Searches for dark matter axions involve the use of microwave resonant cavities operating in a strong magnetic field. Detector sensitivity is directly related to the cavity quality factor, which is limited, until recently, to the use of non-superconducting metals by the presence of the external magnetic field. In this paper, we present a cavity of novel design whose quality factor is not affected by a magnetic field. It is based on a photonic structure by the use of sapphire rods. The quality factor at cryogenic temperature is in excess of 5 × 105 for a selected mode.