Measuring Polarization Extinction Ratio and Polarization-Dependent Loss

Scope

This article gives the procedures for two routine polarization measurements on fiber-coupled parts. Polarization extinction ratio (PER) is measured on polarization-maintaining fiber, PM patch cords and connectors, PM-pigtailed lasers and modulators, and the PM launch into a chip. Polarization-dependent loss (PDL) is measured on fiber-pigtailed passive and active components, including a photonic chip measured through its couplers. Polarization-mode dispersion, which needs different instruments, is covered in its own entry. The polarization states, Jones vectors and Stokes parameters used below are defined in their entries.

Polarization extinction ratio

What a misaligned launch does

Light launched into PM fiber at an angle $\theta$ to the slow axis splits into a slow-axis component carrying $\cos^2\theta$ of the power and a fast-axis component carrying $\sin^2\theta$. The fiber keeps the two apart, so the output PER is set by the launch:

$$\text{PER} \;=\; 10\log_{10}\!\left(\cot^2\theta\right).$$

A PM connector pair or splice adds its own angular error in the same way, and the errors of successive joints combine. A PER specification in the high 20s of dB therefore corresponds to angular alignment of a couple of degrees, which is why key alignment and splice angle dominate PER budgets.

The two components also acquire a relative phase along the fiber, because they travel at different speeds, and that phase drifts with temperature and strain. With a narrow-linewidth source the output is an ellipse whose shape changes as the phase drifts; when the phase happens to be 0 or π, the output is linear, tilted by $\theta$ from the axis, and a rotating polarizer finds a deep null at the tilted angle. A single rotating-polarizer reading can therefore report a high PER from a badly aligned launch. The measurement has to vary the phase and find the worst case.

Equipment

Procedure

1. Connect the source to the device's input with the launch aligned to the slow axis (the connector key, for standard PM connectors) and the device's output to the analyzer.
2. Rotate the analyzer to find the maximum transmitted power, then set it 90° away, near the minimum.
3. While watching the power at the minimum, vary the relative phase by gently warming a section of the fiber, stretching it, or sweeping the laser wavelength. The minimum reading will oscillate.
4. Record the maximum and the highest value of the minimum over at least one full oscillation. The PER is $10\log_{10}(P_\text{max}/P_\text{min})$ using that highest minimum.
5. If the minimum oscillates strongly, the launch is misaligned; rotate the input to reduce the oscillation, which aligns the launch to the axis. When measuring a component's own PER, the launch has to be good enough that its contribution is well below the component's.

With a polarimeter, the same heating or stretching makes the output state trace an arc on the Poincaré sphere. The arc's center lies on the fiber's axis, and its size measures the power in the unwanted axis: a well-aligned launch traces a small arc near the pole of linear polarization along the axis. Commercial PER meters automate this reading.

Failure modes

Measuring without phase variation. The reading depends on the fiber's temperature at that moment and can overstate PER by more than 10 dB.

Polarizer limit. A polarizer with 30 dB extinction cannot measure 35 dB; check it by measuring a known source first.

Stress in the output fiber. Bending or clamping the output lead of a standard single-mode fiber between the device and the analyzer rotates and ellipticizes the state. Keep the lead to the analyzer short and PM, or put the analyzer directly on the device's output connector.

Wrong axis. Some PM parts are specified on the fast axis; an unexpectedly high loss with a good PER usually means the launch is on the wrong axis.

Polarization-dependent loss

PDL is the difference between the maximum and minimum insertion loss over all input polarization states. Two methods are standard.

All-states method

A polarization scrambler or a motorized polarization controller moves the input through many states spread across the Poincaré sphere while a power meter records the transmitted power; PDL is $10\log_{10}(P_\text{max}/P_\text{min})$ over the recording. It is simple and needs no knowledge of the states, and its accuracy depends on how thoroughly the states cover the sphere: a sparse or uneven scramble misses the true extremes and underestimates PDL. It is slow for swept-wavelength measurements, since the scramble has to be repeated at every wavelength.

Mueller four-state method

The device's transmission for any input state is set by the first row of its Mueller matrix, $(m_{11}, m_{12}, m_{13}, m_{14})$, and that row can be found from four measurements with known input states: linear horizontal ($P_0$), linear vertical ($P_{90}$), linear at 45° ($P_{45}$) and right circular ($P_\text{RHC}$), each normalized to the input power in that state:

$$m_{11} = \frac{P_0 + P_{90}}{2},\qquad m_{12} = \frac{P_0 - P_{90}}{2},$$ $$m_{13} = P_{45} - m_{11},\qquad m_{14} = P_\text{RHC} - m_{11}.$$

With $r = \sqrt{m_{12}^2 + m_{13}^2 + m_{14}^2}$, the maximum and minimum transmissions over all states are $m_{11} \pm r$, so

$$\text{PDL} \;=\; 10\log_{10}\!\left(\frac{m_{11} + r}{m_{11} - r}\right).$$

Worked example with normalized transmissions $P_0 = 1.000$, $P_{90} = 0.955$, $P_{45} = 0.990$ and $P_\text{RHC} = 0.970$: $m_{11} = 0.9775$, $m_{12} = 0.0225$, $m_{13} = 0.0125$, $m_{14} = -0.0075$, $r = 0.0268$, and PDL = 0.24 dB. The largest difference between any two of the four readings is 0.20 dB; the four states do not include the worst case, which is why PDL is computed from the matrix rather than read from the measurements.

The method is fast and deterministic, and with a tunable laser it gives PDL at every wavelength of a sweep. It requires the four input states to be accurately known at the device's input, which means the polarization synthesizer is calibrated through the same fiber that leads to the device and the fiber is not moved between calibration and measurement.

Procedure

1. Warm up the source and power meter, and check the source's power stability over the measurement time; a PDL of 0.1 dB is a 2.3% change, and drift of that size is indistinguishable from it.
2. Calibrate the input states and reference powers with the device replaced by a short patch cord, using the fiber path that will feed the device.
3. Insert the device without moving the input fiber, and make the four (or scrambled) measurements.
4. Compute PDL, and for a swept measurement plot it against wavelength alongside the insertion loss.
5. Repeat once with the input fiber reconnected to confirm repeatability; the spread between repeats is the practical resolution of the setup.

Failure modes

Interference fringes. Reflections between connectors and the device with a coherent laser make the power ripple with wavelength and temperature, and the ripple is read as PDL. Use an isolator at the source, angled connectors, and a source linewidth broad enough to wash out the fringes where the method allows it.

Detector PDL. The power meter's own PDL, typically a few hundredths of a dB for a good integrating-sphere or large-area detector, sets the floor. Check it by measuring PDL with the device removed.

Fiber movement. Moving the lead between the polarization synthesizer and the device changes the states at the device, invalidating the Mueller calibration.

Chip couplers. On a photonic chip, grating couplers are strongly polarization-selective, so a chip-level PDL measurement through them reflects the couplers rather than the circuit; edge couplers show much lower PDL and are the better access for this measurement.

References: IEC 61300-3-2, Fibre optic interconnecting devices and passive components: Basic test and measurement procedures, Part 3-2: Examinations and measurements, Polarization dependent loss in a single-mode fibre optic device; D. Derickson (ed.), Fiber Optic Test and Measurement (Prentice Hall, 1998), chapter on polarization measurements; E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1993).