We demonstrate through theoretical analysis that unlike predicted by others, an unbiased coupled resonant optical waveguide (CROW) gyroscope made of $N$ ring resonators has a response to a rotation rate $\Omega$ that is proportional to $(N \Omega)^2$, and hence its sensitivity to small rotation rates is vanishingly small. We further establish that when proper phase bias is applied to the CROW gyro, this response becomes proportional to $N\Omega$ and the sensitivity to small rotation rates is then considerably larger. However, even after optimizing the CROW parameters ($N$ and the ring-to-ring coupling coefficient $\kappa$), the CROW gyro has about the same sensitivity as a conventional fiber optic gyroscope (FOG) with the same loop loss, detected power, and footprint. This maximum sensitivity is achieved for $N = 1$, i.e., when the CROW gyro resembles a resonant FOG. The only benefit of a CROW gyro is therefore that it requires a much shorter length of fiber, by a factor of about $1/ (2 \kappa)$, but at the expense of a stringent control of the rings' optical path lengths, as in a resonant FOG. Finally, we show that the slower apparent group velocity of light in a CROW gyro compared to a FOG is unrelated to this shorter length requirement.
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