The use of analytical and numerical techniques in solving the coupling of evanescent modes in a microwave waveguide through slots can be optimized to create a uniform magnetic field excitation on axis within a waveguide. This work has direct applications in Electron Paramagnetic Resonance (EPR) where a 100 kHz time-varying magnetic field is incident on a sample contained in a microwave cavity. Typical cavity designs do not take into consideration the uniformity of the 100 kHz field modulation and assume it to be uniform enough over the sample region from quasi-static principles. This work shows otherwise and uses Ansoft (Pittsburgh, PA) High Frequency Structure Simulator (HFSS; version 12.0) and analytical dyadic Green's functions to understand the coupling mechanisms.

The techniques described in this work have shown that electromagnetic modes form in a rectangular and cylindrical waveguide domain even at frequencies a number of orders of magnitude below the waveguide cut-off frequencies. With slot thicknesses very small compared to a wavelength, Born's first approximation must be modified to account for a near field secondary wave. Additionally, mutual coupling between multiple slots has been shown to influence the overall magnetic field profile down the axis of the waveguide and in certain circumstances becomes more complex from interactions outside of the domain of the dyadic Green's functions.

A cylindrical TE01U cavity resonant at W-band (94 GHz) is proposed where both the microwave magnetic field and, from this work, the 100 kHz time-varying magnetic field incident on the sample are uniform. This type of resonator is highly desirable in EPR experiments where inhomogeneity of magnetic fields affect signal purity. With the technology outlined in this work, experiments where a uniform field modulation amplitude is swept over the entire spectra to obtain pure absorption is feasible. This work advances the cutting edge of resonator design and enables new experiments to be performed at high field EPR.