beam is focused by a lens onto the nanocone base.The dielectric interface between the lens and the cantilever has a small effect on the beam pro?le,which if necessary can be compensated by placing a solid-immersion lens.The energy is then converted into TM 0SPPs and nanofocused.Since the tip apex is out of focus,the direct light of the FRB is almost negli-gible in the scanning region [27].The device can also be operated in the collection mode,where SPPs generated by a local source near the nanocone tip propagate along the nanocone and radi-ate with a directional pattern towards the collection optics.The weak resonant character of the standing wave adds the important advantage of large operation bandwidths,which were found also for the case of butt-coupling with a nano?ber [14].For example,the minima in Fig.1(b)and,likewise,the peak in Fig.3(c)have a width that is suf?cient for collecting and launching fs pulses in the

device.RB Objective Cantilever

Nanocone Sample (a)(b)-1000

-50005001000Lateral Position (nm)200

4006008001000N o r m a l i z e d E n e r g y D e n s i t y z =1115 nm (cone)z =1100 nm z =400 nm z =20 nm x 2000-30-20-100102030Lateral Position (nm)200

4006008001000N o r m a l i z e d E n e r g y D e n s i t y W W Ez W E ρ

(c)Fig.4.(a)Scheme of a cantilever-based high-throughput SNOM.(b)Normalized energy

density W in a plane located at z =1115nm from the cantilever when a gold cone is

illuminated by a FRB under the same conditions of Fig.3(d)(see text for details).The

plane is 5nm from the cone tip.The graph shows also W for various z when the cone is

not present.(c)Zoom of (b)for the case where a gold cone is present.The contributions

to W due to the two electric ?eld components E z and E ρare indicated as W Ez and W E ρ,

respectively.

#123440 - $15.00 USD Received 28 Jan 2010; revised 29 Mar 2010; accepted 12 Apr 2010; published 10 May 2010

Since the propagation properties of SPPs on metal nanocones have been thoroughly discussed

in the literature[5–7,28–32],here we only emphasize the?eld enhancement and the spatial

resolution of the SNOM device.To this purpose we consider the normalized energy density

W=0.5(ε|E|2+μ|H|2)/W BL,where W BL=P inc k2/(3πc)is the maximum achievable by far-?eld focusing for a given incident power P inc and wavevector k[39].Since in our model the

FRB is propagating from a glass substrate,we set W BL for a homogeneous medium with a

refractive index equal to1.5.

We then chose a gold nanocone with a base radius of160nm and a tapering angle of8o

illuminated by a FRB with a=3.1.The tip apex was a paraboloid(z=ρ2/(3.2nm))and the cantilever was modeled as a semi-in?nite glass substrate.Figure4(b)plots W at a distance z=1115nm from the cantilever,which corresponds to a plane5nm away from the cone tip.A zoom of W is shown in Fig.4(c),where the contributions associated with the longitudinal(E z) and transverse(Eρ)electric?eld components are also indicated.The FWHM for W is of the order of10nm and it is primarily due to E z.The maximum value of W reveals that for the same P inc the nanocone allows energy concentrations that are nearly1000times larger than what can be achieved by far-?eld focusing.Furthermore,the total energy at the observation plane is about65%of that near the focus of the FRB,proving that a large fraction of optical energy can be transported to the nanoscale.Recent experiments on SPP excitation in NWs by adiabatic compressors have indeed found similar ef?ciencies in the near-infrared spectral range[40].

At last it is interesting to note how the features of a FRB can be exploited to minimize

background illumination.To this aim,Fig.4(b)displays the W obtained without gold cone at

different distances from the cantilever and for the same incident FRB.We found that the W of

the FRB near the cone tip(z=1100nm)is more than two orders of magnitude smaller than

the W in the focal region(z=20nm).This corresponds to a strong background suppression

compared to illuminations where the incident beam is focused on the cone tip.

3.Conclusions

We demonstrated an ef?cient scheme for converting free-space photons into SPPs in NWs,and

combined it with nanofocusing to concentrate optical energy below the diffraction limit with

a high throughput.Our approach relies on the directional radiation and low re?ection of SPPs

at the NW end,which occur if the NW radius is chosen according to the operation wavelength

and the supporting substrate.These properties are associated with the formation of a standing

wave at the NW facet,as previously found for the case of butt-coupling with a nano?ber[14].

