Deriving Stokes parameters for polarization

[Ludwig64]

Homework Statement

Hello i am trying to write the Stokes parameters as the amplitude of the averaged EM-wave

We know the stokes parameters are {I,M,C,S} or {S₀,S₁,S₂,S₃} thus a column vector.

And S₀ is defined as S₀=<E²_x0>_T+<E²_y0>_T

S₀ i understand how it was derived since Filter 0 is an isotropic filter it doesn't have any direction preference.

But now comes my problem i`m attempting to derive

S₁ =<E²_x0>_T-<E²_y0>_T

Homework Equations

Eq1 S₀=2I₀
Eq2 S₁=2I₁-2I₀

Whereby I₁ is the transmitted irradiance through a horizontal polarizing filter.

The Attempt at a Solution

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We know I₀=(1/2)*(<E²_x0>_T+<E²_y0>_T)

and I₁=(1/2)*<E²_x0>_T

Thus if i now substitute I₀ and I₁ into Eq 2 i get S₁=-<E²_y0>_T where as it is supposed to be

S₁=<E²_x0>_T-<E²_y0>_T

I think the problem sits in the definitions of I₀ and I₁ so if you see which thinking step I am doing wrong i would appreciate your help.

 

[mark726]

Hi there,

Thank you for your post. It seems like you are on the right track with your attempt at deriving S1. However, I believe the issue lies in your definitions of I0 and I1.

I0, or the total intensity, is the sum of the intensities in the x and y directions, which can be written as <E2x0>T+<E2y0>T. However, I1, or the transmitted intensity through a horizontal polarizing filter, only considers the intensity in the x direction, which is <E2x0>T. Therefore, your definition of I1 should be (1/2)*<E2x0>T, not (1/2)*(<E2x0>T+<E2y0>T).

With this correction, your derivation of S1 should yield the correct result of <E2x0>T-<E2y0>T.

I hope this helps clarify the issue. Let me know if you have any further questions. Good luck with your work!