The Gold Standard of Photonics | Polarization Extinction Ratio and Why an Analyser Can Hide Leakage

A laser can have high total optical power while carrying a small unwanted orthogonal polarization component. A polarizer can reject that component imperfectly. A photodetector finally reports total transmitted power after its optical path, often with dark offset and measurement uncertainty. Three separate objects—source, analyser and detector—contribute to the same pair of readings.

A source PER can be defined as the ratio Pdesired/Porthogonal for two resolved orthogonal linear components. An analyser’s extinction ratio is generally the ratio of its parallel to perpendicular transmission under appropriate incident polarization. A measured scan ratio is what the whole measurement arrangement actually produces. Their numerical equality is not guaranteed.

Begin by writing which ratio a headline specifies. A marketing statement that merely says ‘high extinction’ can refer to a component property or to a source measurement. Good metrology keeps the object and the optical reference planes explicit.

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For optical powers Pmax and Pmin with identical units and a positive denominator, ERdB = 10 log10(Pmax/Pmin). A ratio of 10:1 gives 10 dB, 100:1 gives 20 dB and 1,000:1 gives 30 dB. These values describe powers, so the factor is 10 rather than the factor 20 used for a comparable field-amplitude ratio.

Decibels are differences on a logarithmic scale. Adding 10 dB multiplies the power ratio by ten; adding 3 dB approximately doubles the power ratio. The number written in dB is not a percentage and cannot be substituted into an energy-conservation calculation without conversion.

When a detector sees a minimum signal near its dark noise or stray-light floor, a computed ratio can depend disproportionately on a small uncertain number. Report the floor and measurement range. A ratio inferred from ‘below detection’ should usually be a bound, not an exact decimal.

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Let an idealised analyser transmit a fraction T∥ for incident light polarized along its preferred axis and T⊥ for light polarized along the rejected axis, with T∥ greater than T⊥. For a fully linearly polarized input of power P rotated by angle α relative to the preferred axis, an intensity-based model gives Pout(α) = P(T∥cos²α + T⊥sin²α).

At α = 0°, Pout = PT∥. At α = 90°, Pout = PT⊥. Their ratio is T∥/T⊥, the analyser’s own extinction ratio under these model conditions. An ideal device has T⊥ = 0, whereas every finite-extinction device admits some rejected state.

If the input contains two mutually incoherent orthogonal linear intensity components, Pg and Pb, and the analyser’s axes are aligned to those components, the transmitted powers at the two orthogonal orientations are P0 = PgT∥ + PbT⊥ and P90 = PgT⊥ + PbT∥. This simple mixing model is central to the worked example.

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Use a fictional beam with Pg = 0.990 mW and Pb = 0.010 mW. Its true resolved component ratio is 99:1 and PER = 10 log10(99) ≈ 19.96 dB. Now choose an analyser with T∥ = 0.900 and T⊥ = 0.009, so its own extinction ratio is 100:1 or 20.00 dB.

With the analyser aligned to pass the dominant component, P0 = 0.990 × 0.900 + 0.010 × 0.009 = 0.89109 mW. Rotated through 90°, P90 = 0.990 × 0.009 + 0.010 × 0.900 = 0.01791 mW.

The observed ratio is 0.89109/0.01791 ≈ 49.75:1. Taking 10 log10 gives approximately 16.97 dB. Neither the source nor the analyser has abruptly become worse; the finite analyser leaks the strong component into the nominal minimum reading.

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Decibels for serial attenuation in one selected optical path can be additive, but source polarization purity and analyser extinction are not two sequential filters acting on one unchanged power component. The unwanted reading receives contributions from both the source’s orthogonal component and the analyser’s leakage of the dominant component.

The measured aligned and crossed powers are sums before division. You must form those sums in linear watts or milliwatts, then compute their ratio and logarithm. Multiplying 99 by 100 or adding 19.96 dB and 20 dB would be a physically incorrect interpretation of this test.

In the limit of a perfectly pure source with Pb = 0, the scan ratio becomes T∥/T⊥ and is limited by the analyser. In the limit of an ideal analyser with T⊥ = 0, the scan ratio becomes Pg/Pb, the source ratio. These two limits are useful checks on any general equation.

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Even an ideal analyser transmits part of a beam when its axis is not exactly crossed with a perfectly linear input. For an ideal polarizer a small angular error ε from the crossed state produces a fractional transmission sin²ε. At 1°, sin²1° ≈ 0.0003046, or about 0.0305% of the incident power before other losses.

That small percentage can matter for a high-extinction measurement. If the intended leakage is below one part in ten thousand, a degree-scale angular error is far too large. The required angular control depends on the ratio you are trying to resolve rather than on the apparent simplicity of a rotation stage.

Rotating a polarizer and searching for a minimum is often more informative than making one nominally crossed reading. Record angular resolution, detector settling, beam pointing and whether the sampled polarization axes align with the source’s principal components.

