Pulse amplitude modulation

Inverse scattering techniques are used to investigate the
propagation in an amplifier of a coherent optical pulse
whose initial profile is a left-truncated hyperbolic secant
of area A such that 0< A< 4pi. A two-level nondegenerate
medium is assumed and dissipative effects are neglected. In the limit of extreme inhomogeneous broadening, the exact
solution for the pulse is obtained, and it is found to
evolve into a pi-pulse (for A< 2pi) at the light cone which
exhibits the expected amplification and compression, and
(for 2pi< A<.... 4pi) the above Ti-pulse plus a phase-shifted 2pi
soliton of lesser velocity whose amplitude and width is
related to a zero of the transmission coefficient in the
associated scattering problem. This final area of 3pi is in
agreement with the area theorem of McCall and Hahn.

An exactly solvable model is constructed of amplification
of a coherent optical pulse in the extreme Doppler limit.
The pulse so obtained exhibits the expected evolution
toward a pi pulse with pulse amplification and compression,
but differs from the pulse analyzed previously by G. L.
Lamb in that it possesses a continuous leading edge.