Nonlinear couplings between photons and electrons in new materials give rise to a wealth of interesting nonlinear phenomena [1]. This includes frequency mixing, optical rectification or nonlinear current generation, which are of particular interest for generating radiation in spectral regions that are difficult to access, such as the terahertz gap. Owing to its specific linear dispersion and high electron mobility at room temperature, graphene is particularly attractive for realizing strong nonlinear effects [2]. However, since graphene is a centrosymmetric material, second-order nonlinearities a priori cancel, which imposes to rely on less attractive third-order nonlinearities [3]. It was nevertheless recently demonstrated that dc-second-order nonlinear currents [4] as well as ultrafast ac-currents [5] can be generated in graphene under optical excitation. The asymmetry is introduced by the excitation at oblique incidence, resulting in the transfer of photon momentum to the electron system, known as the

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We implement a Maxwell-Bloch simulation for a two-level system within the finite-difference time-domain method to simulate the seeding of lasers by broadband pulse injection. The model does not make the slowly varying envelope approximation, and the full electromagnetic field is simulated so that we are able to obtain time-resolved seeding by few-cycle pulses. The model is compared to recent results on seeding of THz quantum cascade lasers to aid in the interpretation of their complex signals. The simulations are found to be in good agreement with the data when gain recovery times of 15 ps are used. Furthermore, we find that the emission from the laser depends only weakly on the seed used to initiate laser action. The model is readily applicable to any seeded laser system where few-cycle seed pulses are used.