Fig. 3: Verification of temporal Snell’s law, Fresnel equations, and momentum conservation.
From: Experimental realization of temporal refraction and reflection in elastic beams
a The measured frequencies of the incident (squares) and reflected (circles) signals at x/L = 0.05, and the refracted signal (crosses) observed at x/L = 1, plotted against the incident frequency f0. The top (bottom) panel represents the results for the switch from ON to OFF (from OFF to ON). b Normalized frequencies of the refracted and reflected waves, along with the theoretical prediction of Snell’s law (dashed line). The top (bottom) panel represents the results for the switch from ON to OFF (from OFF to ON). c The measured ratio of the tangent of the refraction angle (\({\eta }_{1}=\tan {\alpha }_{1}\)) to the tangent of the incidence angle (\({\eta }_{0}=\tan {\alpha }_{0}\)), along with the measured ratio of the tangent of the reflection angle (\({\eta }_{1}^{{\prime} }=\tan {\alpha }_{1}^{{\prime} }\)) to the tangent of the incidence angle, is compared with the theoretical prediction based on Snell’s law (represented by the dashed line). The top (bottom) panel represents the results for the switch from ON to OFF (from OFF to ON). d The measured and theoretical magnitudes of the refraction coefficient (top panel) and reflection coefficient (bottom panel) at t/tf = 2/3 for the switch from ON to OFF, plotted against the incident frequency f0. e The measured and theoretical magnitudes of the refraction coefficient (top panel) and reflection coefficient (bottom panel) at t/tf = 2/3 for the switch from OFF to ON, plotted against the incident frequency f0. f The ratio of momentum before and after the temporal interface, along with the theoretical prediction based on momentum conservation (shown as the dashed line). The top panel shows the results for the switch from ON to OFF, while the bottom panel corresponds to the switch from OFF to ON.
