Contemporary Physics, 1991, volume 32, number 3, pages 173-183 Optical excitation of surface plasmons: an introduction J. R. SAMBLES, G. W. BRADBERY and FUZI YANG Beginning from low level concepts the basic understanding for the optical excitation of surface plasmons is developed. Prism coupling using the attenuated total reffection technique is discussed as well as the less traditional grating coupling technique. A brief discussion of some recent developments using twisted gratings is also presented. Finally a short summary of the potential device applications is given 1.Introduction 2. Simple theory The interaction of electromagnetic radiation with an In order that we may study this interface and the interface can generate interesting surface excitations interesting electromagnetic phenomenon which oc ccurs ere are, in electromagnetic terms, a range of interfaces there we need first to examine some relatively simple of interest, for example dielectric to dielectric, dielectric concepts of solid state physics and electromagnetism. Electromagnetic radiation in isotropic media consists of ong orthogonal oscillating electric and magnetic fields rmal transverse to the direction of propagation. If, as is often h are both the case, we pass such radiation through a linear ansm polarizer then the radiation being transmitted will be plane polarized. This means there is a well specified plane ir and in which E or B oscillate, this plane containing the gnetic field vector and the propagation. Now if we consider such ident angle 0. upon a smooth anar interface then we have to consider two important d in figure 1, the incident contains orthogonal to the 0010-7514/91
J.R. Sambles et al. Let us examine in detail an important limit of Snell's law. Suppose that the radiation is incident from a high index medium, n,=VE, on to a low index medium n2=VE2,(where E1, E2 are the relative permittivities) with n2 <n,. Then Snell's law, the conservation of in-surface-plane momentum condition, gives medium 2 sinO2=√e1sin0 Since the greatest in-surface-plane component available in medium 2 is when 02=90, there is a limiting angle Incidence Be, given by Figure 1. Representation of p-polarized electromagnetic 02=√a2/√a (2) radiation incident upon a planar interface between two media at beyond which, for radiation incident from medium an angle of incidenceθ 1, there can be no propagating wave in medium 2. This limiting angle is called the critical angle. Radiation linearly polarized radiation may be readily represented incident beyond the critical angle has more momentum by a sum of the above two cases along the surface plane than can be supported by Now consider that the second medium is a medium 2. For such radiation incident from medium I non-magnetic material, that is at the frequency of the the oscillating E field will cause the charges in medium incident radiation the relative permeability is unity. Then 1, including those at the 1-2 interface, to oscillate. Thus as far as the B part of the electromagnetic oscillation is even though the radiation is now totally reflected at the concerned there is no discontinuity at the interface. In interface there are oscillating charges here which have this case, which represents the majority of materials, it associated radiation fields penetrating into medium 2 govern the behaviour of the radiation on encountering they are spatially decaying fields (evanescent) which the interface. For simplicity we shall throughout this article ignore optical activity, that is the property (the radiation, decaying in amplitude in medium 2 in a chirality)of a material which allows it to rotate the plane direction normal to the interface. At the critical angle the propagating along an axis of symmetry in the syste s decay length is infinte but this falls rapidly to the order of polarization of an incident photon even if it of the wavelength of light as the angle of incidence is Photons, with momentum hk. when in a medium of further increased. This evanescent field for radiation refractive index n,, are regarded as having momentum incident beyond the critical angle is useful for coupling (strictly pseudomomentum)hkn,=hk ,(where k= 2x/a). radiation to surface plasmons as we shall see later. If these arrive at a planar interface they may impart For the moment let us return to the boundary momentum in a direction normal to the interface and so conditions on the E and B field components of our there is no need to conserve the normal component of incident radiation. Since there is no boundary ortho- hoton momentum, hk, For the reflected signal, since gonal to Ex this component is conserved across the hIk,I is conserved, unless the photon frequency is boundary. However this is not the case for E,, the normal changed, and hkx is conserved for a smooth planar component of E. It is the normal component of D, D interface, then it follows that k,, of the reflected signal which