A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR

TL;DR

This paper introduces a continuous Floquet-based framework for designing and analyzing solid-state NMR pulse sequences, enabling reverse engineering of experiments from desired effective Hamiltonians without relying on periodic Hamiltonian assumptions.

Contribution

It extends Floquet theory to non-periodic Hamiltonians using perturbation theory in continuous Fourier space, allowing for reverse design of NMR pulse sequences.

Findings

Framework successfully models non-periodic Hamiltonians in solid-state NMR.

Enables calculation of pulse schemes from target Hamiltonian behaviors.

Demonstrated with MIRROR experiment to optimize rf irradiation based on chemical-shift offsets.

Abstract

We present a framework that uses a continuous frequency space to describe and design solid-state NMR experiments. The approach is similar to the well established Floquet treatment for NMR, but is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behaviour of the sequence.