Effects of arbitrary laser or NMR pulse shapes on population inversion and coherence

Abstract

We present a new perturbation expansion for calculating the effects of arbitrary pulse shapes in two-level systems, even when the effects are grossly nonlinear. The first two terms have simple physical interpretations. This expansion converges rapidly for all values of resonance offset with simple shapes, and for any pulse shape far from resonance. We generate very simple, symmetric, single phase pulse shapes which produce uniform inversion or polarization and which can be combined into multiple pulse sequences. We also show that pulse shape modification is superior to construction of composite pulse sequences, since such sequences must become erratic far from resonance.