Ring Resonators in Photonics

From single-ring notch filters to Kerr frequency combs — how a loop of waveguide does the work of a Fabry-Perot cavity.

Take a straight waveguide and bend it into a circle. Park another waveguide right next to it, close enough that light can hop across the gap. You have just built a ring resonator, the most versatile building block in integrated photonics.

That tiny loop of silicon (or silicon nitride, or lithium niobate) does the same job as a Fabry-Perot cavity, but without any mirrors. Light circulates around the ring, interfering with itself on every pass. When the round-trip phase hits an integer multiple of $2\pi$, you get resonance: constructive interference inside the ring and (if the coupling is right) complete cancellation at the output. One wavelength channel vanishes from the through port. Everything else passes untouched.

This simple geometry does an extraordinary range of jobs. Telecom filters that pluck individual wavelength channels from a fiber. Label-free biosensors that detect a fraction of a monolayer of protein. Electro-optic modulators switching at 50 Gbit/s. Microcombs generating hundreds of equally spaced frequency lines from a single laser. All from a ring 10 to 100 micrometers across.

The all-pass ring

The simplest ring resonator is the all-pass configuration: one ring, one bus waveguide. Light enters from the left, passes the coupling region, and exits to the right. Some fraction couples into the ring, circulates, and couples back out on the next pass.

The coupling region acts like a beam splitter. Define $\kappa$ as the fraction of field amplitude that crosses from bus to ring (or ring to bus), and $r$ as the fraction that continues straight. Energy conservation requires $r^2+{\kappa }^2=1$ for a lossless coupler. The parameter we control in design is the power coupling ratio ${\kappa }^2$, which depends on the gap between waveguides, the coupling length, and the wavelength.

After coupling into the ring, light propagates around the circumference $L=2\pi R$, picking up phase $\varphi =2\pi n_{\text{eff}}L\mathrm{/}\lambda$ and losing some amplitude to scattering and absorption. Define the round-trip amplitude transmission $a=e^{-\alpha L\mathrm{/}2}$, where $\alpha$ is the power attenuation coefficient. For a typical silicon-on-insulator (SOI) waveguide with 3 dB/cm propagation loss and a 10 μm radius ring, $a\approx 0.998$. Almost all the light survives each trip.

The through-port field is the coherent sum of the direct path and all the recirculating contributions. Summing the geometric series gives the transfer function:

The power transmission is:

This is the master equation. Everything interesting about the ring comes from plugging in different values of $r$ and $a$ and sweeping $\varphi$ (i.e., scanning wavelength).

Coupling regimes and the critical condition

At resonance ($\varphi =2m\pi$), the transmission simplifies to:

This single formula contains the entire physics of coupling regimes. When $r=a$, the numerator vanishes: $T_{\text{res}}=0$, complete extinction. All input power is dissipated inside the ring. This is critical coupling, and it is the sweet spot for notch filters and modulators.

When $r>a$ (weak coupling), the ring is under-coupled — most light passes through the bus without entering the ring. The extinction is partial. When $r<a$ (strong coupling), the ring is over-coupled — light enters the ring easily but couples back out before it can be absorbed. Again, partial extinction.

The critical coupling condition is:

For our SOI ring with $a=0.998$, that is ${\kappa }_{\text{crit}}^2=0.00433$, less than half a percent. A very weak coupling, achieved with a gap of about 200 nm between the bus and ring waveguides.

Try it in the widget above: slide ${\kappa }^2$ from 0.001 to 0.5 and watch the resonance dip deepen to maximum extinction at critical coupling, then shallow out again as you over-couple. The calculator labels the regime in real time — watch for the banner to turn green at critical coupling.

Key quantities

For a fixed SOI ring (R = 10 μm, $\alpha$ = 3 dB/cm, $\lambda$ = 1550 nm), the key spectral properties are:

These quantities all depend on ${\kappa }^2$. Rather than tabulating values for every coupling case, use the widget to explore: set ${\kappa }^2=0.1$ (over-coupled) and note the low Q (~10,000) and shallow dip (~0.7 dB). Then set ${\kappa }^2=0.00433$ (critical) and watch Q jump to 123,000 with complete extinction. The derived quantities panel updates in real time.

The add-drop ring

Add a second bus waveguide on the other side of the ring and you get the add-drop configuration: a four-port device that routes specific wavelengths from one waveguide to another.

The transfer functions now involve two couplers with self-coupling coefficients $r_1$ and $r_2$:

The key insight: at resonance with symmetric coupling and no loss ($a=1$), $T_{\text{through}}=0$ and $T_{\text{drop}}=1$. The resonant wavelength transfers completely from the input bus to the drop bus. Everything else passes through untouched. This is a perfect wavelength-selective switch.

With realistic loss, the drop port peak falls below unity. Explore this trade-off in the widget: increase the propagation loss and watch the drop-port peak decrease while the through-port dip becomes shallower.

Phase behavior

The three coupling regimes also differ in their phase response, which matters for modulators and delay lines.

Under-coupled: the through-port phase shifts by $\pi$ across resonance. The direct path dominates, producing partial cancellation.

Over-coupled: the phase shifts by a full $2\pi$ across resonance. This is the regime used for phase-sensitive applications because the full $2\pi$ range is accessible with low insertion loss.

