  We analyze the performance of graphene microstructures as thermal photon
detectors and deduce the range of parameters that define a linear response. The
saturation effects of a graphene thermal detector that operates beyond the
linear range are described in detail for a single-photon detector
(calorimeter). We compute the effect of operating beyond this linear range and
find that sensitive detection occurs for such non-linear operation. We identify
the optimum conditions and find that single-photon detection at terahertz (THz)
frequencies should be feasible.
