Talk:Mueller calculus

Perhaps a worked out example of applying one of the linear polarizers on a realistic Stokes vector might be in order. Not being versed in polarization theory, I'd like to know where the 1/2 normalization factor came from. Could you also explain what you mean by "fast axis".MxBuck (talk) 21:06, 15 September 2009 (UTC)

Jones vs Mueller calculus

"Note that Jones calculus is only applicable to light that is already fully polarized. Light which is randomly polarized, partially polarized, or incoherent must be treated using Mueller calculus." (from Jones calculus page)

"Light which is unpolarized or partially polarized must be treated using Mueller calculus, while fully polarized light can be treated with either Mueller calculus or the simpler Jones calculus. Coherent light generally must be treated with Jones calculus because the latter works with amplitude rather than intensity of light." (from Mueller calculus)

I assume unpolarized means the same as randomly polarized.

Then it seems like these sentences say:

• Jones calculus: must be used whenever light is (fully polarized) OR (coherent)
• Mueller calculus: must be used whenever light is (not fully polarized) OR (incoherent)

I do not equate coherence with polarization.

Does one calculus' domain of applicability strictly contain the other's domain of applicability? Or do both domains only intersect, and both have non-empty differences?

Can light be incoherent yet fully polarized (i.e. fully polarized laser beam with low coherence length), or coherent yet randomly polarized (plane waves at fixed frequency with random polarizations in each plane)? Which model should be used? or neither? — Preceding unsigned comment added by 83.134.167.103 (talk) 10:07, 4 July 2012 (UTC)

The domains intersect, but only slightly. You are right not to equate coherence with polarization. An incoherent beam can be fully polarized. Imagine putting light from a lightbulb through an ideal "perfect" polarizer. One can actually achieve quite high polarization of incoherent light in practice. Conversely, a laser with high coherence can be unpolarized (or "randomly" polarized). This essentially means that the laser emits two collinear beams with perpendicular polarization that are each highly coherent, but which are not coherent with one another. The lack of coherence between the beams has little effect on coherence-related effects, because beams with perpendicular polarization do not interfere with one another anyway.

So, the right interpretation is:

• Jones calculus is used when the light is coherent AND fully polarized
• Mueller calculus is used when the light is incoherent, regardless of its polarization state
• Mueller calculus can sometimes also be used for coherent light, depending on what information you need.
• Generally, some other technique must be used if the light is both coherent and partially polarized.

I'm not sure exactly when you can use Mueller calculus for coherent light—I'm guessing that if you don't need to preserve the phase information and don't need to combine beams that might not be coherent with one another, the Mueller calculus would still work.

Some people do use "randomly polarized" and "unpolarized" as synonyms. Personally, I don't like "randomly polarized", since that term might suggest a beam that has some fixed random polarization. An unpolarized beam is not just polarized randomly; its overall polarization changes moment to moment on very short timescales. On macroscopic scales, the beam has no net polarization.--Srleffler (talk) 02:37, 6 July 2012 (UTC)

Can someone provide a specific reference for the statement above? I feel like Jones calculus should be able to deal with unpolarized light if you treat the observables to be the electric field correlation intensities: <E E^{*T)>.--21:38, 17 July 2012 (UTC)

Does “Coherent light generally must be treated with Jones calculus” indicate “Coherent light generally cannot be treated with Mueller calculus”? Then (if my interpretation is correct), I do not agree to this, and I propose to delete this sentence. WiOp (talk) 08:34, 7 December 2012 (UTC)

I clarified it. The issue is that with the Mueller calculus you lose information about the phase of the light. If you have two beams of light that are coherent with one another, and you pass each through some optics and then recombine them, Mueller calculus will not give the correct result. For fully polarized, coherent light the Jones calculus is applicable to every problem and the Mueller calculus is applicable to a subset of all problems. The Mueller calculus works for beams with incomplete polarization, however, unlike the Jones calculus.--Srleffler (talk) 01:26, 4 April 2013 (UTC)

Incorrect equations?

I believe the combination of the conversion equation and definition of A is incorrect. The equation for M = A(JxJ*)A^-1 is correct if A is redefined as the conjugate of the provided definition of A. That is, the signs of the imaginary parts should be reversed in A. If the current A is maintained, then the equation should be M = A(J*xJ)A^-1. --Treinke (talk) 16:08, 30 December 2021 (UTC)

That is consistent with how the matrix was originally written, back in 2014. An anonymous editor flipped the signs in 2017 with the comment "sign inversion of A(4,2) and A(4,3) - see Azzam/Bashara: Ellipsometry and polarized light. There should be a typo in the appendix of Fujiwara: Spectroscopic ellipsometry". Since that section is supposed to be a direct quote from a reference, I will revert it to the original form.

@Fgnievinski: You added the passage in question. Can you confirm that the original version is correct and the anon from 2017 is wrong?--Srleffler (talk) 04:08, 31 December 2021 (UTC)

@Srleffler: I've checked Savenkov (2009) and it matches to the present version of Wikipedia. fgnievinski (talk) 13:47, 3 January 2022 (UTC)

Thanks.--Srleffler (talk) 03:59, 4 January 2022 (UTC)

The definition used by Fujiwara for the Stokes vector is consistent with https://en.wikipedia.org/wiki/Stokes_parameters (see the first definition under "Representations in fixed bases"). The derivation provided in Fujiwara's appendix is straight-forward and seems correct. Perhaps someone can verify a problem in Azzam/Bashara or find a discrepancy in definitions.--Treinke (talk) 16:31, 31 December 2021 (UTC)

References