  We present a framework to calculate the anisotropic and non-linear
photoconductivity for two band systems with application to graphene. In
contrast to the usual perturbative (second order in the optical field strength)
techniques, we calculate photoconductivity to all orders in the optical field
strength. In particular, for graphene, we find the photoresponse to be giant
(at large optical field strengths) and anisotropic. The anisotropic
photoresponse in graphene is correlated with polarization of the incident
field, with the response being similar to that of a half-wave plate. We predict
that the anisotropy in the simultaneous measurement of longitudinal
($\sigma_{xx}$) and transverse $(\sigma_{yx})$ photoconductivity, with four
probes, offers a unique experimental signature of the photo-voltaic response,
distinguishing it from the thermal-Seebeck and bolometric effects in
photoresponse.
