Giant enhancement of sum-frequency yield by surface-plasmon excitation

Transcription

1 1146 J. Opt. So. Am. B/Vol. 16, No. 7/July 1999 van der Ham et al. Giant enhanement of sum-frequeny yield by surfae-plasmon exitation E. W. M. van der Ham,* Q. H. F. Vrehen, and E. R. Eliel 2 Huygens Laboratory, Leiden University, P.O. Box 9504, 2300 RA Leiden, The Netherlands V. A. Yakovlev, E. V. Alieva, L. A. Kuzik, and J. E. Petrov Institute of Spetrosopy, Russian Aademy of Sienes, Troitsk, Mosow region, Russia V. A. Syhugov General Physis Institute, Russian Aademy of Sienes, Vavilova 38, Mosow, , Russia A. F. G. van der Meer Stihting voor Fundamenteel Onderzoek der Materie (FOM) Institute for Plasma Physis Rijnhuizen, P.O. Box 1207, 3430 BE Nieuwegein, The Netherlands Reeived September 11, 1998; revised manusript reeived Marh 22, 1999 We show experimentally that the radiation generated in infrared visible sum-frequeny mixing at an air silver interfae an be greatly enhaned when the visible input beam exites a surfae plasmon polariton at the interfae. With either a prism or a grating used to ouple the visible radiation with the surfae polariton, the sum-frequeny-generation yield is observed to be enhaned by a fator of 10 2 for the prism and 10 4 for the grating for ounterpropagating infrared and visible input beams. The result for the prism onfiguration an be simply understood in terms of the field enhanement assoiated with the surfae polariton exited by the visible input beam. For the grating onfiguration there is an additional effet in that the nonlinear polarization at the sum frequeny an also ouple with a surfae polariton. As a result the effetive interation length of the sum-frequeny-mixing proess is sizably inreased. The experimental results are in good agreement with estimates based on this model Optial Soiety of Ameria [S (99) ] OCIS odes: , , , INTRODUCTION In reent years seond-order nonlinear optial methods have found widespread appliation in the study of surfaes and interfaes. 1 3 Seond-harmoni generation and sum-frequeny generation (SFG) have been favored for this appliation. Beause SFG is tehnially more ompliated than seond-harmoni generation, the latter tehnique is muh more widely used than SFG. For the study of moleular monolayers, however, SFG offers onsiderable advantages beause the nonlinear optial proess an rather easily be made resonant. Apart from the ensuing signal enhanement, the nonlinear optial proess then also beomes moleule speifi. In the experiment this is realized by the nonlinear optial proess being driven with tunable IR radiation in ombination with fixed-frequeny visible radiation. The frequeny of the IR radiation is then tuned aross various vibrational modes of the moleules that make up the monolayer. The resulting speifiity is of importane when different moleular speies are present in the monolayer or when the supporting substrate partiipates in the nonlinear mixing proess. Metals provide an example of suh substrates. The flux of photons that is generated at the new frequeny (either the seond-harmoni frequeny or the sum frequeny) is small beause nonlinear optial proesses are usually highly ineffiient. In addition, the radiation at the new frequeny is, for monolayers, generated by a sample with essentially zero depth. Nevertheless, even at submonolayer overages seond-harmoni generation and SFG an yield a detetable signal. 4 Yet in many ases there is a real need for an inreased photon flux, partiularly in SFG employing low-frequeny vibrational modes of moleules in an adsorbed layer. This is illustrated by the fat that the sum-frequeny ativity of suh modes is often vanishingly small even though the highfrequeny vibrational modes are easily seen by SFG. 5 Beause of the risk of sample damage, the sumfrequeny yield usually annot be improved by inreasing the flux density of the primary radiation. An attrative route is provided by methods in whih the eletromagneti field at the sample interfae is enhaned relative to the field of the inident radiation. Suh enhanement ours, for instane, in a total-internal-refletion geometry just beyond the angle for total internal refletion or in samples in whih one exites a surfae polariton. 6 Both these methods have been suessfully employed in nonlinear optial experiments Whereas the total-internalrefletion geometry is being applied in some instanes to SFG from adsorbed monolayers, 8 11 the possibilities of /99/ $ Optial Soiety of Ameria

