Coupled mode theory of microtoroidal resonators with a one-dimensional waveguide

We study the transmission of light through a system consisting of an arbitrary number N of microtoroidal resonators coupled to a one-dimensional (1D) waveguide. The transmission T through such a system and its full-width at half-maximum (FWHM) are calculated for various values of N and mutual-mode coupling coefficients. We found that at small mutual-mode coupling, the minimum transmission vanishes exponentially with N while the FWHM is proportional to N. At big mutual-mode coupling, as the number of resonators increases, the mode-splitting is reduced. Our findings contribute to better understanding of novel interfaces between quantum emitters and resonant photonic structures for quantum information processing.