Tool · PIC characterization

Ring Resonator Explorer

What does a ring of a given size, loss and coupling do to light near resonance, and how are Q, extinction and propagation loss read back from a measured dip? The explorer computes the transmission, phase, group delay and circulating field from the coupled-mode transfer functions, and fits a pasted wavelength scan with the same model. Background: ring resonator, free spectral range, and quality factor.

Platform preset

Sets typical n_eff, n_g, α. Values vary by foundry; edit freely.

Ring radius R (µm)

Round trip L = 2πR. Smaller ring, wider FSR.

target FSR GHz

Power coupling κ₁² (%)

Propagation loss α (dB/cm)

Total waveguide loss, bend loss included.

Center wavelength λ₀ (nm)

Window follows: λ₀ ± 5 nm. Enter n_eff, n_g, and α as their values at this wavelength.

Group index n_g

Sets FSR and linewidth. ~4.2 for a 500×220 nm SOI wire.

Effective index n_eff

Sets where resonances sit. ~2.44 for the same wire, TE.

Learn with it

Five short experiments. Each sets the controls, points at the relevant panel, and asks for a prediction before showing the result.

Field view

Probe detuning from resonance (linewidths)

λ_probe circulating intensity × input through

True-scale steady-state field of the device. The transverse profile is the EIM lateral mode of a 500×220 nm SOI wire (evanescent decay 112 nm), carried along the circuit with the same coupled-mode amplitudes the spectrum is built from, at the real guided wavelength, so the fringes, the tails, and their overlap in the coupling gap are physical. The intensity view is quantitative on a 30 dB log scale; the field view is contrast-compressed for visibility. Drawn approximations: the straight-guide profile is applied unchanged along the bend, the 200 nm gap is illustrative (κ comes from the slider, not the drawn gap), and propagation is slowed by roughly 10¹³.

Transmission, 1545–1555 nm

Through-port phase and group delay

At the resonance nearest λ₀

coupling regime:

Resonances in window

Analyze a measured spectrum

Paste a wavelength scan (two columns: λ then transmission, CSV, TSV, or space-separated; nm/µm/m and dB/linear are auto-detected), or load a file. The tool normalizes the baseline, finds the resonances, fits each to the all-pass lineshape, and extracts Q, extinction, and, using the R and n_g set in the controls, κ² and propagation loss for both coupling branches. A power spectrum alone cannot say which branch is real: that is the under/overcoupled ambiguity, and resolving it takes a phase measurement or a trend across wavelength (see the phase panel).

open file

Extraction method: fit FWHM and on-resonance transmission, then invert the all-pass model for the (r, a) pair; the two orderings are the two branches, per W. McKinnon et al., “Extracting coupling and loss coefficients from a ring resonator,” Opt. Express 17, 18971 (2009). Files are read locally in your browser and never leave your machine.

Checked against

On every load this page re-evaluates a fixed reference case (λ₀ = 1550 nm, R = 10 µm, n_eff = 2.44, n_g = 4.2, α = 3 dB/cm, κ² = 1%) with its own code and compares the result to values computed independently in Python from the same equations, plus one internal identity: at critical coupling the loaded Q must equal half the intrinsic Q. The two EIM rows check the embedded slab solver that draws the field view’s transverse mode profile against the same solve run independently in Python.

The table compares the page’s ring model at the reference case above with the same equations solved independently in Python, and checks that the analyzer recovers Q and κ² from a noisy synthetic scan whose true values are known. Tolerances are relative to the reference value: 0.5 % for the closed-form rows, 2 % for group delay, which the page reads from the nearest point of its plotting grid, and 3 % and 10 % for the two fit rows, which carry the scan’s noise.

Terms

FSR is the wavelength spacing between resonances, λ²/n_gL; higher Q does not change it. Loaded Q is what a transmission scan measures (λ/FWHM); intrinsic Q is what the ring would show with the coupler removed, set by loss alone, and the two are related through the coupling regime. Finesse is FSR/FWHM, the number of resolvable lines per period. Critical coupling is κ² equal to the round-trip loss: the through port nulls and extinction diverges. Photon lifetime τ_p = Qλ/2πc is the linewidth’s time-domain twin: energy stored in the ring decays with this constant.

