Single-pulse echo and oscillatory free induction decay: The importance of rephasing

Abstract

The response observed after application of a large-area pulse to an inhomogeneously broadened spin system is analysed in this paper. Particular attention has been devoted to the elucidation of the complex physical mechanisms underlying the single-pulse experiment. The theoretical analysis has been split into three steps. First, the evolution of a generic isochromatic subset of the spin system is calculated by the density-operator formalism. Then, general properties of the macroscopic response are derived from the structure of the expressions describing the coherent signal emitted by each isochromatic subsystem. Finally, numerical simulations of the response are carried out for a large variety of experimental conditions and are explained by reference to the developed theory. It is found that the response comprises three partial signals, namely two free induction decays (FIDs) and one true single-pulse echo, resulting from three different coherence transfer pathways occurring during the experiment. The very first part of the response is the FID arising from the spins which have been locked by the pulse. The other FID is usually negligible. The variety of patterns observed in the response is due to the widely different shapes taken on by the single-pulse echo when the experimental conditions are varied. For off-resonance excitation, the echo is an oscillating signal with a smooth bell-shaped envelope, well separated in time from the locked FID. In the case of on-resonance excitation, the echo is a long oscillating signal, which is already known as oscillatory FID.