Multipole-multimode Floquet theory in nuclear magnetic resonance

In this paper, we present a new analytical approach for describing the spin dynamics of synchronous and asynchronous time-dependent modulations in solid-state nuclear magnetic resonance experiments. The approach, based on multimode Floquet theory, employs the multipole operator basis of Sanctuary for spin description and illustrates the time evolution in the Floquet-Liouville space using the effective Hamiltonians obtained from the contact (or van Vleck) transformation procedure. Since the Hamiltonian and the density operator are expressed in terms of irreducible tensor operators, extensions to higher spin magnitudes (I>12) and multiple spins are quite straightforward and permit analytical treatments for many problems. We outline the general underlying principles involved in this approach with a brief mention of its potential application in other branches of spectroscopy.