Double layered transformation cavities: Crossover between local and global transformations

We study the resonant modes in double-layered transformation cavities consisting of inner and outer layer boundaries where the mode intensity is mainly located inside the inner layer. This is an intermediate design between a transformation cavity and a cavity in a wholly transformed space of transformation optics. We demonstrate the crossover between these two extreme cases as the outer layer of the cavity varies and also explore the properties of the resonant modes in the cavity. While the near-field patterns of the resonant modes do not change as the outer layer becomes larger, the Q-factors approach those of a cavity in the wholly transformed space of transformation optics, and the far-field patterns are modified.