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.