is continuous (there is no free charge) and Ez is simply -kzl, the usual law of reflection at a planar is forced to change if a is changed since Dz interface E,EoEn =E2EoEx2. This discontinuity in E, results in On the other hand inside the second medium the polarization changes at the interface refractive index is n, so the radiation has a new From these simple considerations it is obvious that wavelength, A2= A/nz and a new wavevector k2=n2k. while s-polarized incident radiation will not normally In this medium the radiation propagates in a new cause the creation of charge at a planar interface, direction, conserving k, but allowing k, to change. Now p-polarized radiation will automatically create time k,1=k, sin 6, and k,2= k2 sin 6, where 0, is the angle dependent polarization charge at the interface of refraction. Since the tangential momentum component Suppose now we consider one of the two materials to is conserved, kxI=kx2 and n, sin 0,=n2 sin 0, which is be a metal. A metal may be regarded as a good conductor Snell,s law(resulting from the translational invariance of of electricity and heat and a reflector of radiation. This the system parallel to the interface) is a rather loose definition of a metal which relates to
Optical excitation of surface plasmons the ability of thefree electrons in the metal to respond If we now apply Maxwells equation VE=0 we find to the externally imposed fields. If the electrons are free (still of course constrained inside the metal) then they are able to respond with no scattering to the incident radiation giving an ideal metallic response. Such a E2=-E3 k that is E=0 everywhere inside the metal, must therefore have &=+oo. An ideal metal in which the electrons Then to find the relationship between H, and E respond perfectly to the applied external field, therefore use Maxwell's equation A E=-H:(Faraday's law H cancelling it, is the limit 8--oo. Such a material of course does not exist, for the free electrons inside a metal of electromagnetic induction) which with H= Ho gives the oscillating field. The electrons have a finite mass and they permittivities and the normal component of the suffer scattering with lattice vibrations (phonons), defects wavevectors in the two media and the surface This means that as we increase the frequency of the H (5a) incident radiation the free electrons progressively find =oF (5b) it harder to respond. Ultimately at high enough frequencies, low enough wavelengths, the metal becomes Finally we need to apply the boundary conditions at transparent and behaves more like a dielectric z=0. We know tangential H is continuous and so is tangential E, thus HyI=Hy2 and Ex1= Ex2 leading to the following simple relationship between the relative permittivities and the normal components of the wavevectors in both media 3. More detailed theory From this simplistic treatment of the free electrons in a metal it is easy to show that there is a limiting frequency, k,t k2,z the plasma frequency, (for many metals in the Also we have ultra-violet) above which the metal is no longer metallic In this article we shall concern ourselves only with kzi=i(k:,k2)2, requiring k2>E,k2(7a) frequencies below this limit, that is with long enough wavelengths so that a is largely real and negative. As mentioned for real metals there is resistive scattering and k22=i(k2-6,k2)/, requiring k2>E,k2,(7b) hence damping of the oscillations created by the incident where k= o/c. If the wave is truly a trapped surface E field. This damping causes an imaginary component wave with exponential decays into both media then we E to E. Before, however, concerning ourselves with the need iki >0 and ik22 E, H,=(0, H,i, O)exp [(k, x-or)] exp(ik, z), (3b) Thus we now have satisfied Maxwells equations ar boundary conditions to give a trapped surface wave, with E,=(E,2, 0, E, )exp [i(k, x-or)] exp(ik, z)(3c) real k, and appropriate kx, provided IE2l >&1 and e2 <0 Following the above analysis with purely real g values H2=(, Hy2, O)exp [i(k, x-an)] exp(ik,2 z).(3d) leads to a surface wave having purely real k, which is
J. R. Sambles et al larger than VE,k the maximum value for the medium 1. Thus the shift is inversely proportional to e,,while It is also clear that this surface plasmon resonance is the width of the resonan Ice, which of course is infinitely sharp and has an infinite propagation length. proportional to kxi, is proportional to Exi and inversely As mentioned, for real metals there is resistive proportional to e We therefore see that while at first scattering and hence damping of the oscillations created sight it may appear beneficial to use small Ezi to give a by the incident E field. This damping causes an sharp resonance, this idea has to be balanced with the imaginary component to E, E; Then with, E2= E2r + iE2i, requirement that we need a large negative value of e Indeed if we examine a range of metals it is clear that erally smallest