Polarization Extinction Ratio Measured Using Unpolarized Light

Can the extinction ratio of a polarizing component be measured using an unpolarized light source?

The polarization extinction ratio of an optic under test (DUT) can be estimated by placing the DUT and a reference polarizer with a high extinction ratio between an unpolarized light source and an optical power sensor. This approach measures the maximum power to the minimum power that can be transmitted through the reference polarizer and DUT pair. The ratio of these two power measurements provides an accurate estimate of the DUT's extinction ratio when the extinction ratio of the reference polarizer is significantly higher than that of the DUT. If the reference polarizer and the DUT are linear polarizers of the same type (i.e. they have similar extinction ratios), this approach will provide an estimate that is ~50% of the DUT's actual extinction ratio. The estimate is expected to be ~99% of the DUT's extinction ratio when the reference polarizer's extinction ratio is two orders of magnitude higher than the DUT's.

Click to Enlarge

Figure 1: The extinction ratio of an optic under test (DUT) can be measured using the setup illustrated above. Unpolarized light is provided by a light emitting diode (LED), and both the DUT and a reference linear polarizer are placed between the source and power sensor. The lens tube, which is attached to the power sensor, helps block stray light from the power sensor. For illustrative purposes, it is assumed that the reference polarizer remains stationary, with its transmission axis oriented vertically. A value of P_max  is measured when the transmission axes of the DUT and reference polarizer are parallel (both vertical). A value of P_min  is measured when the transmission axes of the DUT and reference polarizer are perpendicular (i.e. when the DUT's transmission axis is horizontal). The dashed gold lines indicate the two orientations of the DUT's transmission axis that correspond to the two measurements.

Click to Enlarge

Figure 2: The difference between the measured value (ER_est ) of the DUT's extinction ratio and the actual value (ER_DUT ) strongly depends on the extinction ratio of the reference polarizer (ER_ref ). Modelled values (blue curve) and experimental data (squares) recommend using a reference polarizer with an extinction ratio much larger than ER_DUT  to obtain measurement values that better estimate ER_DUT .

Estimating the Extinction Ratio of the DUT
The experimental setup shown in Figure 1 can be used to estimate the DUT's extinction ratio (ER_DUT ). Unpolarized light is transmitted through the reference linear polarizer, whose extinction ratio (ER_ref ) is known. The light is then transmitted through the DUT and measured by the detector.

An estimate of ER_DUT  can be calculated from two optical power measurements. One measurement is taken when the transmission axes of the reference polarizer and DUT are orthogonal (crossed). Crossing their axes minimizes the transmitted power (P_min ). If both components had infinitely large extinction ratios and their axes were crossed, no power would be transmitted to the sensor.

The other measurement records the optical power at the sensor when the two components' axes are parallel, which maximizes the amount of power (P_max ) transmitted to the sensor.

The ratio of P_max  and P_min  is ER_est ,

which provides an estimate of ER_DUT . This estimate is more accurate when ER_ref  is much larger than the ER_DUT , as is discussed in a following section, Choose a High-ER Reference Polarizer. Note that ER_est  can never be larger than ER_DUT , assuming the absence of noise and experimental error in the measurements.

It can be difficult to accurately measure P_min , and measurement error can have a substantial negative impact on the value of ER_est . Following some guidelines can provide the first steps to improving the accuracy of low-power-signal measurements.

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

Reference Linear Polarizer's Placement
If the source light can be considered unpolarized, P_max  and P_min  can be measured with the DUT preceding or following the reference polarizer in the beam. In addition, it will not matter whether the DUT, the reference polarizer, or both are rotated to orient their axes parallel or perpendicular to one another. This can be seen by referencing an equation,

which was derived by multiplying the Mueller matrices for two partial polarizers. The derivation assumed both polarizing components are imperfect, so that they transmit some light polarized perpendicular to their transmission axes. This is realistic, since only ideal polarizers with infinite extinction ratios transmit no light polarized perpendicular to their transmission axes. The value (ER_model ) computed by the equation models the measured value (ER_est ), when the light source is completely unpolarized. The values of ER_ref  and ER_DUT cannot be less than 1, and a value of 1 describes a neutral density filter. [1]

It should be noted that many sources described as being unpolarized actually emit some polarized light. If this is the case, the degree of polarization (DOP) is not zero, and the measurement constraints and equations are different than those described here. One way to investigate the source's DOP is to remove the DUT from the setup in Figure 1 and monitor the detected optical power while rotating the linear polarizer around the optical axis. If the detected power does not vary as the linear polarizer rotates, the source can be considered unpolarized. If the power variation is detectable above the power meter's noise floor, the source should be considered partially polarized.

Choose a High-ER Reference Polarizer
It is important to choose a reference polarizer with an extinction ratio that is significantly higher than that of the DUT. As illustrated by the equation for ER_model , whose calculated values are plotted as the blue curve in Figure 2, the value of ER_est  is theoretically restricted from exceeding the lower of the two components' extinction ratios. In addition, the value of ER_model  only approaches the actual value of the DUT's extinction ratio when ER_ref  is orders of magnitude higher than ER_DUT . Note that when the reference and DUT polarizers have nearly equal extinction ratios, which is notably typical when the reference polarizer and DUT are the same type of polarizer, ER_model is ~50% of ER_DUT .

The red squares plotted in Figure 2 are experimental data (ER_est ). The measurements were made using linear polarizers with known extinction ratios, in which one polarizer was assigned to be the reference linear polarizer and the other was the DUT.

If a reference polarizer with a suitably high extinction ratio is not available, that polarizer can be combined with others into a set. Assemble these polarizers that their transmission axes are all exactly parallel to one another. Then, the effective extinction ratio of this set (ER_set ) is the product of the polarizers' individual extinction ratios, and ER_set  should be used in place of ER_ref  in calculations.

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).