Ring, all-pass
Photonic chips are an experimental feature. Switch them on under Help › Experimental features.
An all-pass ring resonator is a ring of waveguide beside one bus waveguide. Its through port dips at every resonance of the ring, as deep as the coupling matches the ring's loss. It filters, senses, and makes a notch.
Ports
in and through, the two ends of the bus.
The model
The ring is a small network of its own: a directional coupler with a share \(\kappa\) crossing over, and the ring’s waveguide of length \(L = 2\pi R\) from one of its ports back to the other, solved as the chip is. With \(t = \sqrt{1 - \kappa}\) and the round trip
\[A = a\,e^{-i\varphi}, \qquad a = 10^{-\alpha L/20}, \qquad \varphi = \frac{2\pi\, n_\text{eff}(\lambda)\, L}{\lambda},\]the through port carries
\[T = \frac{\lvert t - A\rvert^2}{\lvert 1 - tA\rvert^2} = \frac{a^2 - 2ta\cos\varphi + t^2}{1 - 2ta\cos\varphi + (ta)^2}.\]It dips where \(\varphi\) is a whole number of turns.
- Critical coupling, \(t = a\): the dips go to zero.
- Under-coupled, \(t > a\): shallow dips, narrow lines.
- Over-coupled, \(t < a\): shallow dips, broad lines.
Line spacing and width
Its free spectral range, finesse and Q at 1550 nm are
\[\mathrm{FSR} = \frac{\lambda^2}{n_g L}, \qquad F = \frac{\pi\sqrt{x}}{1 - x}, \quad x = t a, \qquad \delta\lambda = \frac{\mathrm{FSR}}{F}, \qquad Q = \frac{\lambda}{\delta\lambda},\]the loaded finesse and line width. Near a resonance the light goes round many times, so the ring delays it: the chip reports the extra group delay it adds.
The waveguide
The ring’s waveguide is a preset (silicon strip, 220 × 500 nm: \(n_\text{eff} = 2.44\), \(n_g = 4.2\), 2 dB/cm; or silicon nitride: 1.8, 2.0, 0.1 dB/cm) or set by hand, with dispersion to first order (see Photonic chips: waveguides).
Settings
| Field | Default | Meaning |
|---|---|---|
radius | 10 | Radius (µm) |
kappa1 | 10 | Coupling (%) |
neff | 2.44 | n_eff at 1550 nm |
ng | 4.2 | Group index |
loss | 2 | Loss (dB/cm) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Also wg: si, sin or custom, the waveguide preset.
Readouts
The free spectral range (in nm and Hz), the round trip’s length and loss, the loaded finesse, line width and Q, and whether it is critically, under- or over-coupled. The chip’s spectrum between any two ports is drawn below it, with each line found and measured.
Assumptions
- One mode, TE, and no backscatter: the ring’s clockwise and anticlockwise modes do not couple, so there is no line splitting.
- Bend loss is the waveguide’s own loss: it does not grow as the radius shrinks.
- No thermal or nonlinear shift of the resonance with power.
Related
- Ring, add-drop.
- Phase shifter.
- Fibre mirror, for a Fabry–Perot in fibre.