2 van der Ham et al. Vol. 16, No. 7/July 1999/J. Opt. So. Am. B 1147 fered by the appliation of surfae polaritons to SFG of interfaial layers have remained unexplored until reently. There exists, however, a long-standing onnetion between surfae polaritons and seond-order nonlinear optial methods, sine these provide an elegant mehanism to optially exite surfae modes of dieletri rystals. 12,13 Reently we presented preliminary results regarding the inrease of the sum-frequeny yield from a bare silver film. 14 Enhanements ranging between 2 and 4 orders of magnitude were observed. In the present paper we report more extensive results on surfae-polariton-aided SFG, omparing different modes of surfae-polariton exitation, and we present a simple piture explaining the results. 2. SURFACE PLASMON POLARITONS The possibility that eletromagneti waves an propagate on a surfae or interfae was first disussed by Sommerfeld in the ontext of the propagation of radio waves. 15 These solutions to Maxwell s equations exist under welldefined onditions regarding the dieletri funtions a () and b () of the media above (z 0) and below (z 0) the interfae; either Re( a ()) 0 and Re( a ()) Re( b ()) or Re( b ()) 0 and Re( b ()) Re( a ()). The eletri field is p polarized and an be written as E a E x a x E z a z exp a z t K SPP x, (1) E b E x b x E z b z exp b z t K SPP x, (2) where the surfae exitation propagates along the x diretion. Beause of the ontinuity of the tangential omponent of the eletri field and the normal omponent of the displaement field, one has E a x () E b x () and E a z () ( b ()/ a ())E b z (). On both sides of the interfae the amplitude of the wave deays away from the interfae with the deay onstant i K SPP 2 i 2 1/2, i a, b. (3) The (omplex) propagation onstant of the surfae wave is given by K SPP K 1/2 a b, (4) a b with K /. In the present ase we employ surfae waves propagating along the interfae between vauum and a metal at frequenies well below the metal s plasma frequeny P. Hene a () 1 and b () b () b () is omplex with b () 0 and b () a (). A surfae wave along suh an interfae is alled a surfae plasmon polariton (SPP). For P one has b () b () and b () a (); in this ase one an approximate the expressions for a and b as 16 Fig. 1. Dispersion relation of a SPP propagating along the interfae between vauum and a metal (solid urve). The dashed line shows the dispersion relation of free-spae eletromagneti radiation. a 1/2 1, (5) 1 b b b a. (6) The propagation onstant K and damping oeffiient of the SPP an be written as 16 K b 1 b b 3 2 1/2, (7) 1 b b 2 b b 1 3. (8) 1/2 The dispersion relation of the SPP along suh an interfae is shown in Fig. 1 (solid urve) together with that of eletromagneti radiation in free spae. The figure diretly shows the wave-vetor mismath between a SPP and freespae radiation at the same frequeny. Beause of this mismath some element is neessary to ouple free-spae radiation with a SPP at a metal vauum interfae. 3. EXPERIMENTAL METHOD The sum-frequeny spetrometer that is used in the present experiment has been disussed in some detail in Refs Briefly, wavelength tunable (5 ir 110 m) IR radiation from the FELIX free-eletron laser 20 is mixed at the surfae of a silver film with the output of a fixed-frequeny ( vis nm) visible laser system. Both lasers generate bursts (5 s long) of synhronized, short, powerful pulses that overlap temporally and spatially on the sample. In the present experiment FELIX delivers pulses of 1 ps in duration with an energy ontent of 2 J at a 1-GHz repetition rate while the visible laser yields pulses of 7 ps in duration with an energy of 4 J at a repetition rate of 250 MHz. Both laser beams are p polarized. The generated sum-frequeny radiation is emitted as a ollimated beam and is foused on a liquid-nitrogen-ooled CCD amera that serves as a detetor. A narrow-band interferene-filter set with a ompound transmission of 50% at the sum frequeny is used to suppress stray light at the visible input wavelength. In the experiment the IR wavelength is fixed at ir 10.0 m.

