Fig. 2

RF profile and simulation of BADCOP1. a The shaped pulse “BADCOP1” RF amplitude and phase profiles. Note that there are no abrupt changes in amplitude or phase. On an 800 Mhz spectrometer the maximum power is 5.94 kHz (100% amplitude) and the duration is 1 ms. For other field strengths, these values can be scaled appropriately to maintain the same bandwidths and flip angles. b Simulation assuming an initial state of ρ(0) = I_x. We see sinusoidal chemical shift encoding in the transverse plane for the C^α region. This behavior was explicitly built into the optimization. Outside of the C^α region off-resonance effects take over and the encoding is lost. c Simulation assuming an initial state of ρ(0) = I_y also shows encoding. By linearity, the pulse is producing a universal rotation about the z-axis for the C^α region, with rotation angle proportional to chemical shift frequency. d Simulation assuming an initial state of ρ(0) = I_z. The longitudinal magnetization is inverted for all CO and for C^β below about 35 p.p.m. This leads to selective decoupling of resonances in these two regions. The pulse can be run in the middle of an arbitrary-duration indirect encoding period to refocus resonances, without inducing any Bloch–Siegert shifts