Can a linearly polarized light source be used to measure the extinction ratio of a polarizing optic?

The extinction ratio of an optical component under test (DUT) can be measured using light from a laser or other linearly polarized source, but it is often necessary to insert a linear polarizer between the source and the DUT. The linear polarizer is needed when the light from the source has an extinction ratio that is not significantly higher than the extinction ratio of the DUT, which is frequently the case. Obtaining an accurate measurement of the DUT's extinction ratio requires the incident light's extinction ratio to be substantially higher than the DUT's. Inserting one or more linear polarizers between the source and the DUT is one way to improve the extinction ratio of the light incident on the DUT.

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Figure 1: The extinction ratio of the optic under test (DUT) can be estimated from two optical power measurements. One, P_max , requires the transmission axis of the DUT to be parallel with the polarization direction of the incident light, which is vertical in this illustration. The second measurement, P_min , requires the DUT's transmission axis to be perpendicular (crossed with) the incident light's polarization direction. The estimate's accuracy is better when the extinction ratio of the light incident on DUT is much higher than the DUT's extinction ratio. One or more linear polarizers inserted between the source and DUT may be needed to improve the light's extinction ratio, since light from lasers described as linearly polarized often has an extinction ratio too low to achieve the desired accuracy.

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Figure 2: The difference between the measured value (ER_est = P_max / P_min ) and the actual value (ER_DUT ) of the DUT's extinction ratio strongly depends on the extinction ratio of the light incident on the DUT. The incident light's extinction ratio is the product of the extinction ratios of the source (ER_source ) and the linear polarizer (ER_ref ) inserted between the source and DUT. Modelled values (blue curve) and experimental data (triangles and circles) are plotted. In this work, ER_source < ER_DUT . The measurements obtained with no polarizer between the source and DUT corresponds to ER_ref  = 1 and are indicated by triangles. The measurement data obtained with a linear polarizer between the source and DUT are indicated by circles. These data show that without the added linear polarizer, the estimated values of the DUT's extinction ratio were substantially lower than the actual value.

Estimating the Extinction Ratio of the DUT
It is important to note that this approach estimates the absolute extinction ratio of the DUT, rather than the extinction ratio of the light.

Accurately estimating a DUT's extinction ratio requires linearly polarized incident light, whose extinction ratio is much higher than that of the DUT, as well as an optical power sensor. It is sometimes the case that a linearly polarized source provides light whose extinction ratio is adequate (see the discussion in the following section), but it is typically necessary to include one or more linear polarizers between the source and DUT (Figure 1).

Two optical power measurements are needed to estimate the DUT's extinction ratio. The measurement of the maximum power (P_max ) transmitted to the power sensor requires the DUT's transmission axis to be oriented parallel to the polarization direction of the incident light. The measurement of the minimum power (P_min ) transmitted by the DUT requires the DUT's transmission axis to be oriented perpendicular to the polarization direction of the incident light. These two orientations of the DUT's transmission axis are indicated by the dashed gold lines in Figure 1, assuming the polarization direction of the source light is vertical.

The ratio of P_max  and P_min  is ER_est ,

whose value can be used to estimate the DUT's extinction ratio (ER_DUT ). The estimated and actual values can differ by a large amount, and the difference strongly depends on the extinction ratio of the light incident on the DUT. The most accurate estimates of ER_DUT  are provided when the incident light's extinction ratio is orders of magnitude higher than ER_DUT . This is discussed in the following two sections.

It can be difficult to accurately measure the values of P_min , and errors in these measurements can have a substantial negative impact on the the value of ER_est . Following some guidelines can provide the first steps to improving the accuracy of low-power-signal measurements. Note that an unpolarized source can also be used to measure the extinction ratio of a DUT.

Improve the Extinction Ratio of the Source Light
The extinction ratio of the light incident on the DUT can potentially limit the value of ER_est  to a value substantially less than ER_DUT . The value of ER_est  only approaches the value of ER_DUT  when the extinction ratio of the incident light is significantly higher than the extinction ratio of the light incident on the DUT. For example, when the extinction ratio of the incident light equals the value of ER_DUT , ER_est  is only ~50% of the value of ER_DUT . When the extinction ratio of the incident light is two orders of magnitude higher than ER_DUT , ER_est  is ~99% of the value of ER_DUT .

In general, the extinction ratio of light from most lasers is too low to be suitable for measuring the extinction ratios of highly polarizing DUTs, such as linear polarizers. In this case, a linear polarizer placed before the DUT (as shown in Figure 1) can improve the extinction ratio of the incident light. By the same principle, adding an additional linear polarizer at this location will further improve the extinction ratio. The transmission axes of the two polarizers should be aligned exactly parallel to obtain the highest extinction ratio.

Effect of Improving the Incident Light's Extinction Ratio
The value of ER_est  can be modeled for sources with different extinction ratios as well as configurations that do and do not include linear polarizer(s) between the source and the DUT. The modelled value (ER_model ),

is plotted as the blue curve in Figure 2. This equation assumes a single linear polarizer is placed between the source and DUT, and that the extinction ratio of the source is ER_source . The value of ER_source  is set to 1 when the source is unpolarized. The extinction ratio of this polarizer is ER_ref . If a set of polarizers is used instead, the value ER_ref  should be replaced with the set's effective extinction ratio. If there are no polarizers located between the source and the DUT, replace ER_ref  with a value of 1.

If the positions of the linear polarizer and the DUT are switched, so that the DUT is placed closest to the source, the effect can be modeled by exchanging the ER_DUT  and ER_ref  variables in this equation. This change worsens the model's (and the measurement's) estimate of ER_DUT . For best results, the set of linear polarizers should be located closest to the source.

References
[1] Michael Kraemer and Tom Baur, "Extinction ratio measurements on high purity linear polarizers," Proc. SPIE Polarization: Measurement, Analysis, and Remote Sensing XIII, 10655, 1065505 (2018).