the backward GH shift for the reflected plane wave and the corresponding phase of the reflected wave obtained for $x_m=0.08638$. $\delta_r$ is about $-7814$ at $\theta_i=62.3311^\circ$ in this case. We find that the maximal forward and backward GH shifts occur at the same incident angles where the reflectance takes a minimum value.

![\[fig4\] (a) Normalized GH shift of the reflected beam $\delta_r$ plotted versus $x_m$, for several different values of the half-width $W$ of the incident Gaussian beam when $\theta_i=
62.33^\circ$. (b) Half-width of the reflected beam $W_r$ normalized by $W$ plotted versus $x_m$ for the same values of $W$ and $\theta_i$ as in (a).](fig4){width="8.5cm"}

We now consider the case where Gaussian light beams are incident. In figure 4(a), we plot the normalized GH shift of the reflected beam $\delta_r$ versus $x_m$, for several different values of the half-width $W$ of the incident Gaussian beam. The incident angle is fixed to $\theta_i= 62.33^\circ$. For the displayed range of $x_m$ $\in [0.08, 0.09]$, $d_m$ varies from 50.64 nm to 56.97 nm. The thickness of the dielectric layer, $d_d$, is chosen such that $x_d =
d_d / \lambda = 0.5055$, therefore $d_d$ is equal to 319.98 nm. The specific values of $\theta_i$ 