Abstract

The generation of an optical breather in coherent, resonant pulse propagation is studied. The initial field envelope is assumed to be in the form of a hyperbolic secant, with one half inverted so that the total area of the pulse is equal to zero. The Maxwell–Bloch equations for an inhomogeneously broadened atomic line are solved by the inverse-scattering method for all values of the independent variables x and t. The scattering amplitudes are found for any value θ of the absolute area of the initial pulse. For θ = 2πn the reflection coefficients are rational functions of the spectral parameter, and the inverse problem can be solved exactly. It is shown that the x-dependent poles of the reflection coefficients are responsible for the transient pulse shape. Such poles appear only in the presence of inhomogeneous broadening. The threshold for transparency is found at θ = 2π. At this value of the area, a breatherlike decaying solution is obtained. At θ = 4π a breather appears. Its energy amounts to approximately 70% of the initial pulse energy. For θ = 2π and 0 = 4π the solutions are analyzed in detail.

© 1989 Optical Society of America

Collisions of counterpropagating optical solitons

Michael J. Shaw and Bruce W. Shore
J. Opt. Soc. Am. B 8(5) 1127-1134 (1991)

Hamiltonian dynamics of breathers with third-order dispersion

Shayan Mookherjea and Amnon Yariv
J. Opt. Soc. Am. B 18(8) 1150-1155 (2001)

Quantum-nondemolition measurement of optical solitons

H. A. Haus, K. Watanabe, and Y. Yamamoto
J. Opt. Soc. Am. B 6(6) 1138-1148 (1989)

Power-series solutions to the optical Maxwell–Bloch equations

Ljubomir Matulic and Christopher Palmer
J. Opt. Soc. Am. B 6(3) 356-363 (1989)

Hamiltonian dynamics of dispersion-managed breathers

J. Nathan Kutz, Philip Holmes, Stephen G. Evangelides, and James P. Gordon
J. Opt. Soc. Am. B 15(1) 87-96 (1998)