Furthermore,by analyzing the radiation pattern and polarization in the far region we identi?ed

weakly-focused radially-polarized beams as the best way to excite SPPs from the NW facet.

We showed indeed that conversion ef?ciencies of90%can be reached by optimizing the beam

parameters and the position of the NW in the focal region.

In contrast to previous works on metal nanocones and radially-polarized light,which do not

focus the beam on the nanocone base[23–26],our scheme yields a better conversion ef?ciency

and lower background noise caused by direct illumination of the sample.These results were

presented forλ=633nm,but any wavelength from the UV to the near-IR range would work by adjusting the NW radius and composition[14].Moreover,in comparison to a?ber-based high-throughput SNOM[14],the conversion ef?ciency is only slightly lower and the device presented here is easier to implement with existing scanning-probe technology[41].

For the huge intensity that can be achieved at the nanocone tip and the large operation band-

width,we envision not only better implementations of?uorescence,Raman and other nonlinear

(time-resolved)nanoscopies[8–10],but also applications in all areas that would bene?t from

high-throughput concentration of optical energy in nanoscale spots and fs time scales[42].

A.Body-of-Revolution FDTD

The electromagnetic properties of a BOR are conveniently studied in cylindrical coordinates (ρ,φ,z).The general solution of Maxwell’s equations can be expanded into even and odd cylindrical modes with azimuthal dependence cos(mφ)and sin(mφ),respectively.Since the TM0SPP mode is even with m=0,the?eld takes the simple form

E(ρ,z)=Eρ(ρ,z)?ρ+E z(ρ,z)?z,H(ρ,z)=Hφ(ρ,z)?φ.(3) The same holds for the?eld radiated from the NW facet,because coupling to other modes is avoided by symmetry.These equations clearly show that the full electromagnetic problem can be solved by considering only two dimensions.We performed this task using the BOR-FDTD algorithm,where the Maxwell curl equations in cylindrical coordinates are discretized in theρz-plane[43].By this method we could use very?ne meshes without compromising computational speed and memory usage.Furthermore,the implementation of cylindrical symmetry increases the accuracy in comparison with a full three-dimensional FDTD approach that has the same mesh pitch.

The simulation domain was truncated using perfectly matched layers(PML).Either the SPP or the FRB?elds were launched using a line source with amplitude and phase given by the in-cident?eld at that location.This is indicated in Figs.1(a)–1(d),3(a)and3(d)by a red line.The dispersive dielectric function of silver or gold was included by?tting the tabulated values[35] with a Drude dispersion model around the working wavelength.Re?ection and coupling ef?-ciency were obtained by projecting the?eld on the SPP mode,as described in Ref.[14].The FDTD mesh was set to1nm for the NW and0.5nm for the nanocone studies.

B.Near-to-Far-Field Transformation

The near-to-far?eld transformation was performed starting from the electromagnetic?eld ob-tained by BOR-FDTD calculations.On the reference plane shown in Fig.2(a),one de?nes equivalent electric and magnetic surface current densities,which respectively are J s=??n×E and M s=?n×H,where?n is the unit vector normal to the surface.Each current element radiates

to the far?eld as a dipolar source.By integrating the contribution of these elements over that plane,one obtains the electromagnetic?eld in the far region[43].Symmetry considerations imply that on the GRS the electric?eld has only theθcomponent in spherical coordinates(r,θ,?),which reads

E(r,θ)=?ke?ikr

e ikz o cosθ

max

dρρJ1(kρsinθ)

Eρ(ρ,z o)+ZHφ(ρ,z o)cosθ

?θ.(4)

J1is the Bessel function of the?rst kind[44],z o is where the reference plane intercepts the z-axis,Z is the medium impedance and k is the wavevector.ρmax should be large enough to make the contribution of the excluded?eld negligible.

Acknowledgments

We thank F.De Angelis,E.Di Fabrizio,M.Celebrano,K.-G.Lee and S.G¨o tzinger for helpful conversations.This work was supported by ETH Zurich grant TH-49/06-1.