Butterfly-like phase shift: a novel gauge for critical coupling of add–drop resonator

Optical transfer function for add–drop resonator is derived in the presence of coupling loss using the scattering matrix method. A critical coupling condition for ADR is calculated. The response of the ADR under variation of coupling losses and coupling coefficients is studied. The number of allowed states under the critical condition is determined. The full width at half maximum as sharp as 0.17 nm is achieved. It is found that the relative phase shifts of through and drop ports show the same responses under the critical coupling condition. This response emerges in a butterfly-like phase shift, which can be considered as a new evaluating factor for checking the system in critical coupling condition.