A silicon micro-ring waveguide sits beside a straight bus waveguide. Light that is on-resonance couples into the ring, builds up over many round trips, and is absorbed/re-radiated — so it never reaches the far end of the bus. Off-resonance light passes straight through. The all-pass ring transfer function is:
T(λ) = (a² − 2ar·cosφ + r²) / (1 − 2ar·cosφ + (ar)²)
φ(λ) ≈ −2π L n_g (λ − λ_res) / λ0²
r = √(1 − κ²) a = single-pass amplitude transmission
A PN junction is built into the ring. Reverse-biasing it widens the depletion region and sweeps free carriers out of the waveguide core. Fewer free carriers means a higher refractive index (free-carrier plasma dispersion), which red-shifts the resonance:
Δn_eff(V) = k_n · V (k_n ≈ 4×10⁻⁵ per volt, depletion-mode)
Δλ_res(V) = Δn_eff(V) · λ0 / n_g
- Reverse bias slider — pushes λres away from the fixed laser wavelength, sliding the transmission dip out from under the operating point and switching the output from "off" to "on".
- Auto NRZ Modulate — toggles the bias between 0 V and 8 V on a bit clock (with a short RC-like transition) to reproduce real on–off-keyed (OOK) data modulation, the basic scheme silicon ring modulators use in optical links.
- Laser detuning — sets the fixed operating wavelength relative to the unbiased resonance; the steepest point of the notch gives the largest modulation for the smallest voltage swing.
- Coupling κ — near the critical-coupling point the notch is deep and narrow (high Q, strong extinction, slower cavity build-up/decay); pulling κ higher over-couples the ring, trading extinction ratio for a shallower, faster-responding notch — the classic Q-vs-bandwidth trade-off in ring modulator design.
Real-world relevance: this carrier-depletion ring-modulator architecture (Xu et al., Nature 2005, and its many CMOS-photonics descendants) is the workhorse device for encoding electrical data onto light in silicon photonic transceivers used in data-center optical interconnects.