  We present a Floquet scheme for the ab-initio calculation of nonlinear
optical properties in extended systems. This entails a reformulation of the
real-time approach based on the dynamical Berry-phase polarisation [Attaccalite
& Gr\"uning, PRB 88, 1-9 (2013)] and retains the advantage of being
non-perturbative in the electric field. The proposed method applies to
periodically-driven Hamiltonians and makes use of this symmetry to turn a
time-dependent problem into a self-consistent time-independent eigenvalue
problem. We implemented this Floquet scheme at the independent particle level
and compared it with the real-time approach. Our reformulation reproduces
real-time-calculated $2^{nd}$ and $3^{rd}$ order susceptibilities for a number
of bulk and two-dimensional materials, while reducing the associated
computational cost by one or two orders of magnitude.
