On Maxwell-Bloch systems with inhomogeneous broadening and one-sided nonzero background (Q6585693)

The authors present a formulation of the inverse scattering transform for two-level systems with inhomogeneous broadening and one-sided nonzero background. The formalism combines some ideas of the inverse scattering transform with zero background with those from the inverse scattering transform with symmetric, non-zero background. The authors show that the reflection coefficient is always non-zero, so no reflectionless solutions exist. They also analyze the asymptotic behavior of the reflection coefficient for large \(z\); namely, they determine conditions under which the reflection coefficient decays exponentially as \(z\to\infty\). Moreover, it is shown that two different asymptotic regimes arise for the optical pulse, depending on which limit one considers: either \(z\to\infty\) and \(t\) finite or \(t\to\infty\) with \(z\) finite. In an appropriate limit, this formalism reduces to the one with zero background.