Cutback method

The cutback method measures the propagation loss of a waveguide or fiber by comparing the power transmitted through several lengths of it. The input and output coupling losses are the same for every length, so they cancel, and the loss per unit length is the slope of a straight-line fit of insertion loss against length; the intercept of the fit is the coupling loss. In the worked example below, four silicon waveguides from 0.2 to 4 cm long give 1.97 dB/cm, with a 95% confidence interval of ±0.40 dB/cm, and 5.02 dB per grating coupler. For optical fiber, where the method began, a long fiber is measured and then cut back to a short length at the launch end, and the method is the reference test for attenuation in dB/km.

In decibels the insertion loss of a waveguide of length $L$ is

$$\text{IL}(L)=\alpha L+2\text{CL},$$

where $\alpha$ is the propagation loss in dB per unit length and $\text{CL}$ the coupling loss at each end. A straight-line fit of IL against $L$ gives $\alpha$ as its slope and the total coupling loss $2\text{CL}$ as its intercept, without any need to know the source power or the coupling efficiency.

Cutback method procedure

1. A set of waveguides of different lengths, with the same cross-section, couplers and bend design, is laid out side by side; for fiber, or a chip that will be cleaved shorter, a single long sample is used instead.
2. Each length is measured with the same source, wavelength, polarization and coupling arrangement, and its insertion loss is recorded against a reference measurement of the source. Recorded against wavelength, the same data give the loss spectrum.
3. The insertion losses in dB are plotted against the physical lengths of the light paths, taken from the layout for a chip and from the spool length or an OTDR for fiber.
4. A least-squares straight line gives the slope $\alpha$ and the intercept $2\text{CL}$, and the scatter of the points about the line gives the uncertainty of each.
5. The first device is measured again at the end of the run; a change shows drift of the source or the coupling during the measurement.

Worked example: silicon waveguide loss

Four silicon strip waveguides on one chip, 0.2, 1, 2 and 4 cm long, are measured through identical grating couplers at 1550 nm:

A least-squares fit gives a slope of 1.97 dB/cm and an intercept of 10.04 dB, or 5.02 dB per coupler. The points scatter about the line by 0.26 dB (the residual standard error of the fit), which puts the standard error of the slope at 0.09 dB/cm and its 95% confidence interval, with two degrees of freedom, at ±0.40 dB/cm; the intercept has a standard error of 0.21 dB. Four devices spanning 3.8 cm are therefore enough to tell a 2 dB/cm waveguide from a 3 dB/cm one, but not to resolve a few tenths of a dB/cm. More lengths and a wider span shrink the interval: the standard error of the slope is the scatter divided by $\sqrt{\sum (L_i-\bar{L}{)}^2}$.

Destructive and paired-device cutback

Destructive cutback is the original form, used for optical fiber attenuation. The power through a long length of fiber is measured, the fiber is cut back to a short length near the launch without disturbing the input coupling, and the power is measured again. The same form works for a waveguide chip that is cleaved or polished shorter between measurements, at several lengths, with the input coupling re-established each time. The fiber procedure, with launch conditioning and a worked example, is in How to Measure Fiber Attenuation and Bend Loss.

Paired-device cutback measures a set of nominally identical waveguides of different lengths, made side by side on one chip and coupled in the same way. It is the usual form in integrated photonics because it destroys nothing and suits automated wafer-level testing, and foundry process control modules include such sets. Its assumption is that every copy of the coupler performs the same, and the scatter in the fit shows how well that holds.

How many lengths and how long

The loss difference across the set has to be large compared with the scatter of the individual measurements. For four lengths spread evenly over a span $\mathrm{\Delta }L=L_{\text{max}}-L_{\text{min}}$, the standard error of the slope is $1.34{\sigma }_P\mathrm{/}\mathrm{\Delta }L$, where ${\sigma }_P$ is the per-measurement uncertainty, so a span with $\alpha \mathrm{\Delta }L=10{\sigma }_P$ gives the loss to within 13% at one standard error, or ±58% at 95% confidence with two degrees of freedom. Taking a coupling repeatability of 0.5 dB, that span is 2.5 cm for a waveguide of 2 dB/cm and 71 cm for one of 0.07 dB/cm, which is why low-loss platforms measure cutback on spirals tens of centimeters to a meter long. Two lengths give a slope but no check on it. Widening the span helps more than adding lengths: doubling the span halves the standard error, while going from four to eight evenly spaced lengths over the same span lowers it by only 19%.