3 1148 J. Opt. So. Am. B/Vol. 16, No. 7/July 1999 van der Ham et al. We study SPP-aided SFG at the interfae between air and a silver film with the SPP exited by the visible input radiation. The SPP beomes resonantly exited when the omponent of the wave vetor of the inident visible radiation parallel to the interfae mathes the wave vetor K vis of the SPP at that frequeny. Two approahes are employed to realize this mathing: a fused-silia prism in the Kretshmann onfiguration 21 and a grating struture in the silver film. In both experiments involving prism and grating oupling the SFG yield is measured as a funtion of the angle of inidene of the visible input radiation. In addition, we measure the refletivity of the sample as a funtion of this angle. The latter provides us with a measure of the effiieny of SPP exitation. 6 The angle subtended by the two input beams remains onstant during all experiments. For the prism setup this angle is approximately 170, and for the grating setup approximately 91. A. Surfae-Plasmon Polariton Exitation with Prism For these measurements we employ a 90 fused-silia prism with a 50-nm-thik silver film on the hypotenuse (see Fig. 2). Wave-vetor mathing at the air silver interfae is ahieved by our hoosing the appropriate angle of inidene vis of the visible input radiation: vis K vis n vis sin vis, (9) where n( vis ) is the refrative index of fused silia at frequeny vis. The infrared radiation omes in from the opposite side (see Fig. 2). The radiation at the sum frequeny is emitted into the fused silia in a diretion that is somewhat different from that of the speularly refleted visible input beam. The wave vetor of the sum-frequeny radiation has a omponent along the interfae given by k x sfg n sfg n vis sfg vis sin sfg sin vis ir sin ir, (10) where n( sfg ) is the refrative index of fused silia at the sum frequeny and sfg the angle of emission of the generated sum-frequeny radiation. The minus sign in Eq. (10) arises beause the input fields are ounterpropagating; in a opropagating onfiguration this beomes a plus sign. B. Surfae-Plasmon Polariton Exitation with Grating The substrate for this series of measurements is a flat glass plate ontaining the grating struture at its surfae. The grating (groove period a 301 nm, groove depth nm) is written by photolithographi tehniques and subsequent ion ething. The substrate is overoated with a 200-nm-thik silver film, made by thermal evaporation in a vauum hamber. To resonantly exite the SPP, the visible input beam has to ome in at the proper angle of inidene in this ase, also: K vis k x vis Nk grating (11) vis sin vis N 2 a, (12) where N is the diffration order. Here k x ( vis ) is the omponent of the wave vetor of the visible input beam along the sample and k grating 2/a. With vis nm, a polariton is exited when vis 43.5 and N 1. The SPP is then ounterpropagating with the visible input beam (see Fig. 2) and K vis k x ( vis ) k grating. In the hosen geometry the SPP is then odiretional with the IR input beam. The nonlinear polarization at the sum frequeny P (2) (r, t) is given by P 2 r, t P 2 sfg zexpk NL x sfg x sfg t, (13) where P (2) ( sfg ) is the nonlinear surfae polarization of the air metal interfae. Its wave vetor is given by k x NL sfg K vis k x ir, (14) where k x ( ir ) is the omponent of the wave vetor of the IR input radiation parallel to the interfae. In the present onfiguration we have (see below) k NL x ( sfg ) Fig. 2. Configurations for SFG with a SPP at the visible input wavelength. Left, onfiguration of input beams used with the prism; the SPP travels to the right, ounterdiretional to the IR input beam. Right, onfiguration used with the grating; the SPP at the visible input wavelength is odiretional with the IR input beam.

