Coherent excitation with phase-incremented pulses.

Abstract

An outline is given for calculating the evolution of a spin system by a pulse sequence with phase-incremented pulses (PIPs). It is done in a frame with a speed of 2pideltaf=deltaphi/deltatau relative to the rotating frame, where deltaphi and deltatau are the phase- and time-increment of the PIP. This particular frame is defined as the eigenframe, in which the phase of the PIP for the center band is stationary and is subjected to a universal phase shift (UPS=-deltaphi/2), and the strength of the PIP is scaled by a factor of lambda=2[1-cos(deltaphi)]/(deltaphi). The phase differences between different eigenframes can be attributed to the initial phases of the PIPs, making it possible to use the Bloch vector model even in different eigenframes. A new way is provided to construct composite pulses with not only amplitude and phase modulations but also offset modulation. Several examples, including a broadband inversion pulse, a Hahn spin echo, and a selective inversion and null pulse, all composed of PIPs, are discussed in detail.