  The hallmark of superconductivity is the rigidity of the quantum-mechanical
phase of electrons, responsible for superfluid behavior and Meissner effect.
The strength of the phase stiffness is set by the Josephson coupling, which is
strongly anisotropic in layered superconducting cuprates. So far, THz light
pulses have been efficiently used to achieve non-linear control of the
out-of-plane Josephson plasma mode, whose frequency scale lies in the THz
range. However, the high-energy in-plane plasma mode has been assumed to be
insensitive to THz pumping. Here, we show that THz driving of both
low-frequency and high-frequency plasma waves is possible via a general
two-plasmon excitation mechanism. The anisotropy of the Josephson couplings
leads to marked differences in the thermal effects among the out-of-plane and
in-plane response, consistently with the experiments. Our results link the
observed survival of the in-plane THz non-linear driving above $T_c$ to
enhanced fluctuating effects in the phase stiffness in cuprates, paving the way
to THz impulsive control of phase rigidity in unconventional superconductors.
