  A number of experiments have evidenced signatures of enhanced superconducting
correlations after photoexcitation. Initially, these experiments were
interpreted as resulting from quasi-static changes in the Hamiltonian
parameters, for example, due to lattice deformations or melting of competing
phases. Yet, several recent observations indicate that these conjectures are
either incorrect or do not capture all the observed phenomena, which include
reflection coefficient exceeding unity, large shifts of Josephson plasmon
edges, and appearance of new peaks in terahertz reflectivity. These
observations can be explained from a generic perspective of a periodic drive of
system parameters. However, the origin of underlying oscillations remains
unclear. In this paper, we demonstrate that oscillations at a well-defined
frequency are generally expected in superconductors with low-energy Josephson
plasmons following an incoherent pump. The origin of these oscillations is the
parametric generation of plasmon pairs arising from pump-induced perturbation
of the superconducting order parameter. We show that this bi-plasmon response
can persist above the transition temperature as long as strong superconducting
fluctuations are present. Our analysis applies to layered cuprate
superconductors, with low-frequency $c$-axis plasmons, and isotropic materials
such as K$_3$C$_{60}$, which also have a small plasmon gap. We discuss the
relation of our findings to previously observed features of nonequilibrium
superconductors and argue that bi-plasmons can be detected directly using
currently available experimental techniques.