4 van der Ham et al. Vol. 16, No. 7/July 1999/J. Opt. So. Am. B 1149 Fig. 3. Experimental results for the sum-frequeny yield obtained with the prism oupler (filled symbols, sale at left). The open symbols show the fration of the visible input power that is oupled into a polariton (sale at right). sfg /; hene this nonlinear polarization annot radiate into free spae. Sum-frequeny radiation is, however, emitted in a diretion determined by k x sfg k x NL sfg k grating (15) k x vis k x ir (16) vis sin vis ir sin ir, (17) i.e., exatly in the diretion in whih the sum-frequeny radiation from a nonorrugated interfae is emitted for ounterpropagating input beams. There is thus a unique propagation diretion of the sum-frequeny radiation, whether or not the input beams overlap with the grating and one ouples into the SPP. This makes a omparison between SPP-aided and non-spp-aided SFG simple for a grating oupler beause one an swith from one to the other simply by moving the sample relative to the input beams. 4. RESULTS AND DISCUSSION The results for the prism onfiguration are shown in Fig. 3. The dots represent the measured values of the sumfrequeny yield from the air silver interfae as a funtion of the angle of inidene of the visible radiation. The squares show the quantity (1 R), representing the fration of the inident visible-beam energy that is oupled into the surfae plasmon (R is the measured refletivity of the sample). At resonane ( vis 46.3 ) this fration reahes a maximum at a value equal to 0.72, indiating that a large fration of the inident beam energy is oupled into the SPP. The variation of the sumfrequeny yield and of (1 R) with the angle of inidene have very similar shape, demonstrating that the inrease of the sum-frequeny response is really the result of the surfae-plasmon exitation. Both resonanes have a width of roughly 1, a value that is harateristi for the response of a 50-nm-thik silver film when a wellollimated beam at the visible input wavelength is employed. At resonane the sum-frequeny yield is larger by approximately a fator of 100 as ompared with the yield far off resonane. One an define a fieldenhanement fator for the surfae polariton given by vis E SPP vis, (18) E 0 vis where E SPP ( vis ) is the eletri field strength assoiated with the polariton [see Eq. (1)] and E 0 ( vis ) is the field strength of the input radiation. For the Kretshmann onfiguration one alulates 2 vis 100, 22,23 in exellent agreement with the enhanement of the sum-frequeny yield. Clearly, the observed inrease in the sumfrequeny yield an be explained in terms of the enhanement of the visible input field. With grating exitation of the SPP the sum-frequeny yield off the air silver interfae is onsiderably larger than that obtained in the prism onfiguration. 14 For various gratings with slightly different grating parameters we find the SFG yield to be inreased by a fator of Here the enhanement fator is found by omparing the SPP-aided SFG yield with the yield obtained away from the grating. We asertained that all of the enhanement is SPP indued by performing a measurement in whih the wave vetor of the grating is aligned perpendiular to the plane of inidene. In this onfiguration whih usually does not lead to exitation of an SPP (see, however, Ref. 24) the sum-frequeny yield is not enhaned. The fat that this yield is almost exatly equal to that found when the input beams do not overlap with the grating indiates that the surfae roughness of the grating does not give rise to signal enhanement. The field enhanement of the visible input field for the grating onfiguration an be simply expressed in terms of

5 1150 J. Opt. So. Am. B/Vol. 16, No. 7/July 1999 van der Ham et al. the power-oupling effiieny, the inverse attenuation length ( a vis ) 1 of the field normal to the air silver interfae [see Eq. (5)], and the damping oeffiient vis [see Eq. (8)] of the surfae polariton. As the spot size of the visible beam on the sample is onsiderably larger than the damping length of the polariton (2 vis ) 1, the enhanement is given by 25 2 vis E 2 vis SPP vis E 0 vis a os vis. (19) vis At the visible input wavelength ( vis m) we have for the silver film 26 b ( vis ) 1/ , yielding vis a 3.78 m 1 and vis m 1. Together with an estimated oupling effiieny 1, this yields 2 vis 150, muh less than the enhanement fator found in the experiment. The