  We propose a new class of optical resonator structures featuring one or two
metasurface reflectors or metacavities and predict that such resonators support
novel hyperbolic resonances. As an example of such resonances we introduce
hyperbolic Tamm plasmons (HTPs) and hyperbolic Fabry-Perot resonances (HFPs).
The hyperbolic optical modes feature low-loss incident power re-distribution
over TM and TE polarization output channels, clover-leaf anisotropic
dispersion, and other unique properties which are tunable and are useful for
multiple applications.