Model and assumptions

Transfer functions are the standard coupled-mode results for a single ring: all-pass T = (a² − 2ra·cosφ + r²) / (1 − 2ra·cosφ + (ra)²) and the corresponding add-drop pair, with r² + κ² = 1 (lossless coupler), a² = e^−αL, and round-trip phase φ = 2πn_eff(λ)L/λ. These are exact for the stated model; the physics approximations live in the inputs.

Assumed: single mode, coupling independent of wavelength across the 10 nm window, first-order dispersion only (constant n_g), no thermal or nonlinear effects, and α taken as the total round-trip loss, so bend loss is included in the number you enter rather than modeled from R. Moving λ₀ to another band does not update the material inputs for you: n_eff, n_g, and α are whatever you enter, stated at λ₀, and the field view’s transverse profile stays the 1550 nm solve.

Equations follow W. Bogaerts et al., “Silicon microring resonators,” Laser & Photonics Reviews 6, 47–73 (2012).

Runs entirely in your browser. Nothing you enter is uploaded or stored.

The model

In the all-pass configuration a ring of circumference $L$ sits beside one bus waveguide. The coupler passes a fraction $κ^{2}$ of the power into the ring, leaving a self-coupling amplitude $r = \sqrt{1 - κ^{2}}$ ; one round trip multiplies the field by $a = e^{- α L / 2}$ and adds the phase $φ = 2 π n_{e f f} L / λ$ . The through-port power transmission is

T = \frac{a^{2} - 2 r a \cos φ + r^{2}}{1 - 2 r a \cos φ + (r a)^{2}}

Resonances fall where $φ$ is a multiple of $2 π$ . Their spacing, the loaded linewidth and the loaded Q follow as

F S R = \frac{λ^{2}}{n_{g} L}

Δ λ = \frac{(1 - r a) λ^{2}}{π n_{g} L \sqrt{r a}}

Q_{L} = λ / Δ λ, Q_{i} = \frac{2 π n_{g}}{λ α}

At resonance $T = (a - r)^{2} / (1 - r a)^{2}$ , which vanishes when $r = a$ : critical coupling, where the power coupled in equals the power lost in one round trip, $κ^{2} = 1 - a^{2}$ . A larger $κ^{2}$ overcouples the ring and a smaller one undercouples it. The two cases give the same dip depth for swapped values of $r$ and $a$ , which is why a fit reports both branches. The model assumes a lossless point coupler, a single guided mode, $n_{e f f}$ linear in wavelength across the 10 nm window, and no backscattering; the linewidth formula also assumes $r a$ close to 1.

Worked example

The defaults are an all-pass ring with $R = 10 μ m$ (so $L = 62.83 μ m$ ), $n_{e f f} = 2.44$ , $n_{g} = 4.2$ , 3 dB/cm loss and $κ^{2} = 1 %$ at 1550 nm. The round trip loses 0.0188 dB, so $a^{2} = 0.99567$ and critical coupling would need $κ^{2}$ = 0.433%; at 1% the ring is overcoupled. With $r a = 0.99283$ the formulas give FSR = 9.104 nm (1.136 THz), FWHM = 20.9 pm (2.60 GHz), loaded Q = 74,336, finesse 436.6, extinction 8.03 dB and $Q_{i}$ = 246,468, the values the stats panel shows. From $1 / Q_{L} = 1 / Q_{i} + 1 / Q_{c}$ the coupling Q is 106,438. Entering the loaded Q with $n_{g} = 4.2$ in the Q to loss converter returns 9.95 dB/cm, an upper bound on the loss; entering $Q_{i}$ returns the 3.00 dB/cm that was put in. The extraction procedure is described in the article on Q extraction from ring transmission spectra.

References: W. Bogaerts et al., “Silicon microring resonators,” Laser & Photonics Reviews 6, 47–73 (2012). A. Yariv, “Universal relations for coupling of optical power between microresonators and dielectric waveguides,” Electronics Letters 36, 321–322 (2000). W. R. McKinnon et al., “Extracting coupling and loss coefficients from a ring resonator,” Optics Express 17, 18971–18982 (2009).