  A great deal of theoretical and experimental efforts have been devoted in the
last decades to the study of long-wavelength photodetection mechanisms in
field-effect transistors hosting two-dimensional (2D) electron systems. A
particularly interesting subclass of these mechanisms is intrinsic and based on
the conversion of the incoming electromagnetic radiation into plasmons, which
resonantly enhance the photoresponse, and subsequent rectification via
hydrodynamic nonlinearities. In this Article we show that such conversion and
subsequent rectification occur well beyond the frequency regime in which
hydrodynamic theory applies. We consider the nonlinear optical response of
generic 2D electron systems and derive pseudo-Euler equations of motion for
suitable collective variables. These are solved in one- and two-dimensional
geometries for the case of graphene and the results are compared with those of
hydrodynamic theory. Significant qualitative differences are found, which are
amenable to experimental studies. Our theory expands the knowledge of the
fundamental physics behind long-wavelength photodetection.
