Mechanism of chirp excitation

Abstract

In design of a chirp inversion pulse, we keep the sweep rate a≪ω12, where ω1 is the amplitude of the pulse. This is the adiabaticity condition for the inversion to work. We can convert a chirp inversion pulse to an excitation pulse by keeping the chirp rate high, with a>ω12. To be precise a=2.8ω12. The analysis of such a pulse breaks the evolution into three phases. The first and third phase are adiabatic phases while the second phase is non-adiabatic. Starting from north pole such a pulse brings the magnetization to equator, however there is a nonuniform phase which depends on the resonance offsets. We show how by following this pulse with a chirp inversion pulse at twice the sweep rate of excitation pulse, we can refocus this uniform phase. We find there is still some phase dispersion. This can be further eliminated by bringing in a second inversion pulse. The combination of these three chirp pulses allows us to excite arbitrary large bandwidth without increasing the peak amplitude of the pulse. Refocusing properties of pair of chirp has been studied before but our description is very different.