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A finite-extinction analyser sets a measurement limit. If the source is far more pure than the analyser, the minimum power can be dominated by analyser leakage. You cannot recover an arbitrarily large source PER from a one-polarizer maximum/minimum ratio when the device’s own rejection is inadequately known.

Improving the analyser extinction can move the measurement toward the source’s actual component ratio. But the benefit is real only if stray light, detector dark offset, polarization changes in other optics and angular alignment are also controlled.

Specifications depend on wavelength, incidence angle, optical damage and beam geometry. A quoted 10⁶:1 for one component under its test conditions is not automatically available across a broadband source or a tilted beam. Document the wavelength and the instrument configuration actually used.

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A general optical field may be elliptically polarized, partially polarized or vary across the beam. Two incoherent orthogonal intensity components are an appropriate model for some cases, but coherent orthogonal components with a phase relationship require Jones calculus or an equivalent vector-field description. General partial polarization is commonly treated with Stokes parameters and Mueller optics.

A linear analyser’s maximum/minimum scan can characterize one aspect of polarization but may not uniquely identify circular or elliptical content. Two sources could produce similar linear-polarizer scans and still differ in their complete polarization states.

Ask whether the intended application needs a source PER along a defined pair of fiber axes, degree of linear polarization, or the full polarization ellipse. Measurement vocabulary should follow that objective rather than treating ‘polarization’ as a single dimensionless score.

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A credible record includes source wavelength and bandwidth, whether the source is stable during rotation, analyser ER calibration, orientation method, detector range and offset correction, optical path and any polarization-altering elements. Repeat both maximum and minimum at more than one time point when drift is plausible.

Use the detector’s calibrated linear response. A power meter that changes gain or range at the minimum can generate a false ratio. Stray reflections can couple into a crossed analyser and dominate a supposedly tiny rejected signal. Suppress or measure these pathways rather than interpreting every counted photon as the source’s unwanted polarization.

A component under test should be distinguishable from the reference apparatus. If testing a polarization-maintaining fiber, measure launch alignment and the reference polarizer before attributing every change to the fiber itself.

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Is 20 dB equal to 20% leakage? No. An extinction ratio of 20 dB corresponds to 100:1 power ratio. Under a simple two-component normalization, a rejected component of one part in a hundred of the desired component is not twenty percent.

Does a larger detected maximum prove a better polarizer? Not alone. High desired-axis transmission helps throughput, but high rejection requires a low unwanted-axis transmission too. A device can have excellent throughput and modest ER, or strong ER but substantial useful-beam loss.

Can an ideal crossed-polarizer calculation replace a detector-floor test? No. Malus’ law predicts angular dependence under ideal assumptions. It does not remove stray light, dark current, wavelength dependence or finite rejection.

Is the observed ratio always less than both the source and analyser ratios? In the stated positive two-component symmetric leakage model it is limited by their combined imperfections. Different optics, interference, calibration or detector offsets require a fresh derivation rather than reliance on that particular rule.

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Retain the 0.990/0.010 mW source, but improve the hypothetical analyser to T∥ = 0.900 and T⊥ = 0.0009. Its intrinsic extinction is now 1,000:1 or 30 dB.

The aligned reading becomes 0.990×0.900 + 0.010×0.0009 = 0.891009 mW. The crossed reading is 0.990×0.0009 + 0.010×0.900 = 0.009891 mW. The measured ratio is about 90.08:1 or 19.55 dB, much closer to the actual 99:1 source ratio.

Next ask what happens if a dark offset of 0.001 mW is mistakenly added to only the crossed reading: its denominator increases and the inferred ratio drops again. That detector correction, not another optical component, now determines part of the reported accuracy. Write the corrected measurement equation before quoting more digits.

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The gold standard is to identify the optical ratio, the relevant polarization basis, the analyser’s own rejection and the detector’s floor. Compute power sums before converting to decibels and confirm whether the scanned ratio measures the beam or the limitation of the instrument.

Return to the Photonics root for broader study of optical sources, waveguides and detectors. Cascaded optical losses and shared calibration examines what happens when optical power is measured at several successive planes; it addresses correlated loss rather than polarization mixing.

To investigate finite collection independently, continue to étendue and optical acceptance. All three calculations share a useful habit: distinguish what enters the optical system from what the measurement finally reports.

Sources and further reading

The resources below explain the underlying physical principles and the measurement context. Numerical values and comparison cases in this article are original fictional teaching models; they are not reported field or instrument results.

• RP Photonics: Polarizers and Extinction Ratio — Definitions of polarizer throughput and rejected-axis transmission
• Photonics Dictionary: Extinction Ratio — Ratio of maximum to minimum polarization transmission
• Thorlabs: Extinction Ratio Measurements — Measurement configurations and reference polarizer limits
• RP Photonics: Polarization of Light — Degree of polarization and PER in decibels

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