Enhancement of four reflection shifts by a three-layer surface-plasmon resonance

We investigate the effect of a surface-plasmon resonance on Goos-Hänchen and Imbert-Fedorov spatial and angular shifts in the reflection of a light beam by considering a three-layer system made of glass, gold, and air. We calculate these spatial and angular shifts as functions of the incidence angle showing that they are strongly enhanced in correspondence with the resonant angle. In particular, we find giant spatial and angular Goos-Hänchen shifts for the $p$-wave light close to the plasmon resonance. We also predict a similar but less pronounced resonant effect on spatial and angular Imbert-Fedorov shifts for both $s$-wave and $p$-wave light.

Figure 1

Upper panel: Reflectivity $R_{\alpha }$ as a function of the incident angle $\theta$ for $s$-wave ($\alpha =s$, dashed line) and $p$-wave ($\alpha =p$, solid line) monochromatic light. Lower panel: Same as upper panel, but for the phase ${\varphi }_{\alpha }$ of the reflection coefficient $r_{\alpha }=R_{\alpha }^{1/2}{e}^{i{\varphi }_{\alpha }}$. For both panels: Three-layer system with a gold film of thickness $d=30$ nm as glass-air interface and light with wavelength $\lambda =830$ nm.

Figure 2

$p$-wave reflectivity $R_p$ as a function of the incident angle $\theta$ for monochromatic light for four values of the thickness $d$ of the gold film. Three-layer system with a gold film as glass-air interface and light with wavelength $\lambda =830$ nm.

Figure 3

Upper panel: Goos-Hänchen spatial shift ${\Delta }_{\alpha }^{\mathrm{GH}}$ as a function of the incident angle $\theta$ for $s$-wave ($\alpha =s$, dashed line) and $p$-wave ($\alpha =p$, solid line) monochromatic light. Lower panel: Same as upper panel, but for the Goos-Hänchen angular shift ${\Theta }_{\alpha }^{\mathrm{GH}}$. For both panels: Three-layer system with a gold film of thickness $d=30$ nm at glass-air interface and light with wavelength $\lambda =830$ nm. ${\theta }_0$ is the angular spread of the incident beam.

Figure 4

Upper panel: Imbert-Fedorov spatial shift ${\Delta }_{\alpha }^{\mathrm{IF}}$ as a function of the incident angle $\theta$ for $s$-wave ($\alpha =s$, dashed line) and $p$-wave ($\alpha =p$, solid line) monochromatic light of wavelength $\lambda =830$ nm. Lower panel: Same as upper panel, but for the Imbert-Fedorov angular shift ${\Theta }^{\mathrm{IF}}$. For both panels: Three-layer system with a gold film of thickness $d=30$ nm at glass-air interface and light with wavelength $\lambda =830$ nm. ${\theta }_0$ is the angular spread of the incident beam.