in the visible of the E1(2x+iE2) (9) spectrum becoming larger as we move to infra-red E1+e2r+lei wavelengths there is an even more rapid increase in errl In figure 2 we illu dependence of both th which for k,=ku +ik i gives, provided k il <kx, with and imaginary parts of the relative permittivities of silver E2r|》E1andE2; and aluminium from the ultra-violet to the infra-red. This shows that both parameters increase in magnitude with ke12(1 wavelength. However, the width of the surface plasmon resonance is, remember, dictated by a/e and since a changes faster than e, there is, almost without exception, a narrowing of the resonance and consequential increase in observability as the wavelength increases. In figure 3 (10b) this ratio is shown for several metals over the visible and Eir near infra-red region of the spectrum. A ratio of the order of 0.2 is the limit of sensible observability for a surface Hence we find the shift in wavevector, Akar, of this plasmon resonance. This leads to the general conclusion surface plasmon resonance from the critical val that while only a few metals such as Ag, Au, Al support a sharp surface plasmon resonance in the visible many more metals support a sharp resonance in the near △kx=kx-e12k-k (11) infra-red. This is illustrated for nickel and platinum in -120 Figure 2. Wavelength dependence TTTTTTT imaginary, Ei, parts of the relative permittivity (E=E, +ie, for gold Wavelength/nm Wavelength/nm and aluminium Compiled from data in references [1] and [21
Optical excitation of surface plasmons prsm 1000 1200 \\thin metal film Wavelength/nm Figure 3. This shows how the surface plasmon resonance width (oE /E varies with wavelength. Many other metals can support sharp resonances as the wavelength of the incident radiation is increased. Compiled from data in references [1] and [2. 4. Coupling to the surface (c) thin dielectric Before moving on to discuss some experimental results thin metal film we need finally to examine how best to couple radiation dielectric to the surface plasmon resonance given that we have Fi clearly established that its momentum is beyond that Figure 4. Geometries used uple photons into a surface available in the dielectric medium adjacent to the metal mode:(a)Otto,(b)Kretschmann-Raether, and(e)mixed hybrid arran Recall that, for our original two-dielectric system eyond the critical angle of incidence there will be an evanescent field in the second half space. This evanescent radiation at the prism/dielectric interface we vary the field does not propagate in the z-direction, but it has momentum in the x-direction and this allows for simple h the resonance. The fo form of the reflectivity is obvious that since sin 0;> sin 0.(= n2/n,), then curve for gold and silver at 632.8 nm is shown in figure n, hk sin 0:>nhk. Hence we have an enhancement 5, where we also show for comparison that for of the x-component of momentum in the second s-polarized light which is, of course, not capable of dielectric half space, above the limit value of nahk for creating the surface plasmon. The position of the a propagating wave. minimum of the resonance which is a measure of the This enhancement of momentum given by n, (sin 8: surface plasmon momentum, is no longer dictated simply sin Oe)hk may be used to couple radiation to a surface by the dielecric/metal boundary for it is additionally plasmon provided it is possible to place the metal/di- perturbed by the presence of the coupling prism electric interface which supports the surface plasmon Likewise the linewidth, which is a measure of damping close enough to the totally internally reflecting interface. is also perturbed by the presence of the prism. As the An obvious geometry to consider is that shown in figure coupling gap is increased so the perturbation by the Is conventionally called the Otto geometry, prism diminishes and the resonance moves to the after Otto who first demonstrated this coupling position corresponding to the two media surface technique in 1968[3]. An air gap (or a spacer of low plasmon and it also narrows. Of course in this index)less than a few radiation wavelengths thick (fo process, illustrated for gold in figure 6, the resonane visible< 2 um) provides the evanescent tunnel barrier progressively shallows. If we wish to achieve we c across which the radiation couples, from the totally coupling then for visible radiation the gap has to be of internally reflecting situation, to excite the surface the order of 0.5 um which for an air gap demands plasmon at the air (dielectric) metal interface. By extreme care in sample fabrication. This constraint is not e angle of incidence of the p-polarized so severe if we choose instead to work in the infra-red
