Lateral Plasmonic Superlattice in Strongly Dissipative Regime

We study transmission of terahertz radiation through lateral plasmonic superlattice with a unit cell consisting of two regions with different plasma wave velocities, $${{s}_{1}}$$ and $${{s}_{2}}$$ ( $${{s}_{1}} > {{s}_{2}}$$ ). We generalize theory, developed earlier for resonant case, to the non-resonant regime, assuming that the scattering rate, $$\gamma ,$$ is large compared to fundamental gate-tunable frequencies $${{\omega }_{{1,2}}}$$ of plasma oscillations in both regions. We describe evolution of transmission coefficient, $$\mathcal{T},$$ with increasing of radiation frequency, identify several dissipation regimes, construct general diagram describing all these regimes, and find corresponding analytical expressions for $$\mathcal{T}.$$ Most importantly, $$\mathcal{T}$$ sharply depends on the gate voltages, which control velocities $${{s}_{{1,2}}}$$ , and on frequency. In particular, for $${{\omega }_{2}} \ll {{\omega }_{1}}$$ transmission $$\mathcal{T}$$ strongly varies on very small frequency scale, $$\delta \omega \ll \gamma ,$$ determined by the Maxwell relaxation, $$\delta \omega \sim \omega _{1}^{2}{\text{/}}\gamma ,$$ so that the superlattice shows very high responsivity within the narrow frequency interval. Unexpected appearance of a narrow peak deep in the non-resonant regime is a universal phenomenon and can also be observed in a number of other photoelectric effects.