Resonance Wavelength of Integrated Optical Ring Resonator With Small Radius of Curvature

In this letter, we present a new formula for the resonance wavelength of an integrated optical ring resonator with small radius of curvature. Our formula is based on the expansion of the guide effective index as a function of the wavelength and then solving the resonance equation for the extraction of the resonance wavelength and free spectral range. The obtained results are compared with the finite difference time domain results and very good agreement is obtained. Using this new formula, we showed that the error in the resonance wavelength is reduced more than an order of magnitude from ~ 5.73% to be below 0.45%.