Unconventional quantization of 2D plasmons in cavities formed by gate slots

Abstract

We demonstrate that the slot between parallel metal gates placed above two-dimensional electron system (2DES) forms a plasmonic cavity with unconventional mode quantization. The resonant plasmon modes are excited when the slot width $L$ and the plasmon wavelength $λ$ satisfy the condition $L = λ/8 +n \times λ/2$, where $n=0, 1, 2 \ldots$. The lowest resonance occurs at a surprisingly small cavity size, specifically one eighth of the plasmon wavelength, which contrasts with the conventional half-wavelength Fabry-Perot cavities in optics. This unique quantization rule arises from a non-trivial phase shift of $-π/4$ acquired by the 2D plasmon upon reflection from the edge of the gate. The slot plasmon modes exhibit weak decay into the gated 2DES region, with the decay rate being proportional to the square root of the separation between the gate and the 2DES. Absorption cross-section by such slots reaches $\sim 50$ % of the fundamental dipole limit without any matching strategies, and is facilitated by field enhancement at the metal edges.

Figures (4)

• Figure 1: (a) Schematic illustration of a slot-induced resonator for 2D plasmons. The panel also shows the electric field distributions for the three lowest bright cavity modes, excited by an incident plane wave. (b) Schematic illustration of the waves that emerge after the reflection of a plasma wave at the gate edge.
• Figure 2: Reflection of the 2D plasmon at a single gate edge. (a) Magnitude of the reflection coefficient and (b) its phase, both plotted as functions of the normalized gate-2DES separation $k_0 \, d$, where $k_0$ is the free-space wave vector. Different colors correspond to different values of 2DES conductivity, $\eta$, which is assumed purely imaginary ($\{\eta' = 10^{-5}\} \ll \eta"$). Insets show the amplitude and phase of reflection in the non-retarded limit, which depend now only on gate-2DES separation normalized by ungated plasmon wave vector $q_ud$
• Figure 3: (a) The spectrum of absorption cross section $A$ normalized at free-space wavelength as function of slot width $L$. The dashed curves show the slot plasmon modes frequencies (Eq. \ref{['eq-eigenmodes-freqs']}) as function of the slot width $W$ obtained analytically. (b) The linewidth of the plasmon modes $n=0, 2, 4$ calculated analytically using Eq. \ref{['eq-eigenmodes-freqs2']} (dashed curves) and fitted from the simulations data (solid curves).
• Figure 4: The spectrum of absorption cross section $A$ normalized at free-space wavelength $\lambda_0$ as function of $L$ in case of oblique incident wave (incidence angle angle $\alpha=\pi/3$). The dashed and solid curves show the analytically calculated frequencies of the even and odd plasmon modes, respectively.