When the intensity of the incident field is high enough, material
breakdown can occur via plasma generation. Plasma can be produced via
an avalanche process[9] whereby free electrons are accelerated by the
incident light field, causing an explosive cascade growth in electron
density. The generated plasma can, in turn, absorb and defocus the remaining
incident light field (plasma shielding). Of course the plasma itself
can shock causing mechanical rupture of the material. This effect is
particularly important in causing irreversible retinal damage following
exposure to ultrashort intense optical pulses. Multiphoton ionization is
another source of plasma formation which depends instantaneously on the
local light intensity, unlike avalanche ionization which is a cumulative
growth effect. A simple model for plasma
generation is an extension of the Drude model where the growth of
electron density 
is given by[10]
The positive integer K is the order of the multiphoton transition and
simply determines the number of energy quanta ( 
) needed to
offset the bound electronic ground state energy of the material from the onset
of its continuous spectrum (ionization potential). For example, in water
at a wavelength of 
, K = 3. The fact that the order of
the multiphoton ionization is a sensitive function of laser wavelength
proves to be very important in measuring its influence on plasma generation
versus that of the avalanche process. The first term on the RHS is the
avalanche contribution which depends on the integrated pulse energy. The
second term describes a multiphoton ionization source and the third radiative
recombination. The multiphoton ionization term also acts as a source
of free electrons
for the avalanche process. The above plasma equation coupled to the NLS
equation describes the simultaneous occurrence of critical collapse and
plasma generation which will be discussed further in Section 3.1.2 below.