Bend loss enters the fit according to how the bends are distributed. With the same number of bends in every device it adds to the intercept; with the number of bends in proportion to the length it adds a fixed amount to the slope, which then describes that particular path rather than a straight waveguide; any other arrangement distorts the fit. Spiral sets are therefore drawn with the same bend design throughout, and the extracted slope is reported with the bend radius it includes (bend loss).

Sources of error in cutback measurements

• Lengths. The fit needs the true physical length of the light path through each device, bends and transitions included, taken from the layout; an error common to all the lengths carries over to $\alpha$ in the same proportion.
• Coupling variation. Differences between coupler copies, fiber position and angle appear as scatter, and on a small set they bias the slope. Fiber arrays and well-controlled test structures reduce the variation, and the residuals of the fit measure it.
• Drift and polarization. Source power and polarization changes during the run add to the scatter. Remeasuring the first device at the end of the run shows the drift, and a reference tap on the source corrects for it.
• Reflections. Reflections at the couplers or facets form a weak Fabry-Perot cavity whose fringes change the transmission with wavelength; averaging the transmission over a few fringes removes them.
• Substrate leakage. In silicon on insulator, light leaking through a thin buried oxide into the substrate adds a length-dependent loss that the fit reports as propagation loss.

Cutback vs Fabry-Perot and ring resonator methods

Cutback needs several devices and good coupling repeatability but makes no assumptions about the waveguide beyond uniformity. The Fabry-Perot fringe method takes the loss from the contrast of the fringes of a single cleaved waveguide, and ring-resonator methods take it from the quality factor of a ring, which reaches losses far below what cutback can resolve on a chip: with four lengths spanning 4 cm and 0.5 dB of scatter, the standard error of a cutback slope is 0.17 dB/cm. The full procedure, fit and uncertainty analysis are in Waveguide propagation loss by the cutback method, and where cutback sits against the other two methods, and when each is the right choice, is covered in Three ways to measure waveguide loss, compared.

Cutback vs OTDR

For optical fiber the alternative to cutback is the OTDR, which measures the light backscattered along the fiber from one end:

IEC 60793-1-40 makes cutback the reference test method for fiber attenuation and also describes insertion-loss and backscatter methods. An OTDR reading depends on the backscatter coefficient as well as on the loss, so a splice between fibers of different mode field diameters can show an apparent gain from one end, and splice losses are taken as the average of measurements from both ends.

Common questions

Why is it called the cutback method?

From its original form for optical fiber, in which a long fiber is measured and then physically cut back to a short length near the launch to give the reference measurement. The name is kept for integrated waveguides, where usually nothing is cut and a set of waveguides of different lengths is measured instead.

How many lengths does the cutback method need?

Two lengths give a slope but no check on it. Four or more, spread over a span large enough that the loss difference is about ten times the measurement scatter, give both the loss and its uncertainty from the fit: with 0.5 dB of scatter, a 2 dB/cm waveguide needs a span of about 2.5 cm.

Does the cutback method measure coupling loss?

Yes, as the intercept of the fit: the loss extrapolated to zero length is the sum of the input and output coupling losses. In the worked example it is 10.04 dB, or 5.02 dB per grating coupler, with a standard error of 0.21 dB.

What is the difference between the cutback method and an OTDR?

Cutback measures the power transmitted through a long and a short length of fiber, needs both ends and removes a short piece; it is the reference method for attenuation and gives the loss spectrum with a broadband source. An OTDR measures backscatter from one end without cutting and gives the loss along the fiber, but its splice readings between dissimilar fibers have to be averaged over both directions.

What is the lowest loss the cutback method can measure?

It depends on the coupling repeatability and the span of lengths: for four evenly spaced lengths the standard error of the slope is $1.34{\sigma }_P\mathrm{/}\mathrm{\Delta }L$. With 0.5 dB of scatter and a 4 cm span this is 0.17 dB/cm, so losses of a few tenths of a dB/cm and below need spirals tens of centimeters long or a ring-resonator measurement.

References: IEC 60793-1-40, Optical fibres, Part 1-40: Attenuation measurement methods, for the fiber cutback method. D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998), chapters on attenuation and OTDR. G. T. Reed and A. P. Knights, Silicon Photonics: An Introduction (Wiley, 2004), for waveguide loss measurement. Y. A. Vlasov and S. J. McNab, "Losses in single-mode silicon-on-insulator strip waveguides and bends," Optics Express 12, 1622 (2004). R. Regener and W. Sohler, "Loss in low-finesse Ti:LiNbO₃ optical waveguide resonators," Applied Physics B 36, 143 (1985), for the Fabry-Perot fringe method.