experimental enhanement fator thus annot be understood only in terms of the inrease of the visible input field and, onsequently, of the driving nonlinear polarization at the sum frequeny. This is not surprising in view of the fat that this nonlinear polarization annot radiate diretly into free spae, as mentioned earlier. To substantiate the latter statement, we alulate the relevant wave vetors [see Eqs. (7) and (14)]. The real part of the propagation onstant of the polariton at 2/ vis m is given by K vis 2/ m 1. The omponent of the wave vetor of the nonlinear surfae polarization along the interfae then equals k NL x ( sfg ) 2/ m 1 for ir 10.0 m and ir The free-spae wave vetor of the generated sum frequeny has the length sfg / 2/ m 1 ; thus k NL x ( sfg ) sfg /. Beause of this inequality, a freespae radiative solution of the wave equation is not allowed. The wave equation for the field at the sum-frequeny, however, has a solution in the form of a surfae polariton. These solutions to the wave equation are known to have inreased field strength, displaying resonant enhanement when there is wave vetor mathing between the surfae polariton at the sum frequeny and the driving nonlinear polarization. 7,27 The propagation onstant of the polariton at the sum frequeny an be written as with k( sfg ) the phase mismath and sfg the fieldattenuation oeffiient of the surfae polariton at the sum frequeny. For the present experiment we have, with b ( sfg ) (see Ref. 26), K sfg 2/ m 1, k( sfg ) m 1, and sfg m 1. Sine k( sfg ) sfg, we have l k( sfg ) m, dominated by the phase mismath. To quantify the sum-frequeny yield in the present onfiguration, as ompared with that in whih none of the input beams ouples with a surfae polariton, one has to take three fators into aount. First, the field enhanement vis of Eq. (19) leads diretly to an equally large enhanement of the driving nonlinear surfae polarization. Seond, this nonlinear surfae polarization exites a surfae polariton, resulting in a very large inrease of the effetive generation length. This fator equals l /, where l is the oherene length and the effetive thikness (1 nm) of the layer in the metal 28 that ontributes to the sum-frequeny response. Third, one has to take into aount the spatial overlap between the field that is to be generated and the nonlinear surfae polarization. 27 Beause the nonlinear surfae polarization is onfined to a layer that is very thin ompared with the spatial extent ( sfg a ) 1 of the SPP, this overlap is rather small, yielding a fator of order sfg a. Taking everything together, we estimate the sum-frequeny yield to be inreased by a fator G vis 2 l / 2 a sfg 2 vis 2 l a sfg (22) This estimate for the gain fator G is in satisfatory agreement with the values found in the experiment, the more so in view of the approximations that have been made. For instane, the proesses of SPP inoupling and outoupling, damping, and the nonlinear generation proess are disussed as separate phenomena. In reality, of ourse, all these proesses take plae simultaneously. Obviously, this has to be taken into aount when the en- K SPP sfg K sfg sfg, (20) where K sfg and sfg are alulated from Eqs (7) and (8), given the value of b ( sfg ). In general there is a mismath k( sfg ) K sfg k NL x ( sfg ) between the wave vetor K sfg of the polariton at the sum frequeny and the wave vetor of the driving nonlinear polarization k NL x ( sfg ), limiting the resonant enhanement. The generation of a surfae polariton at the sum frequeny by the nonlinear surfae polarization is very similar to SFG in the bulk or in waveguides for the ase in whih the propagation vetors of the driving nonlinear polarization and of the generated field point in exatly the same diretion. This situation gives rise to oherent buildup of the field at the sum frequeny over a length equal to the oherene length, l k sfg 2 sfg 2 1/2, (21) Fig. 4. Experimental results (filled symbols) for the sumfrequeny yield on top of the visible grating as a funtion of the angle of inidene of the visible input radiation. The dotted dashed urve shows the exitation effiieny of the polariton at the visible input wavelength (input oupling), and the dashed urve displays the phase mathing between the nonlinear polarization and the polariton at the sum frequeny. The solid urve gives the produt of these two fators saled to the experimental results.

