Plasmonic Time Crystals

We study plasmonic time crystals, an extension of dielectric-based photonic time crystals to plasmonic media. Remarkably, we demonstrate that such systems may amplify both longitudinal and transverse modes. In particular, we show that plasmonic time crystals support \emph{collective resonances} of longitudinal modes, which occur independently of the wave vector $k$, even in the presence of significant dissipation. These resonances originate from the coupling between the positive- and negative-frequency branches of the plasmonic dispersion relation of the unmodulated system and from the divergence of the density of states near the plasma ($\varepsilon$-near zero) frequency $\omega_p$. The strongest resonance arises at a modulation frequency $\Omega = 2 \omega_p$, corresponding to a direct interband transition. We demonstrate these resonances for various periodic modulation profiles and provide a generic perturbative formula for resonance widths in the weak modulation limit. Furthermore, we propose transparent conducting oxides as promising platforms for realizing plasmonic time crystals, as they enable significant modulation of the electron effective mass while maintaining moderate dissipation levels. Our findings provide new insights into leveraging time-modulated plasmonic media to enhance optical gain and control wave dynamics at the nanoscale.