Tool · PIC characterization

Q Factor to Propagation Loss Converter

How much propagation loss does a measured ring-resonator Q factor imply for the waveguide it is made of? The tool converts intrinsic quality factor Q_i to the loss coefficient α in dB/cm, cm⁻¹ and dB/m, and reports the photon lifetime and FWHM linewidth that the same Q implies. Background: quality factor, propagation loss, and photon lifetime.

Presets

Each preset loads one row of the reference table at 1550 nm; the first reproduces the worked example on this page.

Intrinsic Q (Q_i)

E.g., 1e5 or 100000. Loaded Q from a transmission spectrum includes coupling loss, so it gives an upper bound on propagation loss; use intrinsic Q for the loss value.

Wavelength (nm)

Platform

Group index n_g

Selecting a platform sets n_g automatically. Editing this field reverts to custom.

Results

α: 7.5702 dB/cm
α: 1.7431 cm⁻¹
α: 757.02 dB/m
Photon lifetime τ: 82.28 ps
Linewidth (FWHM): 1.934 GHz

The address holds Q_i, wavelength, platform and n_g.

Relation: α [nepers/m] = ω · n_g / (c · Q), a power (intensity) coefficient. Conversion: α [dB/cm] = 4.343 × α [cm⁻¹]. Photon lifetime τ = Q / ω. FWHM linewidth = f₀ / Q. Runs entirely in your browser. Nothing you enter is uploaded or stored.

Reference values at 1550 nm

Platform	n_g	α (dB/cm)	Q_i
SOI 220 nm strip	4.3	2	3.8 × 10⁵
SOI 220 nm rib	3.8	0.5	1.3 × 10⁶
SiN 200 nm	1.7	0.1	3.0 × 10⁶
SiN 800 nm	2.0	0.01	3.5 × 10⁷
InP shallow ridge	3.6	2	3.2 × 10⁵
LNOI ridge	2.3	0.05	8.1 × 10⁶

Typical foundry values. Best-in-class devices reach 1–2 orders of magnitude higher Q in the SiN and LNOI platforms.

Loaded vs. intrinsic Q

The transmission-spectrum linewidth gives the loaded Q (Q_L), which combines intrinsic resonator losses and coupling losses: 1/Q_L = 1/Q_i + 1/Q_c.

Using Q_L in this calculator gives an upper bound on the propagation loss, because Q_L also counts the power leaving through the bus coupler. For accurate loss extraction, decompose Q_L into Q_i and Q_c from extinction depth or gap-sweep data. See the methodology article below.

Methodology

For the derivation of the Q–loss relation, the decomposition of loaded Q into intrinsic and coupling Q, and a worked example, see the article Loaded and Intrinsic Q Factor Extraction from Ring Resonator Transmission Spectra. For direct measurement of waveguide propagation loss without a resonator, see Waveguide Propagation Loss by the Cutback Method.

The model

The converter treats the resonance as a single mode whose stored energy decays at the rate $ω / Q$ and whose light travels at the group velocity $c / n_{g}$ . Dividing one by the other gives the power attenuation per unit length,

α = \frac{2 π n_{g}}{λ Q_{i}}

with $α$ in nepers per meter as a power coefficient, so that $α_{d B} = 4.343 α$ (the factor is $10 / \ln 10$ ; 8.686 belongs to field coefficients). The same Q gives the photon lifetime $τ = Q / ω$ and the FWHM linewidth $Δ f = f_{0} / Q$ .

Loaded and intrinsic Q

The width of a dip in a measured transmission spectrum gives the loaded Q, which counts both the power lost inside the ring and the power that leaves through the bus coupler:

\frac{1}{Q_{L}} = \frac{1}{Q_{i}} + \frac{1}{Q_{c}}

Since $Q_{L} < Q_{i}$ , entering the loaded Q returns a loss that is too large, which makes it an upper bound on the propagation loss. For an all-pass ring with on-resonance power transmission $T_{0}$ , the intrinsic Q is

Q_{i} = \frac{2 Q_{L}}{1 \pm \sqrt{T_{0}}}

with the plus sign when the ring is undercoupled and the minus sign when it is overcoupled; at critical coupling $Q_{i} = 2 Q_{L}$ . A single spectrum does not say which branch applies, which is why gap sweeps or phase measurements are used to settle it. The procedure is set out in the article on Q extraction from ring transmission spectra, and the Ring Resonator Explorer fits a measured scan and reports both branches.

Assumptions

All intrinsic loss is attributed to the waveguide: bend radiation, scattering at the coupler and material absorption are lumped into one $α$ , so for tight bends the result overstates the straight-guide loss. The relation assumes a small loss per round trip (the tool warns below Q = 1000), a group index that applies at the measured wavelength, and a single resonance rather than a doublet split by backscattering.

Worked example

Select the SOI strip preset ( $n_{g} = 4.3$ ), keep $λ = 1550$ nm and enter $Q_{i} = 3.8 \times 10^{5}$ . The relation gives 2π × 4.3 / (1.55 × 10⁻⁶ m × 3.8 × 10⁵) = 45.87 m⁻¹, or 0.4587 cm⁻¹, which is 1.992 dB/cm (199.2 dB/m). This matches the 2 dB/cm SOI strip row of the reference table. The photon lifetime is 312.68 ps and the linewidth 0.509 GHz.

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).