1 research outputs found
Matched Pulse Propagation in a Three-Level System
The B\"{a}cklund transformation for the three-level Maxwell-Bloch equation is
presented in the matrix potential formalism. By applying the B\"{a}cklund
transformation to a constant electric field background, we obtain a general
solution for matched pulses (a pair of solitary waves) which can emit or absorb
a light velocity solitary pulse but otherwise propagate with their shapes
invariant. In the special case, this solution describes a steady state pulse
without emission or absorption, and becomes the matched pulse solution recently
obtained by Hioe and Grobe. A nonlinear superposition rule is derived from the
B\"{a}cklund transformation and used for the explicit construction of two
solitons as well as nonabelian breathers. Various new features of these
solutions are addressed. In particular, we analyze in detail the scattering of
"invertons", a specific pair of different wavelength solitons one of which
moving with the velocity of light. Unlike the usual case of soliton scattering,
the broader inverton changes its sign through the scattering. Surprisingly, the
light velocity inverton receives time advance through the scattering thereby
moving faster than light, which however does not violate causality.Comment: 20 pages, Latex, 12 eps figure files some comments and references are
added. postscript file with 12 figures can be obtained at
http://photon.kyunghee.ac.kr/~qhpark