How to Calculate 4-Stokes Parameters

Polarization is a property of light, as are color and intensity.

Weather, plant growth, animal activity---life itself is dependent upon energy garnered from light. So it is no surprise that people through the ages have been fascinated by light. We control the color, the intensity, the placement of light to create our environment. But there is one other characteristic of light that is not quite as evident: polarization, the direction in which the electromagnetic fields oscillate. Stokes parameters are tools scientists use to concisely characterize light with mixed polarization.

Things You'll Need

• Light source
• Linear polarizer
• Quarter-waveplate
• Optical power meter

Instructions

1. Create a light beam, if necessary. That is, if the source is not directional, put an aperture in place to select a well-defined section on which to perform the measurements.

2. Measure the intensity of the beam before entering the region of interest, and record it as I0.

3. Measure the intensity of the beam at the end of the region of interest, and record it as I1.

4. Put a linear polarizer in the beam, with the axis oriented horizontally. Measure the intensity and record it as Ih.

5. Rotate the linear polarizer so that its axis is at 45 degrees relative to the horizontal. Measure the intensity and record it as Ia.

6. Insert a quarter-waveplate in front of the linear polarizer, with its fast axis aligned horizontally. Measure the intensity and record it as Ic.

7. 

   Once the measurements are made, calculating the Stokes parameters is simple algebra.

   Calculate the four Stokes parameters with the measurements recorded in Steps 2 through 6.

   S0 = I1/I0

   S1 = ((2 * Ih) / I0) - S0

   S2 = ((2 * Ia)/I0) - S0

   S3 = ((2 * Ic)/I0) - S0

Tips & Warnings

• If you're just measuring an undisturbed beam, you can skip Step 3 and just record S0 as equal to 1. If you're trying to characterize the polarization effects of a component or system, measure I0 prior to the system and I1 after it.

• Optics texts will provide more detail on the Stokes parameters and their use and interpretation.

References

• BYU:Physics of Light and Optics Text