Note · Silicon photonics
Microring resonators for circuit designers
If you design analog or RF circuits, you already understand most of a microring resonator. It behaves like an LC tank: it stores energy at a resonant frequency, it has a Q, and how strongly you couple to it decides whether it is over-, under-, or critically loaded. This note maps the photonics vocabulary onto the circuit ideas you already have.
The structure
A microring is a waveguide bent into a closed loop, placed next to a straight “bus” waveguide. Light in the bus couples partly into the ring through the gap between them. Light that travels around the ring and arrives back in phase with itself builds up. That is resonance.
When does it resonate?
The ring resonates when a whole number of wavelengths fit around its circumference L = 2πR:
Unlike an LC tank, a ring has many resonances, one for each integer m. The spacing between neighboring resonances is the free spectral range (FSR), set by the group index ng:
The LC-tank dictionary
| LC tank | Microring | Notes |
|---|---|---|
| Resonant frequency 1/√(LC) | λres from eq. (1) | A ring has a comb of resonances, one per FSR |
| Q = f0/Δf | Q = λres/ΔλFWHM | Same definition, measured from the dip width |
| Unloaded Q (resistor loss) | Intrinsic Q (waveguide loss) | Set by sidewall roughness and absorption |
| External Q (load coupling) | Coupling Q (bus gap) | Smaller gap means stronger coupling and lower Qc |
| Matched load | Critical coupling | Qc = Qi, and the through port goes to zero on resonance |
The loaded Q combines the two loss paths the same way parallel resistors do:
Numbers for a typical silicon ring
A ring with R = 10 µm has L ≈ 62.8 µm. With ng ≈ 4.2 at 1550 nm, eq. (2) gives an FSR of about 9.1 nm. A loaded Q of 10,000 gives a linewidth of 1550/10,000 = 0.155 nm, so the finesse (FSR divided by linewidth) is about 59. Those are realistic values for a modulator or filter ring.
The catch: temperature
Silicon's refractive index changes with temperature (dn/dT ≈ 1.8×10−4 per K), which moves the resonance by roughly 0.07–0.08 nm per kelvin near 1550 nm. With a 0.155 nm linewidth, a drift of about 2 K moves the ring a full linewidth off resonance. In circuit terms, it is like an LC tank whose capacitor drifts by a few percent with every degree. That is why practical ring circuits include a heater and a feedback loop to hold the ring on resonance.
Takeaways
Treat a ring as a high-Q tank with periodic resonances. Q, coupling, and matching mean the same things you already know. The new parts are the comb of resonances and the strong temperature sensitivity, which turns every ring into a small control-loop problem.
Further reading
- W. Bogaerts et al., “Silicon microring resonators,” Laser & Photonics Reviews, vol. 6, no. 1, pp. 47–73, 2012.
- L. Chrostowski and M. Hochberg, Silicon Photonics Design, Cambridge University Press, 2015.
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