Semi-Analytical Representation of the Two-Dimensional Time-Domain Green's Function of a Graphene Sheet in the Intraband Regime

The 2-D time-domain Green's function of a graphene sheet is here derived, by assuming a local Drude-like model for the graphene conductivity valid in the absence of biasing magnetic fields and when both spatial-dispersion effects and interband terms are negligible (i.e., up to the low terahertz range). The sought Green's function is derived in a semi-analytical form through a modified Cagniard-De Hoop approach. This allows for deriving simple semi-analytical expressions for the fields radiated by a pulsed line source in the presence of a graphene sheet, which can be computed in a fast and straightforward way. Theoretical and numerical validations are presented by obtaining the known results for nondispersive metallic sheets as limiting cases and through comparisons with results obtained numerically through an exact canonical double inverse Fourier transform.