178 I.R. Sambles et al 1·2 S 08 Gold 323334353637383940 Angle/deg Figure 5. Form of the reflectivity, frss fe Coupling gap urve for p-polarised and Reflectivity curves obtained from a palladium film on s-polarised (.=6328mm) thick gold and silver prism(n= 1- 699) using 3 391 um radiation, the films with a prism(n=1·766) asmon occurs at about 45. Coupling gap for (a)is is 0-5 um for gold and 1.0 um for silver. 445 m and for(b)is90μn which normally oxidize[4, 5]. Of course there is no simple manner in which it may be changed to use as a sensor or to optimize coupling at other wavelengths. It is for this reason and also because of the small air gap required for coupling in the visible that the Otto geometry has received rather limited attention over the years Fortunately this has not severely impeded progress in he area of the optical excitation of surface plasmons This is because there is an alternative and much simpler y. Rather than dielectric Gretsch mann and Raether[6] realized that the metal itself could be used as the evanescent tunnel barrier provided it was thin enough to allow radiation to penetrate to the other figure 6. Variation of the surface plasmon resonance (at side. All that is now needed is a prism with a thin coating 0-75 um and(e)1-0 um. The s upling gaps of (a)o-s ymw hes It some suitable metal. This is illustrated in figure 4(6) a= 632. 8 nm) in gold for ce rapidly with increasing gap. It is an easy matter to deposit a thin film(<50 nm)of a metal such as silver or gold on to a prism and create a suitably smooth film which may support a very strong surface plasmon resonance. A typical result for silver in of the spectrum, yet here surprisingly little this geometry is shown in figure 8. The continuous line in mental work has been conducted. We illustrate in this figure is, as in figure 7, the fit obtained using simple 7 results for palladium in this region of the Fresnel reflectivity theory for a 2-interface system. For the Otto geometry the real and imaginary parts of the The spacing problem created by the Otto geometry metal permittivity and the air gap thickness are unknown may be addressed in quite a different manner by using, variables in the fitting procedure, while for the layer(or perhaps a spun polymer). This of course gives are unknown plus the thickness of the metal film. By a non-adjustable gap but at least the fabrication is simple carefully recording data and comparing with theoretic for now it is only necessary to evaporate, on top of the ally generated curves it is possible to obtain useful appropriate thickness dielectric, a thick metal layer to information as regards the dielectric response of the give the resonance. This particular procedure may indeed metal which supports the surface plasmon. (In table I we be very beneficial in the study of protected interfaces as list reported a values for gold and silver using the for example in the case of magnesium or aluminium Kretschmann-Raether technique
Optical excitation of surface plasmons Table 1 Values for the permittivity of gold and silver obtained using surface plasmon excitation in the Kretschmann-Raether geometry Wavelength (nm) Gold 40 030 7 03 8 572 7979 345 124 14 147 90419 79797 159 135 80 -224 1-32 213 750 6 1·57 887878787878787 162 800 0842 20 2 have(in the absence of the prism) the same wavevector. This means that they couple together to give two coupled modes, one which is symmetric in surface charge and the other which is antisymmetric. The first of these modes has very weak electric fields in the metal and is the so-called long range surface plasmon(after Sarid[1on while the second is labelled the short range surface plasmon since it has large fields in the metal and is therefore strongly attenuated through Joule heating. One could choose to examine even more elaborate multi 0-00+ layered structures which support more complex coupled modes but this illustrates no particularly new physics and provides little extra potential for device development Figure 8. Surface plasmon resonance for film using the If we choose to have a non-planar interface then we Kretschmann-Raether geometry. Note this case the are not necessarily restricted to the prism-coupled critical angle is clearly visible at 34.5 olid line shows geometry. One possible technique, a somewhat un- the quality of fit which can be obtained to Fresnel theory satisfactory one, is to study a deliberately roughened interface. If we Fourier analyse the roughness there is 5. Experimental studies likely to be a component that supplies the extra momentum needed to couple radiation directly to the These two types of attenuated total reflection arrange- surface plasmon. While this may yield a broad band ments have formed the basis of most of the studies of optically excited surface plasmons over the past twenty response it is not a very satisfactory interface on which years although more intricate arrangements have also perform carefully controlled scientific experiments. A been devised. For example there are possible hybrid better and more systematic approach is to use a geometries in which a thin metal film is deposited on to diffraction grating with a well specified sinusoidal surface a dielectric spacer layer as illustrated in figure 4(c). This having known wavelength and groove depth. The grooves in the grating surface break the translational gives an Otto type plasmon on the first (dielectric invariance of the interface and allow k, of the outgoing spacer/metal) interface and a Kretschmann-Raether type wave to be different from that of the incoming wave plasmon on the second. If now we add a final overcoating Conservation of momentum now gives in the x direction of dielectric with the same constants as the first(both of course lower than the prism) then the two surface modes k, (outgoing)=k, (incoming)+ NG,(12)
