Exploring the limits of broadband excitation and inversion pulses

The design of broadband excitation and inversion pulses with compensation of B₁-field inhomogeneity is a long standing goal in high resolution NMR spectroscopy. Most optimization procedures used so far have been restricted to particular pulse families to keep the scale of the problem within manageable limits. This restriction is unnecessary using efficient numerical algorithms based on optimal control theory. A systematic study of rf-limited broadband excitation by optimized pulses and broadband inversion by optimized pulses with respect to bandwidth and B₁-field is presented. Upper limits on minimum pulse lengths are set for different degrees of pulse performance.