damping [@Liu; @Okamoto2]. As the thickness of the dielectric or metal layer is varied, the GH shift becomes positive if the intrinsic damping (absorption loss in the lossy layer) is less than the radiative damping (leakage from the dielectric layer to the prism), and negative otherwise. Our result is consistent with this argument, since the intrinsic damping is inversely proportional to the thickness of the metal layer [@Okamoto2]. Thus the reduction of $d_m$ enhances the intrinsic damping, resulting in the negative GH shift in figure 4(a).

Zeller [*et al.*]{} have also performed a theoretical analysis of the reflection coefficient associated with $s$-polarized SPPs in the Otto configuration containing a layer of a negative-index metamaterial instead of a metal layer [@Zeller3]. They have found that the sign of the GH shift changes from negative to positive as the thickness of the dielectric layer, $d_d$, increases.

In figure 4(b), we plot the half-width of the reflected beam $W_r$ normalized by $W$ versus $x_m$. This value takes a maximum at $x_m
\approx 0.08647$ for $W =  320$, 160 and 80 $\mu$m. The thickness for the maximum $W_r/W$ increases slightly to $x_m = 0.08683$ for $W =
10$ $\mu$m. Thus the maximum distortion of 