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

We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it 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 behavior of the sequence. (C) 2022 Author(s).

Automated summary

We propose a framework that utilizes a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. This approach allows reverse engineering of experiments and is based on perturbation theory in a continuous Fourier space, resulting in time-independent effective Hamiltonians. The pulse scheme can be back-calculated from the desired effective Hamiltonian as a function of spin-system parameters. An example is provided to demonstrate how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.