Ring Resonator Size, Loss and Photon Lifetime for an Integrated Heralding Circuit

On a photonic chip, a ring resonator stores light for a time set by its circumference and its propagation loss. That storage time, together with the free spectral range, decides whether the ring can act as a filter, a delay, or a photon-pair source enhancement. This study computes the quantities that follow from stated assumptions for silicon nitride waveguide rings, group index 2.0, wavelength 1550 nm, propagation loss 0.1, 0.5 and 1.0 dB per centimetre, using the relations set out in the Methods. The headline results are Q at 0.1 dBcm = 3.521e+06, lifetime at 0.1 dBcm s = 2.897e-09, Q at 1 dBcm = 3.521e+05, lifetime at 1 dBcm s = 2.897e-10, FSR at 100 um Hz = 2.386e+11. The central question is stated as follows: For silicon nitride rings of radius 20 to 200 micrometres with stated propagation losses, what quality factor, photon lifetime and free spectral range follow, and which combination reaches a lifetime of one nanosecond? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Integrated rings are reported with quality factors from ten thousand to above ten million depending on material and loss, so the computed table spans the practical interval. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs.