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This paper presents the modeling and design of a photonic crystal (PhC) cavity in gallium nitride on sapphire. Using the 3D finite difference time domain method, we explore the suitability of asymmetric dielectric layer structures as a platform for L3 PhC cavities. The paper explores the origin of losses and modification to the cavity modes introduced by asymmetric layers. Based upon this analysis, a cavity design is proposed, which is optimized to provide enhancement for fluorescent molecule detection. A central air hole in the cavity allows the positioning of molecules in a high field region. Also, the hole modifies the cavity modes to have a smaller mode volume. Both of these properties are used to simultaneously enhance the absorption and spontaneous emission of fluorescent molecules.