Time-Domain Measurements of Reflection Delay in Frustrated Total Internal Reflection

We present experimental evidence that the contribution of the Goos-Hänchen shift to tunneling delay is suppressed in frustrated total internal reflection. We use a Hong-Ou-Mandel interferometer to perform direct time measurements of reflection delays with femtosecond resolution at optical frequencies, and take advantage of a liquid-crystal-filled double-prism structure to dynamically change the refractive index of the barrier region.

Figure 1

Diagram of the double-prism system. In (a) a liquid crystal cell is sandwiched between two glass equilateral prisms. An exploded diagram of the liquid crystal cell is shown in (b), with the liquid crystal (LC), indium tin oxide (ITO) layer and polyimide alignment (PI) layer labeled.

Figure 2

Abbreviated setup diagram showing FTIR measurements in the reflection geometry. Panel (a) shows the Hong-Ou-Mandel arrangement and placement of components. PDC is the parametric down-conversion crystal, CC is a corner cube retroreflector, BS is a nonpolarizing $50/50$ beam splitter, IF are 10-nm bandpass interference filters centered at 727 nm, APD are avalanche photodiode single-photon counting modules. Inset (b) shows a detailed view of the FTIR region, with two prisms of index $n_{\mathrm{glass}}$ and a barrier region of liquid crystals with an effective index $n_{\mathrm{eff}}$ due to the applied voltage $V$. Inset (c) shows an example data trace containing a Hong-Ou-Mandel dip, along with a numerical Gaussian fit.

Figure 3

Reflection delay in FTIR from a double-prism barrier system. The black line is the arithmetic mean of four individual data sets, shown in colored dots. Each data point represents an individual Hong-Ou-Mandel trace with 102 seconds of integration time.

Figure 4

Predicted $\partial {\Phi }_R/\partial \omega$ based on the $4\times 4$ matrix method described in the text for 727-nm light propagating through an 8-micron liquid crystal cell. The parameters used are $\theta =63.5°$, $n_{\mathrm{glass}}=1.77$, $n_e=1.63$, and $n_o=1.54$.