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.