Time symmetry: an application to shaped pulse excitation of spin-1 systems

The role of time symmetry in the design of amplitude-modulated (shaped) pulses for spin-1 excitation is examined. The quaternion calculus is used to calculate the quaternion elements (Euler–Rodrigues parameters) of each shaped pulse. In this manner, it is shown how the simplicity and compactness of the Euler–Rodrigues parametrization can be used to significantly expedite a computer search for optimal time-symmetric shaped pulses. Theoretical and experimental tests of a new class of symmetric quadrupole-shaped (SQUASH) pulses identified by this procedure show a significant improvement in both excitation bandwidth and efficiency in comparison to the time-asymmetric QUASH shaped pulse previously identified.