What is the best planar cavity for maximizing coherent exciton-photon coupling

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.