  A fundamental brick of light-matter interaction at large optical intensities
is the generation of a plasma. The optically-induced plasma in turn plays a
fundamental role in determining the optical propagation. The plasma generation
is a result of the interplay between multi-photon, tunnel and avalanche
ionization. Here we use the basic rate equations to discuss an analytical model
for the interaction between these physical effects. After defining a nonlinear
impulse response for the system, we describe how the interplay depends on the
features of the optical pulses. Our approach strongly simplifies the modelling
of the propagation of ultrashort-pulses, paving the way to a much easier and
faster interpretation of experimental observations, with potential impact on
the broad fields of ultrafast light-matter interaction and laser
micro-machining.
