which lies on a dielectric substrate, at room temperature. Both the prism and the substrate are assumed to have the same refractive index of 1.77 corresponding to sapphire. The refractive index of the dielectric layer is 1.46 corresponding to fused silica (${\rm SiO_2}$). Then the critical incident angle $\theta_c$ is equal to $55.57^\circ$. The vacuum wavelength of the incident wave $\lambda$ is 633 nm and the dielectric permittivity of the metal layer $\epsilon_m$ is $-16+i$ corresponding to silver at $\lambda =
633$ nm. In figure 1, we show the schematic of our configuration. We note that we have a propagating wave in the substrate in the present geometry.

![\[fig2\] GH shift normalized by the wavelength, $\delta_r = \Delta_r /
\lambda$, of the reflected wave calculated from Artmann’s formula for plane waves when $\theta_i= 62.33^\circ$ plotted versus the thickness of the metal layer normalized by the wavelength, $x_m = d_m / \lambda$.](fig2){width="8.5cm"}

We first consider the case where plane waves are incident. In figure 2, we plot the GH shift normalized by the wavelength, $\delta_r = \Delta_r /
\lambda$, of the reflected wave calculated from Artmann’s formula for plane waves versus the thickness of the metal layer normalized by the wavelength, 