
Beam Trapping and Filaments 209
nonlinear polarization. The condition for the existence of a temporal soliton
is that (anomalous) dispersion
ik
2
∂
2
∂t
2
balances self-temporal lensing (positive
SPM)
in
2
k
n
0
|E|
2
˜
E. Normal dispersion and a negative SPM can also lead to soliton
solutions [71].
3.9. BEAM TRAPPING AND FILAMENTS
Once the beam power is sufficient for self-focusing to overcome diffraction,
the beam collapses to a point. In general, after the beam has collapsed, it diffracts.
However, numerous experiments have shown self-guiding of high peak power
infrared femtosecond pulses through the atmosphere [72–77]. Similar observa-
tions were made in the