6 van der Ham et al. Vol. 16, No. 7/July 1999/J. Opt. So. Am. B 1151 Fig. 5. Wave-vetor omponents parallel to the interfae for the grating oupler for (right) ounterpropagating and (left) opropagating onfigurations of the input beams. The bottom arrows indiate the wave-vetor mismath for the respetive ases. hanement fator is alulated more quantitatively. Of partiular importane here is the question of whether the outoupling does not destroy the oherent buildup of the sum-frequeny field. The values of the parameters all apply to an angle of inidene for whih the surfae polariton at the visible input frequeny is optimally exited ( vis 43.5 ). At this angle the wave-vetor mismath k( sfg ) is rather large. When the sample is rotated in suh a way that the angle of inidene is modified, the oupling with the surfae polariton at the visible input frequeny deteriorates. However, the wave-vetor mismath at the sum frequeny k( sfg ) may beome smaller in the proess, thereby improving the nonlinear generation proess. This is atually the ase here, as is shown in Fig. 4. Here the dashed dotted urve shows the exitation probability (basially 2 vis ) of the SPP at the visible input wavelength as a funtion of vis ; it peaks at vis 43.5 and has a width determined by vis. The dashed urve shows the variation of the effiieny of the nonlinear generation proess that is due to the oupling with the SPP at the sum frequeny for a given nonlinear surfae polarization (basially l 2 ). The SFG enhanement fator is given by the produt of these two fators [see Eq. (22)]; it is displayed as the solid urve in Fig. 4. The latter is saled to the experimental data for the SFG yield, shown as dots. The agreement between the solid urve and the experimental data is exellent, whih shows that the enhanement fator is well understood. With the grating oupler we also used a opropagating arrangement of the input beams (in ontrast to the experiment disussed above). In the opropagating setup we find the sum-frequeny yield to be enhaned by a fator of the order of 100 under optimal oupling onditions. In this onfiguration the wave-vetor mismath k( sfg ) at optimal inoupling is substantially larger than that for the ounterpropagating setup (see Fig. 5). When the sample is oriented suh that the wave-vetor mismath vanishes, the visible input radiation an no longer ouple effiiently with a SPP. Therefore only a single enhanement fator omes into play for the grating oupler in a opropagating onfiguration. The situation is quite similar for the prism oupler, exept that the role of the opropagating and ounterpropagating geometries are interhanged. For the ounterpropagating geometry we find, as disussed above, that field enhanement of the input wave is all that omes into play. Coherent buildup of the sum-frequeny field is preluded beause k NL x ( sfg ) K vis k x ( ir ) and k NL x ( sfg ) n( sfg ) sfg /: The nonlinear polarization an diretly radiate into the prism. In a opropagating arrangement k NL x ( sfg ) K vis k x ( ir ) and k NL x ( sfg ) n( sfg ) sfg /. The nonlinear polarization annot radiate into free spae and has to ouple with a SPP at the sum frequeny. Hene for a prism oupler in a opropagating setup one expets an enhanement of the sumfrequeny yield similar to that attained with the grating in a ounterpropagating onfiguration. We have been able to onfirm this experimentally. It has, however, not been possible to reord the full angular dependene of the sum-frequeny yield for the prism oupler in a opropagating arrangement of input beams beause the radiation at the sum-frequeny is not easily separated from that of the refleted visible input beam (for ir 10.0 m). 