Abstract

For small radius ring resonators, the estimation of the resonance wavelength and Free Spectral Range FSR using the group index fails to give accurate results consistent with the FDTD calculation. In this work we present a new formula for the calculation of these parameters. The formula is based on the expansion of the ring effective index as a function of the wavelength and then solving the resonance equation to get the resonant wavelength and the FSR. Using this form, the error in estimating the resonance wavelength is reduced from 5.7% to less than 0.3% when compared with the FDTD calculation.

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