Perspectives on microwave coupling into cylindrical and spherical rotors with dielectric lenses for magic angle spinning dynamic nuclear polarization.

Continuous wave dynamic nuclear polarization (DNP) increases the sensitivity of NMR, yet intense microwave fields are required to transition magic angle spinning (MAS) DNP to the time domain. Here we describe and analyze Teflon lenses for cylindrical and spherical MAS rotors that focus microwave power and increase the electron Rabi frequency, ν1s. Using a commercial simulation package, we solve the Maxwell equations and determine the propagation and focusing of millimeter waves (198 GHz). We then calculate the microwave intensity in a time-independent fashion to compute the ν1s. With a nominal microwave power input of 5 W, the average ν1s is 0.38 MHz within a 22 μL sample volume in a 3.2 mm outer diameter (OD) cylindrical rotor without a Teflon lens. Decreasing the sample volume to 3 μL and focusing the microwave beam with a Teflon lens increases the ν1s to 1.5 MHz. Microwave polarization and intensity perturbations associated with diffraction through the radiofrequency coil, losses from penetration through the rotor wall, and mechanical limitations of the separation between the lens and sample are significant challenges to improving microwave coupling in MAS DNP instrumentation. To overcome these issues, we introduce a novel focusing strategy using dielectric microwave lenses installed within spinning rotors. One such 9.5 mm OD cylindrical rotor assembly implements a Teflon focusing lens to increase the ν1s to 2.7 MHz within a 2 μL sample. Further, to access high spinning frequencies while also increasing ν1s, we analyze microwave coupling into MAS spheres. For 9.5 mm OD spherical rotors, we compute a ν1s of 0.36 MHz within a sample volume of 161 μL, and 2.5 MHz within a 3 μL sample placed at the focal point of a novel double lens insert. We conclude with an analysis and discussion of sub-millimeter diamond spherical rotors for time domain DNP at spinning frequencies >100 kHz. Sub-millimeter spherical rotors better overlap a tightly focused microwave beam, resulting in a ν1s of 2.2 MHz. Lastly, we propose that sub-millimeter dielectric spherical microwave resonators will provide a means to substantially improve electron spin control in the future.