  We compare alternative planar cavity structures for strong exciton$-$photon
coupling, where the conventional distributed Bragg reflector (DBR) and three
unconventional types of cavity mirrors$-$ air/GaAs DBR, Tamm $-$ plasmon mirror
and sub$-$wavelength grating mirror. We design and optimize the planar cavities
built with each type of mirror at one side or both sides for maximum vacuum
field strength. We discuss the trade$-$off between performance and fabrication
difficulty for each cavity structure. We show that cavities with
sub$-$wavelength grating mirrors allow simultaneously strongest field and high
cavity quality. The optimization principles and techniques developed in this
work will guide the cavity design for research and applications of
matter$-$light coupled semiconductors, especially new material systems that
require greater flexibility in the choice of cavity materials and cavity
fabrication procedures.