Critically coupled: the amplitude passes through zero, so the phase is undefined at exact resonance. It jumps discontinuously.

Most practical devices operate either critically coupled (maximum extinction for notch filters and sensors) or over-coupled (full $2\pi$ phase range for modulators and delay lines). Switch to the Phase tab in the calculator to see this directly.

Thermal tuning

Silicon has a large thermo-optic coefficient: $dn\mathrm{/}dT=1.86\times {10}^{-4}$ per kelvin. Heating the ring shifts the effective index, which shifts the resonance:

For our SOI ring: $\mathrm{\Delta }\lambda =68.6$ pm/K. A 10 K heater shifts the resonance by 0.69 nm, enough to fine-tune onto a specific wavelength channel. To shift by a full FSR (9.10 nm) requires 133 K, achievable with an integrated micro-heater consuming about 20 mW.

Silicon nitride, by contrast, has $dn\mathrm{/}dT=2.5\times {10}^{-5}$ per kelvin, about 7 times smaller. SiN rings are thermally stable (good for passive filters and sensors) but harder to tune actively.

Applications

WDM filters

A cascade of add-drop rings, each tuned to a different resonance wavelength, can demultiplex a wavelength-division multiplexed (WDM) signal. Each ring plucks one channel from the bus and routes it to its own drop port. With an FSR of 9.10 nm, a single SOI ring covers 11 channels on the ITU 100 GHz grid. For denser channel plans, larger rings (R = 20-50 μm) give narrower FSR and higher Q.

Biosensors

A ring resonator exposed to a liquid sample acts as a label-free biosensor. When molecules bind to the ring surface, they change the local refractive index, shifting the resonance wavelength. The shift is proportional to the surface mass density.

The sensitivity $S=\mathrm{\Delta }\lambda \mathrm{/}\mathrm{\Delta }n$ relates the resonance shift to the bulk refractive index change. For a typical SOI strip waveguide, $S$ is about 55 nm/RIU (refractive index units). The detection limit depends on how precisely you can track the resonance peak, which scales with Q. At $Q=\mathrm{100,000}$, the linewidth is 15.5 pm, and surface mass changes of a few pg/mm² are detectable.

Modulators

A ring modulator encodes data by shifting the resonance on and off the laser wavelength. In silicon, the free-carrier plasma dispersion effect changes $n_{\text{eff}}$ when you inject or deplete carriers in a PN junction embedded in the ring waveguide. A shift of $\mathrm{\Delta }{n}_{\text{eff}}\approx 0.002$ detunes the resonance by about one linewidth, switching the through-port transmission from near-zero (on resonance) to near-unity (off resonance).

Small rings ($R=5\mu \text{m}$) are preferred for modulators: the shorter circumference means less capacitance, enabling modulation speeds above 50 Gbit/s. The trade-off is a broader linewidth (${\kappa }^2$ must be large for the photon lifetime to be shorter than the bit period), but that is acceptable because the modulator only needs to switch between two transmission states.

Frequency combs

Pump a high-Q ring with a continuous-wave laser and four-wave mixing generates new frequencies, cascading into a Kerr frequency comb: hundreds of equally spaced lines spanning an octave or more. SiN rings with $R=100\mu \text{m}$, $\alpha =0.1$ dB/cm, and ${\kappa }^2=0.005$ achieve Q near 800,000 and finesse of 970. Microcombs have applications in optical clocks, spectroscopy, lidar, and coherent communications.

Going deeper

This tutorial covered the fundamentals: transfer functions, coupling regimes, FSR, Q, and thermal tuning. Several important topics are worth exploring further:

Coupled rings. Cascading multiple rings (CROW or SCISSOR configurations) creates flat-top bandpass filters, tunable delay lines, and dispersion compensators. A chain of N coupled rings with apodized coupling coefficients gives a Butterworth or Chebyshev filter shape, something a single ring (which is always Lorentzian) cannot achieve.

Dispersion engineering.Near resonance, the group delay changes rapidly with wavelength, producing large anomalous or normal dispersion. A single SOI ring can produce group delay dispersion equivalent to kilometers of optical fiber in a footprint of 100 μm².

Nonlinear optics. Beyond Kerr combs, ring resonators enhance any nonlinear interaction: second-harmonic generation, stimulated Brillouin scattering, optomechanical oscillation. The enhancement factor scales as $F^2$ for processes involving two resonant fields.

Keep reading

Open the Ring Resonator Calculator and experiment with different configurations. Switch between all-pass and add-drop. Slide the coupling from under-coupled through critical to over-coupled and watch the extinction ratio peak. Compare the SOI and SiN presets to see how material platform affects Q and FSR.

If you need accurate $n_{\text{eff}}$ and $n_g$ values for a specific waveguide cross section, the PIC Mode Solver computes them from geometry.

For the underlying cavity physics, see the Fabry-Perot Resonators and Q-Factor of Optical Cavities tutorials.

References

1. Bogaerts et al., “Silicon microring resonators,” Laser Photonics Rev. 6, 47–73 (2012).
2. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electron. Lett. 36, 321–322 (2000).
3. Chrostowski and Hochberg, Silicon Photonics Design, Cambridge University Press (2015), Chapter 5.
4. Marin-Palomo et al., “Microresonator-based solitons for massively parallel coherent optical communications,” Nature 546, 274–279 (2017).