Numerical study of transient absorption saturation in single-layer graphene for optical nanoscopy applications

Transient absorption, or pump-probe microscopy is an absorption-based technique that can explore samples ultrafast dynamic properties and provide fluorescence-free contrast mechanisms. When applied to graphene and its derivatives, this technique exploits the graphene transient response caused by the ultrafast interband transition as the imaging contrast mechanism. The saturation of this transition is fundamental to allow for super-resolution optical far-field imaging, following the reversible saturable optical fluorescence transitions (RESOLFT) concept, although not involving fluorescence. With this aim, we propose a model to numerically compute the temporal evolution under saturation conditions of the single-layer graphene molecular states, which are involved in the transient absorption. Exploiting an algorithm based on the fourth order Runge-Kutta (RK4) method, and the density matrix approach, we numerically demonstrate that the transient absorption signal of single-layer graphene varies linearly as a function of excitation intensity until it reaches saturation. We experimentally verify this model using a custom pump-probe super-resolution microscope. The results define the intensities necessary to achieve super-resolution in a pump-probe nanoscope while studying graphene-based materials and open the possibility of predicting such a saturation process in other light-matter interactions that undergo the same transition.