Three Ways to Measure Waveguide Loss, Compared

Scope

This article compares the three methods used to measure the propagation loss of an integrated waveguide: cutback, Fabry-Perot fringe contrast, and ring-resonator Q extraction. Each has a full procedure elsewhere on this site (cutback, ring Q extraction, and the coupler de-embedding that both depend on); what is collected here is the comparison: what each one actually measures, where its uncertainty comes from, the range of loss it handles well, and how to interpret disagreement between them. The Q-to-loss calculator does the ring conversion, and the ring resonator explorer shows how loss and coupling shape a resonance. Background entries: propagation loss, cutback method, Fabry-Perot resonator, quality factor.

What each method measures

The three methods agree on the quantity, the power attenuation coefficient $\alpha$ in dB/cm, and on nothing else.

The Includes row is the one most often forgotten. A spiral cutback measures the average loss of a path that is mostly bends of a particular radius; a ring measures a bend of one radius at a handful of wavelengths; a Fabry-Perot measurement on a straight bar measures a straight waveguide plus whatever its two facets scatter. Three correct measurements of three different things are allowed to disagree.

Cutback

Cutback fits a straight line to insertion loss against length; the slope is $\alpha$ and the intercept is the coupling loss. Its uncertainty is a regression problem. For $N$ lengths $L_i$ with an insertion-loss scatter of $\sigma$ per device, the slope uncertainty is $\sigma / \sqrt{\sum (L_i - \bar{L})^2}$. With five spirals at 0, 1, 2, 3, and 4 cm and a coupling repeatability of 0.3 dB, the slope is known to $0.3/\sqrt{10} = 0.095$ dB/cm; with only three lengths at 0, 1, and 2 cm it is $0.3/\sqrt{2} = 0.21$ dB/cm. The method therefore rewards length spread more than it rewards more devices at the same lengths, and it is only as good as the coupling repeatability, which is the subject of the alignment protocol in the de-embedding article. At 0.1 dB/cm and 0.3 dB of scatter, the same five spirals give a 95% uncertainty of $\pm 0.19$ dB/cm, twice the answer; measuring low loss by cutback needs tens of centimeters of spiral, which is real estate and, in a lossy bend design, a measurement of the bends rather than the straights.

Cutback's virtue is that it makes no assumption about the waveguide: no reflectivity, no group index, no coupling regime. Its result is a broadband spectrum of loss if the insertion loss is recorded against wavelength, which none of the other methods gives as directly.

Fabry-Perot fringe contrast

A straight waveguide with two cleaved or etched facets is a low-finesse Fabry-Perot resonator, and its transmission ripples with wavelength. The fringe contrast $K = (I_\mathrm{max} - I_\mathrm{min})/(I_\mathrm{max} + I_\mathrm{min})$ depends only on the product of facet reflectivity and single-pass transmission, $R\,e^{-\alpha L}$, through

$$R\,e^{-\alpha L} = \frac{1 - \sqrt{1 - K^2}}{K},$$

so a scan of transmission against wavelength with a narrow-linewidth tunable laser gives $\alpha$ from one device, with no coupling calibration at all: the contrast is a ratio, and coupling loss cancels. That independence from coupling is why the method survives on cleaved bars that cannot be aligned repeatably.

Its weakness is the reflectivity. With $K = 0.5$ the product $R\,e^{-\alpha L}$ is 0.268; on a 5 mm bar with $R = 0.30$ that gives $\alpha = 0.226$ cm$^{-1}$, or 0.98 dB/cm. Take $R$ as 0.28 instead and the same data gives 0.38 dB/cm; take 0.32 and it gives 1.54 dB/cm. A $\pm 0.02$ uncertainty in facet reflectivity, which is ordinary for a cleaved facet whose exact modal reflectivity depends on the mode shape and the cleave quality, spans a factor of four in the loss. The method is therefore only as good as the independent knowledge of $R$, from a modal reflectivity calculation or from a measurement on a very short bar where $\alpha L$ is negligible and the contrast gives $R$ directly. It also requires a single lateral mode (a second mode adds a second fringe period and lowers the apparent contrast), a laser linewidth well below the fringe spacing, and a wavelength step fine enough to resolve the fringes, which for a 5 mm silicon bar with a group index of 4 are 0.06 nm apart. The contrast saturates at both ends: as $\alpha L \to 0$ the contrast tends to $2R/(1 + R^2)$ and carries no loss information, and as $\alpha L$ grows past a few dB the fringes vanish into the noise.

