A unified theory for surface emitting chirped circular grating lasers

We develop a unified theory to analyze the modal properties of surface emitting chirped circular grating lasers. Based on solving the resonance conditions which involve two types of reflectivities of chirped circular gratings, this theory is both easy to understand and convenient to apply to different configurations of circular grating lasers. Though in a more concise format, this approach is shown to be in agreement with previous derivations which use the characteristic equations. With this unified analysis, the modal properties of circular DFB, disk-, and ring- Bragg resonator lasers are obtained and compared.