R. Sambles et al theoretical fit which is no longer trivial to generate 080 interface Fresnel equations are no longer usable and a much more elaborate model is needed using a Fourier expansion description of the interface. In the results shown here we have used Chandezon's approach[11] where the sinusoidal surface is transformed into a new frame in which it is flat and in which all radiation fields are expressed in this new frame One entirely new aspect of surface plasmon excitation using grating coupling which is only just beginning to emerge is associated with rotating the grating so that the grooves are no longer perpendicular to the plane of 0-0 110120130140150160170 incidence[ 12]. This breaks the symmetry of the system Angle/deg and has some very exciting implications for the use of Figure 9. Fitted experimental surface plasmon data (i these surface resonances in sensors 632. 8 nm), obtained from a silver coated grating of pitch In the twisted geometry shown in figure 10(a) the 8008 nm and depth 24. 5 nm. The fitted silver film permittivity momentum conserving equation Is. now a two- isE=-1598+j072. dimensional vector equation of the form k sin 0. = ksp NG (14) where= 2x/ig, 2 being the grating wavelength and N an integer. If the grating is relatively shallow(depth 2g) This is illustrated in figure 10(b) for the situation where then kse on the grating surface will be little changed IGAo, Now we from ksp on a planar surface. Thus all we need do to note that ksp is no longer collinear with G and so the excite the surface plasmon on the grating surface is to surface plasmon E fields are no longer just in the plane satisfy the equation of incidence since in propagating across the grooves a k sin 0=ksp±NG (13) tilted component exists on rising up the side or dropping down the other side of a peak, which cannot be in the This then allows direct excitation of the surface plasmon incident plane. Thus we have created's' character in the from the dielectric half-space without imposing con- radiation field associated with the surface plasmon straints upon film thickness or dielectric spacer thickness. Indeed with the angle of twist, equal to 90 we have However now the coupling strength is dictated by the no 'p'coupling to a surface plasmon only '.We groove depth and this is not as readily controlled as the illustrate this fully in figure 11 where we show coupling air gap or the metal film thickness. Typical data for to a silver surface plasmon for both p and s radiation at coupling radiation to a surface plasmon on a silver various angles of twist of the grating. The primary coated grating is given in figure 9. The smooth curve is a implication of this observation is that now we have p to plane of incidence polarizer n beam splitter reference detector in grating coupling. The full circles are the maximum k values obtainable for the zero and +I diffraction orderntum conservation Figure 10. (a)Schematic diagram of grating coupling using a twisted geometry (b) Vector representation of mome
1-0 d=45 0-6 )( 0 d=9 Figure 11. Surface plasmon reso- nance for silver coated grating. Rpe is the relative reflectivity for p-polarized incident and reflected s-polarized radiation. (a)Rop for 00+ 中=0,(b) R for中=45,(c) R,for 15161718192021 Angle/deg. d( dR for中=90.For Angle/deg p=45 both polarizations can couple qually well to the plasmon. A=5()nm o s conve A=7(I nm as a A=750 nm with this grating pitch on increasing A=8 nm the wavelength the maximum conver sion occurs. at smaller angles of
