Analysis of All-Optical Generation of Graphene Surface Plasmons by a Frequency-Difference Process

The generation of graphene surface plasmons (SPs) by a frequency-difference nonlinear (NL) process caused by the interaction of two optical beams was experimentally demonstrated several years ago by measuring the differential reflectance of the probe beam. However, the understanding of these results requires much larger second-order optical conductivities of graphene than calculations performed so far can yield. In this work, we carefully calculate the relevant NL conductivities and show that, indeed, the experimental observations of the differential reflectance must have originated from physical processes beyond the coherent frequency-difference generation of SPs described by the density-matrix perturbation theory approach, presumably by hot-electron effects. We also suggest an alternative way of detecting optically generated SPs, which can be feasible at lower powers of the optical pulses. Such additional experiments are expected to help understand the remaining discrepancy between the theory and the existing experimental data.