Effect of a conductive layer on Fabry-Pérot resonances

Using terahertz spectroscopy, we investigate resonant transmission through a dielectric slab with a conducting layer of varied mobility on one side. We observe the well-known Fabry-Pérot resonances in the transmission. Two fundamentally different regimes of the electrodynamic response of the system are established. In the clean limit, when the radiation frequency exceeds the carrier relaxation rate, $\omega \tau \gg 1$, the system exhibits a plasmonic response. As a result, there is a continuous shift in the Fabry-Pérot resonances with respect to the system parameters. By contrast, in the dirty regime, when $\omega \tau \ll 1$, there is an abrupt $\pi$ shift in the resonance frequency, as the renormalized film resistance matches the impedance of free space. We find that under this condition, Fabry-Pérot oscillations disappear entirely over a broad frequency range. Such a matching effect might be of interest in various terahertz applications, for example, involving broadband filters or absorbers.

Figure 1

Top panel: Schematics of the experimental setup. Bottom panel: Fabry-Pérot resonance frequency $\omega /{\omega }_d$ as a function of the retardation parameter $A$. The inset depicts transmission data for three GaAs samples: $d=0.2$ mm without 2DES (black circles, $A=0$); $d=0.19$ mm, $n_s=6.4\times {10}^{12}{\text{cm}}^{-2}$ (blue circles, $A=1.7$); and $d=0.65$ mm, $n_s=6.4\times {10}^{12}{\text{cm}}^{-2}$ (red circles, $A=3.1$). For clarity, the curves are offset vertically by one unit.

Figure 2

Frequency dependence of the transmission through silicon samples with chromium films of different conductivities. The high-resistivity silicon substrate has the thickness $d=0.4$ mm (${\varepsilon }_{\mathrm{Si}}=11.7$), and the Cr film thickness is varied in the range of $8–40$ nm. The impedance matching phenomenon is observed at ${\sigma }_s/\left({\varepsilon }_{0}c\right)\approx 2.35$, where the Fabry-Pérot resonances exhibit a $\pi$ shift. The curves are plotted without offset.

Figure 3

Fabry-Pérot resonance frequency $\omega /{\omega }_d$ plotted as a function of the chromium layer conductivity, ${\sigma }_s/\left({\varepsilon }_{0}c\right)$. Experimental data do not include $N=0$ Fabry-Pérot resonance due to the frequency restriction in the terahertz quasioptical setup.