Nonlinear Chirp Sequence for Broadband \(\pi \) Rotation Using Hyperbolic Secant Pulse

This article introduces an approach to implement a wide-range \(\pi \) rotation in nuclear magnetic resonance (NMR) spectroscopy using nonlinear chirp pulse sequences. The rotation pulse sequences consist of hyperbolic-secant (HS) pulses and are specifically designed to serve as efficient refocusing pulse elements in spin echo sequences. The composite pulse sequences are composed of three pulse elements, which undergo adiabatic full passage at specific rates chosen to compensate phase distortion incurred. We explore various combinations of these HS pulse sequences, all of which achieve a broadband \((\pi )_y\) rotation. The theory behind these composite hyperbolic secant pulse sequences is detailed, along with simulations and experimental results. For experimental implementation, we employ phase modulated pulse sequences and the experimental measurements are performed on a \({750\,\mathrm{\text {M}\text {Hz}}}\) spectrometer using a sample consisting of \(99.5\%\ \text {D}_2\text {O}\) and \(0.5\%\ \text {H}_2\text {O}\).