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