Ring Q

A ring resonator converts loss into a linewidth. The intrinsic quality factor $Q_i$ of a resonance relates to the power loss coefficient through

$$\alpha = \frac{2\pi n_g}{\lambda\, Q_i},$$

with $n_g$ the group index, and the conversion to dB/cm is a factor of 4.343 (a power coefficient, not a field one; the Q-to-loss calculator applies it). At 1550 nm with $n_g = 4.3$, a $Q_i$ of $2 \times 10^5$ is 3.8 dB/cm, $10^6$ is 0.76 dB/cm, and $5 \times 10^6$ is 0.15 dB/cm. The precision is excellent: a 5% uncertainty in $Q_i$ at $10^6$ is $\pm 0.04$ dB/cm, half an order of magnitude better than a good cutback, and the structure is a single small ring. Below about 1 dB/cm this is the method of choice, and below 0.1 dB/cm it is the only one that fits on a chip.

Its trap is the assignment of the coupling regime. The transmission dip of an all-pass ring has the same shape whether the ring is undercoupled or overcoupled, but the two assignments swap the roles of the intrinsic and coupling Q. The damage depends on how far the ring is from critical coupling. A resonance with a loaded Q of $10^5$ and a 3 dB dip on a 280 µm racetrack gives 6.5 dB/cm if read as undercoupled and 1.1 dB/cm if read as overcoupled, a factor of six; the same ring with a 22 dB dip gives 3.3 and 2.8 dB/cm, 15% apart. The ambiguity bites hardest exactly where the dip is shallow and the measurement looks easiest. It is resolved in the Q extraction article by a phase measurement, by comparing rings with different gaps, or by the add-drop configuration, and it has to be resolved: an unresolved regime is not a measurement with a large error bar but a coin toss between two answers. The second caveat is what the ring measures. The light circulates in a bend of the ring's radius, so the extracted loss includes bend loss at that radius, and it is sampled only at the resonance wavelengths. A ring of 5 µm radius on a platform whose bends are lossy will report a loss that a 50 µm spiral never sees.

Choosing

The decision follows from the expected loss and from what is on the chip. Above about 2 dB/cm, cutback is direct and the ring is compromised (a $Q_i$ of $10^5$ is barely resolvable and depends on a sharp coupling assignment); use spirals, and use the Fabry-Perot method when the sample is a cleaved bar with no test structures. Between 0.5 and 2 dB/cm all three work; cutback and ring together are the strongest combination, because they fail differently and their agreement validates both the coupling repeatability of the one and the regime assignment of the other. Below 0.5 dB/cm, the ring is the measurement, with a long spiral as a sanity check, and the Fabry-Perot method has run out of contrast. Whatever the method, the wavelength should be stated: loss in silicon nitride at 1550 nm, in silicon near 1310 nm, and in any platform near an absorption band differs by more than the method uncertainties.

When they disagree

Disagreement of 20% or so between cutback and ring on the same platform is normal and usually informative. The ring includes bend loss and the spiral includes different bends; the spiral samples a continuum of wavelengths and the ring a few; the spiral's straights and the ring's curve have different sidewall interaction. A ring reading higher than the spiral points to bend loss or a coupling-regime error; a spiral reading higher points to substrate leakage or defects that a long path accumulates and a small ring does not, or to coupling drift that was folded into the slope. A Fabry-Perot result that disagrees with either by a factor of two is almost always the reflectivity, and the fix is to measure $R$ rather than to assume it. The productive response to disagreement is to identify which of the Includes rows differs, not to average the numbers.

References: R. Regener and W. Sohler, "Loss in low-finesse Ti:LiNbO₃ optical waveguide resonators," Appl. Phys. B 36, 143 (1985), for the Fabry-Perot fringe method; G. Tittelbach, B. Richter and W. Karthe, "Comparison of three transmission methods for integrated optical waveguide propagation loss measurement," Pure Appl. Opt. 2, 683 (1993); Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Opt. Express 12, 1622 (2004), for spiral cutback; W. Bogaerts et al., "Silicon microring resonators," Laser Photonics Rev. 6, 47 (2012), for the Q-to-loss relation and the coupling regimes. All worked numbers above are computed from the stated parameters.