  We investigate the microwave magnetic field confinement in several microwave
3D-cavities, using 3D finite-element analysis to determine the best design and
achieve strong coupling between microwave resonant cavity photons and solid
state spins. Specifically, we design cavities for achieving strong coupling of
electromagnetic modes with an ensemble of nitrogen vacancy (NV) defects in
diamond. We report here a novel and practical cavity design with a magnetic
filling factor of up to 4 times (2 times higher collective coupling) than
previously achieved using 1D superconducting cavities with small mode volume.
In addition, we show that by using a double-split resonator cavity, it is
possible to achieve up to 200 times better cooperative factor than the
currently demonstrated with NV in diamond. These designs open up further
opportunities for studying strong and ultra-strong coupling effects on spins in
solids using alternative systems with a wider range of design parameters.
