Calculation of coupling coefficients for diamond micro-ring resonators

We deduce equations to calculate coupling coefficients of diamond micro-ring resonators. The equations can be used universally at any wavelength but not limited to the transmission peaks/valleys, and can be adapted with triangular cross-sections and tapered waveguides. Consequently, we build three models in accordance to different diamond processing technologies. These models deal with ring resonators with either rectangular cross sections, or triangular cross sections, or with tapered bus for triangular cross sections. The calculated coupling coefficients can be well fitted by exponential decay functions of gap d. Due to geometrical limitations, triangular-cross-sectional diamond resonators are shown to have much smaller (factor 20) coupling coefficients than those of rectangular-cross-sectional resonators. A tapered bus is shown to be beneficial to increase the coupling coefficient. Besides the calculation of coupling coefficients, the method presented in the paper can also be used to calculate the bending loss of micro-ring resonators, as a complement to the existing methods.