  We propose and design photonic crystal cavities (PCCs) in hexagonal boron
nitride (hBN) for diverse photonic and quantum applications. Two dimensional
(2D) hBN flakes contain quantum emitters which are ultra-bright and photostable
at room temperature. To achieve optimal coupling of these emitters to optical
resonators, fabrication of cavities from monolithic hBN is therefore required,
to maximize the overlap between cavity optical modes and the emitters. Here, we
design 2D and 1D PCCs using anisotropic indices of hBN. The influence of
underlying substrates and material absorption are investigated, and spontaneous
emission rate enhancements are calculated. Our results are promising for future
quantum photonic experiments with hBN.
