Physical Mechanisms of Spin Echoes. I. Two-pulse Locked Echo

The locked echo is the result of the application, to an inhomogeneously-broadened system, of a pulse sequence consisting of a short ?/2 pulse, a free evolution period of length r and a long pulse with high turning angle (HTA). In this paper the nature and features of the signal detected after such a pulse sequence are reported upon by analysing the underlying physical mechanisms in the framework of the density operator formalism. It is found that the total signal does not contain any contribution from Free Induction Decay (FID)-like or anti-echo signals but comprises a group of several distinct echoes: the true simultaneous locked echo, arising from locked magnetization, and two or three non-simultaneous, oscillatory echoes similar to those observed in the single-pulse experiment. Properties of these echoes are deduced from the structure of the density operator at the end of the experiment. Extensive numerical simulations provide independent evidence of the correctness of the developed theory, display the variety of patterns shown by the locked echo when experimental conditions are changed, and also permit one to investigate the locked echo shape beyond the approximations introduced in the theory.