Generating accurate tip angles for NMR outside the rotating-wave approximation

TL;DR

This paper investigates how to generate accurate tip angles in low-field NMR where the rotating-wave approximation fails, proposing strategies involving phase-dependent shifts and pulse shaping validated by simulations and experiments.

Contribution

It introduces methods to correct tip angles outside the rotating-wave approximation using phase-dependent Bloch-Siegert shifts and pulse shaping, supported by simulations and low-field NMR experiments.

Findings

Phase-dependent Bloch-Siegert shift can correct tip angles.

Pulse shaping reduces deviations from expected trajectories.

Strategies improve accuracy of NMR in low static fields.

Abstract

The generation of accurate tip angles is critical for many applications of nuclear magnetic resonance. In low static field, with a linear rather than circular polarized rf field, the rotating-wave approximation may no longer hold and significant deviations from expected trajectories on the Bloch sphere can occur. For rectangular rf pulses, the effects depend strongly on the phase of the rf field and can be further compounded by transients at the start and end of the pulse. The desired terminus can be still be achieved, however, through the application of a phase-dependent Bloch-Siegert shift and appropriate consideration of pulse timings. For suitably shaped rf pulses, the Bloch-Siegert shift is largely phase independent, but its magnitude can vary significantly depending on details of the pulse shape as well as the characteristics of the rf coil circuit. We present numerical simulations and low-field NMR experiments with 1H and 3He that demonstrate several main consequences and accompanying strategies that one should consider when wanting to generate accurate tip angles outside the validity of the rotating-wave approximation and in low static field.