De-Embedding Coupler Loss with Reference Structures

Scope

This article describes the procedure for extracting the insertion loss of an on-chip device from fiber-coupled measurements, by measuring and removing the fiber-to-chip couplers with a back-to-back reference structure. It covers the loopback measurement itself, per-coupler loss spectra, spectral subtraction, the alignment-repeatability protocol that sets the error floor, and the diagnosis of Fabry-Perot ripple. Grating-coupler access is assumed; the same logic applies to edge couplers with minor changes noted at the end. Alignment technique itself is covered in first light on a grating coupler.

The problem

Every fiber-coupled measurement contains two couplers and one device, summed in dB:

$$T_\text{meas}(\lambda) = -\mathrm{IL}_\text{GC,in}(\lambda) - \mathrm{IL}_\text{DUT}(\lambda) - \mathrm{IL}_\text{GC,out}(\lambda) + T_\text{ref,fibers}(\lambda).$$

A grating coupler contributes typically 3 – 6 dB each with a roughly Gaussian passband 30 – 40 nm wide (3 dB, full width). Both numbers dwarf many devices under test: measure a 0.3 dB MMI through two 4.8 dB couplers and the thing you care about is 3% of the raw loss. Worse, the couplers' curvature bends every measured spectrum, turning flat devices into apparent 30 nm bandpass filters. De-embedding fixes both.

Procedure

1. Calibrate the fiber path. Connect the input fiber directly to the output fiber (or through the same mating sleeve you will use all day) and record $T_\text{ref,fibers}(\lambda)$. Everything after this step is referenced to the chip's fiber tips.

2. Measure the loopback. Land on the back-to-back structure, two nominally identical couplers joined by a short waveguide, peak the alignment at the coupler's center wavelength, and sweep. The per-coupler loss spectrum is half the loopback loss:

$$\mathrm{IL}_\text{GC}(\lambda) = \tfrac{1}{2}\left[T_\text{ref,fibers}(\lambda) - T_\text{loopback}(\lambda)\right].$$

The halving assumes the two couplers are identical, which on one die is usually good to a few tenths of a dB; the error budget section below says when it isn't.

3. Quantify your landing repeatability. Lift the fibers, re-land, re-peak, re-sweep; repeat five times. The standard deviation of peak transmission across landings, commonly 0.05 – 0.2 dB per facet with good stages, is the floor under every de-embedded number you will produce today. Report it with your results. A loss map whose color scale is finer than its landing scatter is decoration, not data.

4. Measure the device path and subtract. Sweep the device structure under identical conditions (same polarization state, same temperature, same sweep settings), then

$$\mathrm{IL}_\text{DUT}(\lambda) = T_\text{ref,fibers}(\lambda) - T_\text{meas}(\lambda) - 2\,\mathrm{IL}_\text{GC}(\lambda).$$

Subtraction in dB is division in linear power, so this only works on a common wavelength grid; interpolate the reference onto the device sweep's grid, never the reverse if the device has sharp features.

5. Fit, don't read, the coupler curve. Near its peak a grating coupler's transmission in dB is well modeled by a parabola, $T(\lambda) \approx T_0 - a(\lambda - \lambda_0)^2$. Fitting the parabola over the points within a few dB of the peak gives the center wavelength $\lambda_0$, per-coupler peak loss, and the 1 dB and 3 dB bandwidths ($\mathrm{BW}_{X\,\text{dB}} = 2\sqrt{X/a}$) far more repeatably than reading the maximum sample, which rides on ripple and noise. The Grating Coupler Spectrum Fitter does this on a pasted scan, including the ripple analysis below.

Reading the ripple

Periodic fringes on the spectrum are a parasitic Fabry-Perot cavity, and their period tells you where it is:

$$\Delta\lambda \;=\; \frac{\lambda^2}{2 n_g L} .$$

Worked example: a loopback scan peaks at $-9.6$ dB at 1547 nm (so 4.8 dB per coupler), with 0.4 dB peak-to-peak ripple of period 0.32 nm. With $n_g = 4.2$, the implied cavity is $L = \lambda^2/(2 n_g \Delta\lambda) = 1547^2/(2 \times 4.2 \times 0.32) \approx 0.89\,\text{mm}$, matching the coupler-to-coupler waveguide length on the die: the ripple is coupler back-reflection, not the laser. The fringe contrast bounds the reflectance: 0.4 dB peak-to-peak corresponds to an amplitude ratio $\rho \approx 0.023$ between the circulating and direct fields, i.e. about $-33$ dB of round-trip reflection product. If the period had instead implied several millimeters, the suspects would be the chip facets.

Error budget

Edge couplers

The same procedure applies with two changes: the reference is a straight-through waveguide between two facets rather than a loopback loop, and the passband is broad and flat, so the "curvature" correction matters less but the facet Fabry-Perot matters more (the facets are better mirrors than gratings). Length-dependent structures then separate facet loss from propagation loss exactly as in the cutback method.

Handoff

Paste a loopback scan (wavelength, transmission) into the Grating Coupler Spectrum Fitter: it fits the parabola, reports center wavelength, per-coupler loss, 1 dB and 3 dB bandwidths, and analyzes the residual ripple, period, amplitude, and the implied parasitic cavity length. Background: the de-embedding and grating coupler glossary entries.

References: Chrostowski & Hochberg, Silicon Photonics Design (2015), Ch. 9 on test structures and wafer-scale metrology.