5. CONCLUSIONS In this study of visible-spp-assisted infrared visible sum-frequeny generation we have shown that, without great effort, the sum-frequeny yield an be enormously enhaned. In onfigurations involving prism and grating oupling with ounterpropagating input beams we have ahieved an inrease of the sum-frequeny response by 2 4 orders of magnitude. The 2 orders of magnitude, observed in the experiment with the prism oupler, are explained in terms of the field-enhanement assoiated with the onentrating effet that is due to the exitation of a surfae polariton. To explain the even larger effets assoiated with the employed grating onfiguration, an additional mehanism is invoked. It involves oupling with a surfae polariton at the sum frequeny, giving rise to a substantial inrease of the effetive interation length of the nonlinear optial proess. We have also shown that for a opropagating arrangement of the input beams similar enhanement fators are found. In that ase the enhanement fator is largest for the prism oupler. Beause of the orders-of-magnitude inrease in signal yield, SPP-aided SFG holds great promise for sumfrequeny spetrosopy of overlayers on top of metals. 29 An additional appealing aspet is that the SPP enhane-

7 1152 J. Opt. So. Am. B/Vol. 16, No. 7/July 1999 van der Ham et al. ment ombines well with the self-dispersive method for sum-frequeny spetrosopy. 18,19 ACKNOWLEDGMENTS This work was supported by the Tehnology Foundation (STW), the Stihting voor Fundamenteel Onderzoek der Materie (FOM), and the Russian Foundation for Fundamental Researh under grant We highly appreiate the skillful assistane of the FELIX staff and gratefully aknowledge A. G. Mal shukov and G. Knippels for stimulating disussions. Finally, we thank I. F. Salakhtudinov for help with the sample preparation. *Present address, Nederlands Meetinstituut, P.O. Box 654, 2600 AR Delft, The Netherlands. 2 E. R. Eliel s address is eliel@molphys.leidenuniv.nl. REFERENCES 1. Y. R. Shen, Nature (London) 337, 519 (1989). 2. J. F. MGilp, D. Weaire, and C. H. Patterson, Epioptis, Linear and Nonlinear Optial Spetrosopy of Surfaes and Interfaes (Springer-Verlag, Berlin, 1995). 3. P.-F. Brevet, Surfae Seond Harmoni Generation (Presses Polytehniques et Universitaires Romande, Lausanne, 1997). 4. T. F. Heinz, C. K. Chen, D. Riard, and Y. R. Shen, Phys. Rev. Lett. 48, 478 (1982). 5. R. Braun, B. D. Casson, C. D. Bain, E. W. M. van der Ham, Q. H. F. Vrehen, E. R. Eliel, A. M. Briggs and P. B. Davies, J. Chem. Phys. 110, 4634 (1999). 6. G. N. Zhizhin, M. A. Moskalova, E. V. Shomina, and V. A. Yakovlev, in Surfae Polaritons, V. M. Agranovih and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap Y. R. Shen, Phys. Rep. 194, 303 (1990). 8. S. R. Hath, R. S. Polizotti, S. Dougal, and P. Rabinowitz, Chem. Phys. Lett. 196, 97 (1992). 9. J. C. Conboy, J. L. Dashbah, and G. L. Rihmond, J. Phys. Chem. 98, 9688 (1994). 10. J. C. Conboy, M. C. Messmer, and G. L. Rihmond, J. Phys. Chem. 100, 7617 (1996). 11. J. Löbau and K. Wolfrum, J. Opt. So. Am. B 14, 2505 (1997). 12. D. N. Mirlin, in Surfae Polaritons, V. M. Agranovih and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap Y. R. Shen and F. de Martini, in Surfae Polaritons, V.M. Agranovih and D. L. Mills, eds. (North-Holland, Amsterdam, 1982), Chap E. V. Alieva, Y. E. Petrov, V. A. Yakovlev, E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, A. F. G. van der Meer, and V. A. Syhugov, JETP Lett. 66, 609 (1997). 15. A. Sommerfeld, Ann. Phys. (Leipzig) 4, 665 (1909). 16. C. A. Ward, R. J. Bell, R. W. Alexander, G. S. Kovener, and I. Tyler, Appl. Opt. 13, 2378 (1974). 17. E. R. Eliel, E. W. M. van der Ham, Q. H. F. Vrehen, G. W. t Hooft, M. Barmentlo, J. M. Auerhammer, A. F. G. van der Meer, and P. W. van Amersfoort, Appl. Phys. A: Solids Surf. 60, 113 (1995). 18. E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Opt. Lett. 21, 1448 (1996). 19. E. W. M. van der Ham, Q. H. F. Vrehen, and E. R. Eliel, Surf. Si. 398, 96 (1996). 20. D. Oepts, A. F. G. van der Meer, and P. W. van Amersfoort, Infrared Phys. 36, 297 (1995). 21. E. Kretshmann, Z. Phys. 241, 313 (1971). 22. W. N. Hansen, J. Opt. So. Am. 58, 380 (1968). 23. B. Pettinger, A. Tadjeddine, and D. M. Kolb, Chem. Phys. Lett. 66, 544 (1979). 24. R. A. Watts, T. W. Preist, and J. R. Sambles, Phys. Rev. Lett. 79, 3978 (1997). 25. I. A. Avrutsky, P. V. Basakutsa, and S. Surov, Waveguide Corrugated Strutures in Integrated and Fiber Optis (Nauka, Mosow, 1991). 26. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972). 27. Y. R. Shen, The Priniples of Nonlinear Optis (Wiley, New York, 1984). 28. J. Rudnik and E. A. Stern, Phys. Rev. B 4, 4274 (1971). 29. E. V. Alieva, L. Kuzik, and V. A. Yakovlev, Chem. Phys. Lett. 292, 542 (1998).