  We calculate transmission coefficient, $\mathcal T,$ 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, when the scattering rate, $\gamma,$ is large compared to fundamental
gate-tunable frequencies $\omega_{1,2}$ of plasma oscillations in both regions.
We find that absorption, and consequently $\mathcal T$, strongly depends on
density modulation amplitude and on the frequency of the incoming radiation. We
describe evolution of the absorption with increasing of radiation frequency
from the quasi-static regime of very low frequency to the high-frequency
regime, identify several dissipation regimes and find analytical expression for
absorption, and, accordingly, for $\mathcal T,$ in these regimes. A general
phase diagram of non-resonant regime in the plane $(\omega,\omega_2)$ for fixed
$\omega_1$ is constructed. Most importantly, $\mathcal T$ sharply depends on
the gate voltages and frequency. In particular, for $\omega_2 \ll \omega_1,$
$\mathcal T$ strongly varies on the very small frequency scale, $\delta \omega
\ll \gamma,$ determined by the Maxwell relaxation, $\delta \omega \sim
\omega_1^2/\gamma,$ so that the superlattice shows high responsivity within the
frequency band $\delta \omega.$
