Discovery of Slot Plasma Excitations in a AlGaN/GaN Plasmonic Crystal

Abstract

We experimentally investigate the terahertz spectrum of plasma excitations in a plasmonic crystal based on AlGaN/GaN two-dimensional electron system (2DES). While screened plasmon modes with linear dispersion are readily observed in the plasmonic crystals, the existence of unscreened modes localized in the slots between the gates has remained unobserved until now. We discover this slot plasma excitation exhibiting square-root dispersion. It turned out that these slot plasmons follow an unconventional wave-vector quantization rule, $q_u=(N + 1/4) \times π/l_u$ for even integers $N$, and require the condition for excitation $q_u h \ll 1$, where $h$ is the gate-to-2DES distance and $l_u$ is the slot width. We develop an analytical model that accurately captures the found dispersion and relaxation, revealing a non-trivial $-π/4$ phase shift upon plasmon reflection at the gate edge. Experiments demonstrate that the slot plasmons persist up to room temperature, thereby enabling a broad range of opportunities for the advancement of plasmonic devices.

Figures (5)

• Figure 1: A schematic of the plasmonic crystal.
• Figure 2: Transmission spectra of the plasmonic crystal for various grid filling factors $f=0.38, 0.46, 0.70, 0.77$ and $0.82$, corresponding to slot widths $l_u = 5.0, 4.3, 2.4, 1.8$, and $1.4$ µm, respectively. The crystal period is fixed at $p = 8$ µm. The arrows point to the frequency positions of the $N=2$ slot plasmon mode. The inset displays transmission spectra for three samples with identical slot widths $l_u = 4.0$ µm, but different periods: $p = 8$ µm (green curve), $12$ µm (red curve), and $24$ µm (purple curve).
• Figure 3: Frequency of the fundamental slot‑plasmon mode ($N=2$) versus the inverse slot width, $1/l_u$. Solid red dots: experimental resonance frequencies. Solid red line: theory from Eq. (\ref{['plasmon']}) using the wave vector $q_u=(2 \pi + \pi/4)/l_u$. Dashed red line: Eq. (\ref{['plasmon']}) with standard quantization rule $q_u = 2 \pi/l_u$. Empty symbols: the frequencies of the screened plasmon modes with $M=1$ (empty purple dots), $M=3$ (empty blue dots), and $M=5$ (empty green dots). Straight lines: theoretical prediction from Eq. (\ref{['scr_plasmon']}) with $q_g=M \times \pi/l_g$.
• Figure 4: (a) Representative transmission spectra for crystals with equal ungated and gated widths $l_u=l_g=12$ µm (red) and $l_u=l_g=8$ µm (blue), showing the fundamental slot mode and its higher‑frequency harmonics. (b) Squared resonance frequency $f_N^2$ plotted versus mode index $N$. The linear dependence confirms the unscreened plasmon dispersion [Eq. (\ref{['plasmon']})]. Experimentally observed bright resonances correspond to even mode indices $N = 2, 4, 6, 8$. The data reveal a nontrivial phase offset of 1/4 in the mode sequence.
• Figure 5: (a) Dependence of the fundamental slot‑plasmon quality factor $Q$ on the dimensionless parameter $q_u h$. Experimental data (points) and the best fit of $Q \sim 1/\sqrt{q_u h}$ (solid blue curve) are shown. $Q$ increases as the wave vector $q_u$ decreases. (b) Temperature dependence of the transmission spectra for the plasmonic crystal with $l_u=4$ µm and $l_g=6$ µm, measured at $T = 5, 125, 200$ and $295$ K.