# Measuring Stokes parameters leading to a degree of polarisation greater than one

I am trying to measure the stokes parameters of a laser beam using the rotating waveplate method detailed here:

The relevant equations are

The laser wavelength is 355nm, and the QWP is also designed for 355nm - https://www.thorlabs.com/thorproduct.cfm?partnumber=WPQ05M-355

However, when I calculate the parameters S0 often ends up being smaller than some or all of S1, S2 and S3, leading to a degree of polarisation much greater than one, which seems to be obviously nonsense.

I have triple checked the maths in the paper and the experimental setup, and I'm pretty sure what I'm doing is the same as what is detailed in the paper, and also this youtube video by Thorlabs based on the paper: https://www.youtube.com/watch?v=pR4r7gMyN5U&t=688s.

Is the paper wrong, or is there some subtle thing that I'm missing that needs to be taken into account when measuring Stokes parameters? Can I just ignore the crazy high degree of polarisation and say "That is effectively 1"? If I add an offset angle to the measured angle then the results I get for degree of polarisation change, but a) this feels like a fudge, and b) I aligned my polariser and QWP 0 position to the horizontal axis as best I could so any offset angle should only be small.

I don't know how to link my data, but here is a table of three different measurements I took (all in mW, and under different input polarisations so they shouldn't be the same).

Angle Measurement 1 Measurement 2 Measurement 3
0 270 447 660
20 60 256 550
40 29 20 220
60 255 72 13
80 331 262 80
100 393 248 209
120 211 60 251
140 25 80 305
160 96 316 490
180 291 432 660

Any help would be greatly appreciated.

• Can you include the calculation of how you go from this data to the degree of polarization? Also, have you made sure you've normalized the data properly/
– JQK
Nov 24, 2023 at 14:35
• The calculations are in the paper I linked, but I can reproduce them in the text if you want
– Toby
Nov 24, 2023 at 14:53
• @EdV: I did try that for Measurement 1 - I got a degree of polarisation of 1.1, which is better than 14 and possibly within the error of the measurement, however the stokes parameters are very different. I might try it again either this afternoon or on Monday –
– Toby
Nov 24, 2023 at 15:00
• @JQK: How would you suggest normalising? I could divide by the power measured without the QWP/polariser, or I could divide by the max of each measurement, but neither of those will affect the degree of polarisation
– Toby
Nov 24, 2023 at 15:01
• Thanks @EdV, it's nice to see that confirmed. Do you have a link to the software you are using? It would be useful to be able to run simulations like that myself
– Toby
Nov 24, 2023 at 17:10