Ring resonator

A ring resonator is a waveguide bent into a closed loop and placed close enough to a straight bus waveguide that light couples across the gap. On resonance (when the round trip accumulates an integer multiple of $2\pi$ in phase), light builds up in the loop and the through-port transmission dips sharply.

The resonance condition is $m\lambda_{res} = n_{eff} L$, where $L$ is the ring circumference and $m$ an integer. Adjacent resonances are separated by the free spectral range $\mathrm{FSR} = \lambda^2 / (n_g L)$; the sharpness of each resonance is set by round-trip loss and coupling, summarized by the loaded quality factor $Q$.

Two configurations dominate. The all-pass ring (one bus) acts as a notch filter and phase element. The add-drop ring (two buses) transfers resonant wavelengths to a second port, forming a wavelength-selective channel filter. The ratio of coupling to intrinsic loss defines the operating regime: under-coupled, critically coupled (complete extinction at the through port), or over-coupled. That distinction matters for modulators and sensors alike.

Rings earn their ubiquity from size and sensitivity. A silicon ring of 5–20 µm radius has an FSR of several nanometers and fits by the thousand on a chip; carrier injection or depletion in a p-n junction across the waveguide turns it into a compact microring modulator; and because the resonance shifts with anything that perturbs $n_{eff}$ (temperature, cladding index, adsorbed molecules), rings are equally standard as thermometers and biosensors. The same sensitivity is the operational headache: silicon rings drift roughly 10 GHz per kelvin and generally require an integrated heater and feedback to stay on channel.

Typical loaded $Q$: $10^4$–$10^5$ for silicon rings ($10^6$ achievable), $10^6$–$10^7$ for thin silicon nitride, higher still in ultra-low-loss SiN where rings serve as the cavity for Kerr frequency combs.