Micro-resonator loss computation using conformal transformation and active-lasing FDTD approach and applications to tangential/radial output waveguide optimization I: Analytical approach

Understanding the physics of the loss mechanism of optical microresonators is important for one to know how to use them optimally for various applications. In these three-paper series, we utilized both analytical method (Conformal Transformation Approach) and numerical method (Active-Lasing Finite-Difference Time-Domain method) to study the resonator loss and cavity quality Q factor and apply them to optimize the radial/tangential waveguide coupling design. Both approaches demonstrate good agreement in their common region of applicability. In Part I, we review and expand on the conformal transformation method to show how exact solution of radiation loss for the case of cylindrical micro-resonator under both TE and TM polarizations can be obtained. We show how the method can be extended to apply to microdisk case.