  We report on the observation of a nonlinear intensity dependence of the
terahertz radiation induced ratchet effects in bilayer graphene with asymmetric
dual grating gate lateral lattices. These nonlinear ratchet currents are
studied in structures of two designs with dual grating gate fabricated on top
of encapsulated bilayer graphene and beneath it. The strength and sign of the
photocurrent can be controllably varied by changing the bias voltages applied
to individual dual grating subgates and the back gate. The current consists of
contributions insensitive to the radiation's polarization state, defined by the
orientation of the radiation electric field vector with respect to the dual
grating gate metal stripes, and the circular ratchet sensitive to the radiation
helicity. We show that intense terahertz radiation results in a nonlinear
intensity dependence caused by electron gas heating. At room temperature the
ratchet current saturates at high intensities of the order of hundreds to
several hundreds of kWcm$^{-2}$. At $T = 4 {\rm K}$, the nonlinearity manifests
itself at intensities that are one or two orders of magnitude lower, moreover,
the photoresponse exhibits a complex dependence on the intensity, including a
saturation and even a change of sign with increasing intensity. This complexity
is attributed to the interplay of the Seebeck ratchet and the dynamic carrier
density redistribution, which feature different intensity dependencies and a
nonlinear behavior of the sample's conductivity induced by electron gas
heating. Our study demonstrates that graphene-based asymmetric dual grating
gate devices can be used as terahertz detectors at room temperature over a wide
dynamic range, spanning many orders of magnitude of terahertz radiation power.
Therefore, their integration together with current-driven read-out electronics
is attractive for the operation with high-power pulsed sources.
