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 IG< ksp or since kspl -|1-05kI then 2g>Ao, 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