  Higgs modes emerge in superconductors as collective excitations of the order
parameter amplitude when periodically driven by electromagnetic radiation. In
this work, we develop a Floquet approach to study Higgs modes in
superconductors under time-periodic driving, where the dynamics of the order
parameter is captured by anomalous Floquet Green's functions. We show that the
Floquet description is particularly powerful as it allows one to exploit the
time-periodic nature of the driving, thus considerably reducing the complexity
of the time-dependent problem. Interestingly, the Floquet approach is also
enlightening because it naturally offers a physical explanation for the
renormalized steady-state order parameter as a result of photon processes
between Floquet sidebands. We demonstrate the usefulness of Floquet engineering
Higgs modes in time-periodic $s$-wave superconductors.