J. R. Sambles et al s conversion via the excitation of the surface plasmon stepped integrally [16]. This then allows determination hence we may record with suitable polarizers a surface of the assumed isotropic relative permittivities and plasmon resonance maximum. This has only very thicknesses of the organic overlayers. A range of different recently been examinated in detail and compared with experiments have also been performed with inorganic theory by developing Chandezon's model further for the overlayers, again to study their dielectric properties. In broken symmetry situation. The maximum p to s a sense this is relatively unexciting; of more interest are conversion occurs with a twist angle of 45 and studies where changes in the overlayer occur. For with the maximum groove depth Results for maximum example the progressive laser-induced desorption of p to s conversion using a surface plasmon on a silver organic films, predeposited onto the active metal layer, coated grating are illustrated in figure 12. These may be studied [17], or the inverse, the condensation observations are particularly exciting because prism through the attractive potential between a volatile coupling, at least for isotropic media, can never provide organic and a metal film may be readily observed[18] the required symmetry breaking, and this therefore opens In the latter case this leads, with careful experimentation. up a new range of potential devices to the determination of the bonding potential of organics on to the metal layer[19]. A variant of monitoring changes in the thickness of overlayers is the study, again 6. Applications by measuring the shift in the resonance position, of the This then brings us to examine the possible exploitation effective relative permittivity of the overlayer as a of this novel surface mode in devices. Perhaps we need consequence of exposure to gas[20]. This technique, with first address the question of why it is of interest at all. the appropriate overlayers has applications in optical gas The basic answer is that the momentum of the surface sensing. Extending this idea, solutions rather than gases plasmon, which is readily monitored by coupling may be placed adjacent to the metal film and then incident radiation to it, is easily changed by thin layers changes in the region of the surface plasmon decay lengt of material deposited on the metal surface[ 13] or by may once again be readily monitored. This opens up small changes in the dielectric constant of the material potential for immunoassay using antigen protein films adjacent to the metal on the metal layer which bind to specific antibodies in One of the simplest studies that may be undertaken is solution[21]. As the antibodies bind to the antigen that of the chemical contamination of the metal the surface plasmon resonance is shifted in angle and a supporting the surface plasmon. For example it is simple, direct optical measure of antigen concentration can be by monitoring the surface plasmon resonance of silver in obtained. In the same context, of fluids adjacent to the the Kretschmann-Raether geometry to observe the active metal surface there are a large range of studies, progressive growth of silver sulphide on exposure to the from optical examination of electrochemical proces- atmosphere. Kovacs[ 14] performed this experiment and ses [22], to studies of liquid crystal alignment [23, 24] and o y monitoring the shift in resonance angle over many more complex processes such as the kinetics of adsoption days found for his particular environment that 2 nm of of block copolymers from solution[251 silver sulphide formed after about thirty days of Currently there is much interest in the use of optical exposure. This is sufficiently slow to allow most excitation of surface plasmons in these and related areas experiments with silver to be conducted in air without of physics, physical chemistry and biophysics. Added to undue concern over this overlayer formation. On the this is a perceived potential for device application in other hand if the same type of experiment were areas other than just sensors. For instance, fibre conducted with a thin film of aluminium the initial polarizers with very high extinction ratios have already exposure to air results in the rapid formation of a been fabricated in which thin metal layers provide the relatively stable aluminium oxide layer some 3 to 4 nm necessary surface plasmon resonance absorption thus thick[15]. While these studies are intrinsically interesting destroying one polarization component[26]. There is there is more interest in deliberately overcoating the also interest in the use of surface plasmon excitation in surface plasmon supporting metal, the active medium, scanning surface microscopy[27]. Small variations in with other types of layers. For example studies have been overlayers on an active metal film are easily converted performed with organic multilayers deposited using the into large differences in reflectivity by setting the system Langmuir-Blodgett technique. By careful control of the at the angle of the surface plasmon excitation and deposition of these layers, well-defined stepped structures scanning across the sample may be fabricated. For these the angular dependent Another area with potential for the use of surface reflectivity for the Kretschmann-Raether geometry plasmons is non-linear optics. The optical excitation of shows a surface plasmon resonance which steps this surface-travelling wave resonance results in strong progressively to a higher angle as the layer thickness is enhancement of the optical field at the surface supporting
