The ultrafast optical switching phenomena in a dense medium of two-lev
el atoms induced by arbitrary varying pulses are explained in terms of
the adiabatic cancellation of the pulse by the induced polarization.
The final population inversion of the medium after the passage of the
pulse is found to depend on the number of oscillations the inversion e
xhibits during the time interval when the normalized pulse amplitude e
xceeds the maximum allowed value of the atomic polarization. If the in
version undergoes an integer number of oscillations in this region, th
en the final state of the system returns to the ground state. On the o
ther hand, if the inversion undergoes a half integer number of oscilla
tions in this region, the final state of the system is fully inverted.
This behavior is explored analytically and illustrated numerically fo
r the constant, sine and secant pulse shapes.