Transformation cavities with a narrow refractive index profile

Recently, gradient index cavities, or so-called transformation cavities, designed by conformal transformation optics, have been studied to support resonant modes with both high -factors and emission directionality. We propose a new, to the best of our knowledge, design method for transformation cavities to realize a narrower width of the refractive index profile, a great advantage in experimental implementations, without losing the benefits of conformal mapping. We study resonant modes with both high -factors and directional emission in newly designed transformation cavities, where the refractive index profile is 50% narrower than in previously proposed transformation cavities. By varying a system parameter with a fixed maximal value of the refractive index profile inside the cavity, the width of the refractive index profile narrows, the -factors become higher, and the near and far field patterns maintain their properties, namely, conformal whispering gallery modes and bidirectional emission, respectively.