insight review articles The second consequence of the interaction between the surface lectromagnetic field is that, gating nature of SPs along the surface, the field perpendicular to the surface decays exponentially with distance from the surface. The field in this perpendicular direction is said to be evanescent or near field in nature andisaconsequence of the bound, non-radiative nature ofSPs, which prevents power from propagating away from the surface There are three main techniques by which the missing momentum can be provided. The first makes use of prism coupling to enhance the omentum of the incident light. The second involves scattering rom a topological defect on the surface, such as a subwavelength pro- erate use ora perl iodic corrugation in the metal surface". Indeed, over 100 years ago, Woodreported anomalous behaviourin the diffraction of light by metallic diffraction grating some of these phenomena are now known to arise from coupling to SPs. The diffraction(scattering) of light by a metallic diffraction g 0.8 matched and thus coupled to SPs". Importantly the reverse process also allows the otherwise non-radiative SP mode to couple with light in a controlled way with good efficiency which is vital if SP-based photonic circuits are to Surface plasmon propagation Once light has been convertedintoan SP mode on flat metal surface it will propagate but will gradually attenuate owing to losses arising from absorption in the metal. This attenuation depends on the dielectric function of the metal at the oscillation frequency of the SP The propagation length, Ssp can be found by seeking the imaginary ksp=ksp+ik sP, from the SP dispersion equation(1)(ref. 15). 1cEm+Edz(em) 2ksp o EmEd) am (2) wherea mandE"mare the real andimaginary partsof the dielectric func tionofthe metal, thatis, E ie' Silver isthe metal with the low est losses in the visible spectrum: propagation distances are typically in the range 10-100 um, increasing towards 1 mm as one moves into the .5 umnear-infrared telecom band(see Box 2). In the past, absorption by the metal was seen as such a significant problem that SPs were not considered viable forphotonicelements: the SP propagationlength was Figure 1 An SPwaveguide. a, a scanning electron micrograph image of a 40nm smaller than the size of components at that time. This view is now thick, 2.5 um wide gold stripe lying on a glass substrate(courtesy of J.C.Weeber. anging thanks primarily to recent demonstrations of SP-based com- Universite de Bourgogne,, France). b, The optical functionality of the stripe visualized nents that are significantly smaller than the propagation length". by PSTM: an extended SP, launched on the larger area by a spot (indicated by the red Such developments open the way to integrate many SP-based devices ellipse)generated by total internal reflection illumination(wavelength=800 nm) into circuits before propagation losses become toosignificant. through the substrate, is used to excite one af the stripes SP eigen modes featuring In addition to dealing with the problem of loss owing to absorp- three maxima. The photon scanning tunneling microscopy(PSTM) image tion in the metal, there is another key loss mechanism that must demonstrates that SPs are bound to the metaL. C, A crOSs-section across the stripe considered: unwanted coupling to radiation. To build SP-based cir- shows that this mode is much better confined to the guiding materal!(indicated by the cuits one will need components that convert one SP mode into AFM topology--pale blue line) sustaining the mode than would be the case in another, for example, a switch to re-route SPs without scattering the dielectric-based waveguides. Not only the height of the guide but also the square root SP mode insuch a way as tolose its energy to freely propagating light. of the waveguide cross-section features a subwavelength size, underlining the fact that the SP mode is essentially bound to the metal surface rather than being a Surface plasmon band structure and periodic surfaces standing wave confined inside the metal volume. One of the key developments inphotonicsin the past 15 years has been that of photonic bandgap(PBG)materials. These synthetic materials elength-scale periodicstructures to manipulate the interaction When the period of the nanostructure is half that of the effective wave between light and matter so as to build new photonic structures-a lengthof the SP mode, scattering may lead to the formation of SP stand- good example being that of the photonic crystal fibre.These develop- ing waves and the opening of an SP stop band2 (see Box 3).When the ments have been predominantly made in periodically structured insu- surface is modulated in bothin-plane directions, for example by a peri lating and semiconducting materials. By making use ofSPs, metals too odic array of bumps, SP modes may be prevented from travelling in an be used as PBG materials, this time in the form of photonic sur- in-plane direction, thus leading to a full PBG for SP modes( Fig. 2) faces Fig 2 provides a nice demonstration of how the problems associated The nature of SPs changes when they propagate on metal surfaces with absorption by the metal can be overcome. It shows that, although that are periodically textured on the scale of the wavelength of light. finite, the SP propagation lengths more than enough to allow the SPto NatuRevOl42414AugUst2003www.nature.com/nature e 2003 Nature Publishing Group 825The second consequence of the interaction between the surface charges and the electromagnetic field is that, in contrast to the propa￾gating nature of SPs along the surface, the field perpendicular to the surface decays exponentially with distance from the