The two-level atom model describes the absorption or amplification of an
incident light field due to a dipole coupled resonant or near-resonant
interaction with two quantum states of an atom or molecule. Figure 3(a) depicts
a schematic of a two-level atom energy levels. An incident photon of energy
, whose frequency 
is close to the two-level atom
transition frequency 
, may be absorbed
or amplified, depending on whether the atom is initially in the lower
energy level ( 
) or upper energy level ( 
), respectively. The
dynamics of population transfer between the two quantum levels is described
by the two-level optical Bloch equations[3]
where, 
is the off-diagonal density matrix element,
is the population difference between the lower
and upper states, p is the dipole moment in the field direction,
and 
and 
are phenomenological damping
constants for the population and polarisation, respectively.
The initial inversion density 
determines whether the two-level material
is an absorber 
or an amplifier 
. The case of a strongly
absorbing nonlinear interface will be discussed under the heading of the
dynamic nonlinear optical skin effect in Section 3.3. The damping coefficients
and are strongly material dependent and the physics
of the coupling will also depend on whether the optical pulse duration
is longer or shorter than the inverse of these decay rates. When
we have the phenomenon of self-induced
transparency (SIT) where the optical pulse appears to pass through the material
unattenuated. What in fact happens is that the optical pulse and material
oscillation exchange energy back and forth in a coherent fashion giving rise
to an SIT soliton[11].