The application of spinors to pulse synthesis and analysis

We show how spinors may be used to solve many problems in pulse synthesis and analysis. They provide an elegant simple notation for many problems. We show how one can specify the component of a spinor and then, by exactly solving the Bloch equations, synthesize a hard pulse sequence or a soft pulse which will yield the desired spinor. This is done by generalizing our previous approach to inverting the Bloch equations. This can be applied to synthesizing refocusing pulses. Finally, some simple consequences about symmetric pulses are derived. It is shown that given a symmetric inversion pulse, one can always synthesize an asymmetric inverting pulse of the same duration, which, as an inversion, is better.