Long-range surface-plasmon modes in silver and aluminum films.pdf

July 1983/Vol.8,No.7/OPTICS LETTERS 377Long-range surface-plasmon modes in silver and aluminum filmsJ.C.Quail,J.G.Rako,and H.J.SimonDepartment of Physics and Astronomy,The University of Toledo,Toledo,Ohio 43606Received April 4,1983We report the first observation to our knowledge of a sharp minimum in the attenuated total reflectivity of a thinmetal film between index-matching layers.The resonance is due to the excitation of the long-range surface-plas-mon mode on both sides of the thin metal films,as originally discussed by Sarid Phys.Rev.Lett.47,1927(1981).The angular widths of the observed resonance in silver and aluminum films are both reduced by over an order ofmagnitude relative to that associated with the Kretschmann excited mode.The recent prediction1of long-range surface-plasmonmodes on thin metal films has stimulated theoreticalinterest in this topic.2The applications to nonlinearoptics of the large field enhancement associated withthis new mode were recently discussed by several au-thors.3-5This new geometry consists of a metal filmwith a substrate on one side and a thin dielectric layer,index-matched to the substrate,on the other side.Light is coupled into the metal through the thin di-electric layer from a high-index prism.For appropriatemetal-film and dielectric-layer thicknesses,either Ottoor Kretschmann surface-plasmon modes may be excitedat one or the other of the two metal interfaces.As themetal-film thickness is decreased,however,the twomodes couple to form a symmetric and antisymmetric(in transverse electrical field distribution)pair,and theattenuated total reflection(ATR)as a function of in-cident angular dependence is expected to show twoseparate resonances.For an optimal choice of metalthickness and dielectric-layer thickness the angularwidth of the ATR resonance that is due to the sym-metric mode may be reduced by an order of magnitude.This results from the fact that this mode has a smallerfraction of its field inside the film than the normalsurface-plasmon mode and hence the absorption andangular width are sharply reduced.The coupling ofsymmetric and antisymmetric modes in layered mediahas been observed6;however,the sharp resonancesdiscussed here were not seen earlier because of the rel-atively thick(-500-A)metal films used.In this Letterwe present experimental results for sharp ATR reso-nances observed from thin metal-dielectric layers.The linear reflectance from multifilm layers in theATR regime is well known.7The reflectance of theprism-dielectric-metal film-substrate system,whichis shown in the inset in Fig.1,may be written as2=r12+R234exp(i2k2zd2)1+rl2R234exp(i2k2zd2)whereR234=r23+r34exp(i2k3zd3)1+r2 3r3 4exp(i2k3zd3)Here rij is the Fresnel reflection coefficient for p-pola-rized light and ki,is the normal component of the wavevector;they are given by=/Cos i-Sa co Cos Cos Qi+I-Ci Cos Oj(3)andhi,=(ci-El sin201)1/2.(4)The subscripts i,j=1-4 refer to the prism,the dielec-tric,the metal,and the substrate,respectively,whereqi and di are the dielectric constant and the thicknessof the appropriate medium.The angle of the wavevector in each medium is given by 0i,and w and c are theangular frequency of the incident wave and the speedof light,respectively.The resonances that are due toexcitation of the long-and short-range surface-plasmonmodes are associated with the poles of the reflectance.The angles of incidence for exciting the resonances maybe found by locating the poles in the complex planeformed by the real and the imaginary components of theincident tangential wave vector8;however,the directcalculation of the reflectance by the use of Eqs.(1)-(4)over an appropriate range of the angle of incidence isessential for comparing theory with experiment.Allthe theoretical curves displayed in Figs.1 and 2 werecalculated using SPEAKEASY program language.Aluminum and silver films were thermally evaporatedonto a fused-silica optical flat substrate.The filmthicknesses were measured with a Sloan 200 digitalthickness monitor and independently determined froma fit to the Kretschmann mode ATR of a co-evaporatedprism.A few drops of a Cargille Laboratory immersionliquid whose index of refraction,n2=1.4564,matchesthat of the fused silica,n4=1.4569,at the He-Newavelength to better than I part in 103 was placed ontop of the metal film.The sample was then mechani-cally clamped to one face of an equilateral high-index,n,=1.94325,SF-59 coupling prism.Adjustment of theclamping pressure permitted control and optimizationof the thickness of the liquid dielectric layer.The prismassembly was mounted on an NRC 470 precision rota-tion stage,which permitted incremental rotation steps0146-9592/83/070377-03$1.00/0 1983,Optical Society of America378 OPTICS LETTERS/Vol.8,No.7/July 19831.00.050 52 54 56ANGLE(a)1.00.50.050 52 54 56ANGLE(b)1.049.0 49.1 49.2 49.3ANGLE(c)Fig.1.Reflectance from multilayered system consisting ofSF-59 prism-index-matching liquid layer-metal film-index-matched fused-silica substrate versus interior angle ofincidence.The metal film is silver;d2 is the thickness of theliquid layer,and d3 is the thickness of the metal film.(a)Kretschmann mode,d2=100 A and d 3=605 A;lb)coupledsymmetric and antisymmetric modes,d2=5000 and d,=505 A;(c)long-range surface-plasnion mode,d2=12 000 Aand d 3=170 A.Note change in angular scale.ANGLEFig.2.Same configuration as given in Fig.1 but with analuminum metal film.Long-range surface-plasmon mode,d2=8600 A and d3=145 A.Note angular scale.of less than 0.02.A p-polarized He-Ne beam was in-cident upon the prism in the vicinity of the angle fortotal internal reflection,and the reflected beam wasobserved either directly on a screen or with a photo-electric detector.The thickness of the liquid layer is the most criticalexperimental parameter for any given metal film.Thisthickness can be controlled by observing the ATR atangles less than the critical angle.In this angular regionthe dielectric and metal-film layers form a Fabry-Perotinterferometer with the fringe spacing determined bythe thickness of the liquid layer.For too thick a liquidlayer multiple ATR resonances are observed,whereasfor too thin a layer only a broad ATR feature is ob-served.The reflectance as calculated from Eqs.