The scattering problem for a phase-modulated hyperbolic secant pulse

Abstract

The hyperbolic secant pulse has been found to have remarkable properties when used as a radio frequency pulse in nuclear magnetic resonance. The author computes explicitly the scattering data corresponding to this pulse as the potential in a Zakharov-Shabat system. The author finds that, once again, one is in the presence of some exceptional localisation properties. These features should be a good guide in the study of the inverse problem that results when one tries to design a specific pulse in order to achieve a specified spin profile.