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The nonlinear optical(NLO)studies of porphyrins(Cu,Zn,H2MHTP)and their covalently linked composites with graphene oxide(GO)have been studied by numerically solving the rate equations and field intensity equation with an iterative predictor-corrector finite-difference time-domain(FDTD)technique [1] in picosecond(ps)time domain.A simple three-level scheme is introduced to illustrate the two-photon absorption(TPA)mechanism and our numerical results show that GO-porphyrin composites show enhanced nonlinear absorption properties compared with individual porphyrin molecules due to the strong electron acceptor capability of the GO molecule,which match quite well with the experimental results [2].Moreover,our initial results clearly demonstrate that the thickness of the absorber as well as the pulse duration plays key roles on the TPA cross section of the medium.