(1)-(4)can be used as a guide to predict the desired ATRstructure in this regime.Either by adjusting theclamping pressure or by translating the beamtransversely across the prism face,the experimentalreflectivity that best matches the calculated interfero-metric reflectance may be found.Thus the optimalliquid-layer thickness for observation of the long-rangesurface-plasmon mode is determined.Typical results for three ATR experiments performedin silver films,9E3=-18+iO.47,with varying thick-nesses of metal and liquid layers are shown in Fig.1.The experimental points are normalized to the theo-retical reflectance off resonance,and the angular scaleis the internal angle of incidence.For the first case,shown in Fig.1(a),the silver film is relatively thick,d3=505 A,and the prism is tightly clamped so that theliquid-layer thickness,d2=100 A,is effectively zero.This configuration corresponds to the standardKretschmann excitation10of the surface plasmon on themetal-dielectric substrate interface and is displayed forcomparison purposes only.In the second case,shownin Fig.1(b),the same metal film as above is used,d3=505 A,but the clamping of the prism is relaxed until theliquid-layer thickness d2=5000 A in order that bothcoupled modes can be observed.Finally,in Fig.1(c)forJuly 1983/Vol.8,No.7/OPTICS LETTERS 379an optimal choice of metal,d3=170 A,and liquid,d2=12 000 A,thicknesses the sharp resonance associatedwith the excitation of the long-range surface-plasmonmode is displayed.Note the change in angle-of-inci-dence scale between Figs.1(a)and 1(c),which illustratesthat the angular width of the resonance is reduced byover an order of magnitude.In Figs.1(a)and 1(b)theagreement between theory and experiment is excellent.Only minor adjustments(-1%)in the value of either d2or dq were required to match the angular half-widths.However,for the long-range surf ace-plasmon mode inFig.1(c),the theoretical half-width is a factor of 2 nar-rower than that observed.This discrepancy is due tothe diffraction effects associated with the finite widthof the laser beam.Numerical calculations predict4that,for even thinner silver films,d3=100 A,the angularwidth of the resonance should be narrowed by anotherorder of magnitude.We observe that for thinner silverfilms the resonance does indeed further narrow but thatthe depth of the ATR minimum decreases.Experi-ments with expanded beams are in progress to deter-mine the limiting factors for obtaining supernarrowresonances.The result for a similar experiment with an alumi-num,11E3=-47+i18,film is shown in Fig.2.Wedisplay only the narrow resonance with d3=145 A andd2=8600 A that is due to the long-range surface-plas-mon mode.Again the angular width of the resonancerelative to the Kretschmann mode is reduced by overan order of magnitude.Although the absorption ofaluminum is much greater than that of silver,the sym-metric field distribution of the mode in the metal filmstill results in a sharp resonance in the aluminum film.As before,the theoretical half-width is narrower thanthe experimental half-width,and again slightly nar-rower but shallower ATR resonances were observed forthinner aluminum films.In conclusion,we have observed in both silver andaluminum films the narrow ATR resonances associatedwith the excitation of the long-range surface-plasmonmode originally predicted by Sarid.Observation of thisphenomenon depends critically on adjusting thethickness of the index-matching liquid layer.The an-gular width of this resonance relative to that of thestandard Kretschmann mode is reduced by over anorder of magnitude.Experiments on the applicationof the resonant enhancement of this mode to second-harmonic generation are in progress.The authors gratefully acknowledge Conversationswith R.T.Deck regarding the properties of the long-and short-range surface-plasmon modes.We alsothank Dror Sarid for sending us,before submission ofthis Letter,a manuscript by Alan Craig et ai.of theUniversity of Arizona describing a related measurementof the propagation constant of the long-range surface-plasmon mode.References1.D.Sarid,Long-range surface plasma waves on very thinmetal films,Phys.Rev.Lett.47,1927(1981).2.D.Sarid et al.,Optical field enhancement by long-rangesurface-plasma waves,Appl.Opt.21,3993(1982).3.G.I.Stegeman,J.J.Burke,and D.G.Hall,Nonlinearoptics of long range surface plasmons,Appl.Phys.Lett.41,906(1982).4.R.T.Deck and D.Sarid,Enhancement of second-har-monic generation by coupling to long-range surfaceplasmons,J.Opt.Soc.Am.72,1613(1982).5.D.Sarid,R.T.Deck,and J.J.Fasano,Enhanced non-linearity of the propagation constant of a long-rangesurface-plasma wave,J.Opt.Soc.Am.72,1345(1982).6.G.J.Kovacs and G.D.Scott,Optical excitation of sur-face plasma waves in layered media,Phys.Rev.B 16,1927(1977);G.J.Kovacs,Optical excitation of resonantelectromagnetic oscillations in thin films,Ph.D.Thesis(University of Toronto,Toronto,Canada,1977).7.M.Born and E.Wolf,Principles of Optics(Pergamon,New York,1964).8.R.T.Deck,University of Toledo,Toledo,Ohio 43606(personal communication).9.P.B.Johnson and R.W.Christy,Optical constants ofthe noble metals,Phys.Rev.B 6,4370(1972).10.E.Kretschmann,The determination of the opticalconstants of metals by excitation of surface plasmons,Z.Phys.241,313(1971).11.D.E.Gray,ed.,American Institute of Physics Handbook(McGraw-Hill,New York,1972).