surface. The field in this perpendicular direction is said to be evanescent or near field in nature and is a consequence of the bound, non-radiative nature of SPs, which prevents power from propagating away from the surface. There are three main techniques by which the missing momentum can be provided. The first makes use of prism coupling to enhance the momentum of the incident light10,11. The second involves scattering from a topological defect on the surface, such as a subwavelength pro￾trusion or hole, which provides a convenient way to generate SPs locally3,12. The third makes use of a periodic corrugation in the metal’s surface13. Indeed, over 100 years ago, Wood14 reported anomalous behaviour in the diffraction of light by metallic diffraction gratings— some of these phenomena are now known to arise from coupling to SPs. The diffraction (scattering) of light by a metallic diffraction grat￾ing allows incident light to be momentum matched and thus coupled to SPs15. Importantly the reverse process also allows the otherwise non-radiative SP mode to couple with light in a controlled way with good efficiency16,17, which is vital if SP-based photonic circuits are to be developed. Surface plasmon propagation Once light has been converted into an SP mode on a flat metal surface it will propagate but will gradually attenuate owing to losses arising from absorption in the metal. This attenuation depends on the dielectric function of the metal at the oscillation frequency of the SP. The propagation length, dSP, can be found by seeking the imaginary part, k88SP, of the complex surface plasmon wavevector, kSP4k8SP&ik88SP, from the SP dispersion equation (1) (ref. 15), (2) where ;8mand ;88mare the real and imaginary parts of the dielectric func￾tion of the metal, that is, ;m4;8m&i;88m. Silver is the metal with the low￾est losses in the visible spectrum: propagation distances are typically in the range 10–100 mm, increasing towards 1 mm as one moves into the 1.5 mm near-infrared telecom band (see Box 2). In the past, absorption by the metal was seen as such a significant problem that SPs were not considered viable for photonic elements; the SP propagation length was smaller than the size of components at that time. This view is now changing thanks primarily to recent demonstrations of SP-based com￾ponents that are significantly smaller than the propagation length18. Such developments open the way to integrate many SP-based devices into circuits before propagation losses become too significant. In addition to dealing with the problem of loss owing to absorp￾tion in the metal, there is another key loss mechanism that must be considered: unwanted coupling to radiation. To build SP-based cir￾cuits one will need components that convert one SP mode into another, for example, a switch to re-route SPs without scattering the SP mode in such a way as to lose its energy to freely propagating light. Surface plasmon band structure and periodic surfaces One of the key developments in photonics in the past 15 years has been that of photonic bandgap (PBG) materials. These synthetic materials use wavelength-scale periodic structures to manipulate the interaction between light and matter so as to build new photonic structures—a good example being that of the photonic crystal fibre19. These develop￾ments have been predominantly made in periodically structured insu￾lating and semiconducting materials. By making use of SPs, metals too can be used as PBG materials, this time in the form of photonic sur￾faces20. The nature of SPs changes when they propagate on metal surfaces that are periodically textured on the scale of the wavelength of light. δSP == ( ) 1 2kSP" εmεd ' εm + εd c ' ω 3 2 εm" εm' 2 ( ) When the period of the nanostructure is half that of the effective wave￾length of the SP mode, scattering may lead to the formation of SP stand￾ing waves and the opening of an SP stop band21 (see Box 3). When the surface is modulated in both in-plane directions, for example by a peri￾odic array of bumps, SP modes may be prevented from travelling in any in-plane direction, thus leading to a full PBG for SP modes20,22 (Fig. 2). Fig. 2 provides a nice demonstration of how the problems associated with absorption by the metal can be overcome. It shows that, although finite, the SP propagation length is more than enough to allow the SP to insight review articles NATURE | VOL 424 | 14 AUGUST 2003 | www.nature.com/nature 825 KSP 30 µm Normalized intensity Normalized intensity 0 0.2 5 10 15 0.4 0.6 0.8 1 y (µm) a b c 0.4 0.2 0 0 5 10 15 5 10 15 x (µm) x (µm) Figure 1 An SP waveguide. a, a scanning electron micrograph image of a 40 nm thick, 2.5 mm wide gold stripe lying on a glass substrate (courtesy of J. C. Weeber, Université de Bourgogne, France). b, The optical functionality of the stripe visualized by PSTM; an extended SP, launched on the larger area by a spot (indicated by the red ellipse) generated by total internal reflection illumination (wavelength=800 nm) through the substrate, is used to excite one of the stripe’s SP eigen modes featuring three maxima. The photon scanning tunnelling microscopy (PSTM) image demonstrates that SPs are bound to the metal. c, A cross-section across the stripe shows that this mode is much better confined to the guiding material (indicated by the AFM topology—pale blue line) sustaining the mode than would be the case in dielectric-based waveguides. Not only the height of the guide but also the square root of the waveguide cross-section features a subwavelength size, underlining the fact that the SP mode is essentially bound to the metal surface rather than being a standing wave confined inside the metal volume. © 2003 Nature PublishingGroup