# Deriving Stokes parameters for polarization

• Ludwig64
In summary, the Stokes parameters can be written as {I,M,C,S} or {S0,S1,S2,S3}, with S0 being defined as S0=<E2x0>T+<E2y0>T. The attempt at deriving S1 using equations Eq1 and Eq2 shows that I0 and I1 were incorrectly defined. The correct definition of I1 should be (1/2)*<E2x0>T, leading to the correct result of S1=<E2x0>T-<E2y0>T.
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=<E2x0>T+<E2y0>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 =<E2x0>T-<E2y0>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)*(<E2x0>T+<E2y0>T)

and I1=(1/2)*<E2x0>T

Thus if i now substitute I0 and I1 into Eq 2 i get S1=-<E2y0>T where as it is supposed to be

S1=<E2x0>T-<E2y0>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.

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!

## 1. What are Stokes parameters in polarization?

Stokes parameters are a set of four values that describe the polarization state of a beam of light. They represent the intensity, degree of polarization, and orientation of the polarization ellipse.

## 2. How are Stokes parameters calculated?

Stokes parameters are calculated by measuring the intensity of the light in four different polarization states and using these values in a mathematical formula. This can be done using a polarimeter or other specialized equipment.

## 3. What is the significance of Stokes parameters in polarization measurements?

Stokes parameters are significant because they provide a quantitative description of the polarization state of light, which is important in many scientific and technological applications. They also allow for the characterization and comparison of different sources of polarized light.

## 4. Can Stokes parameters be used to measure circular polarization?

Yes, Stokes parameters can be used to measure circular polarization. In this case, the values for the third and fourth parameters (S3 and S4) would be non-zero, indicating the presence of circular polarization in the light.

## 5. How do Stokes parameters relate to other polarization parameters, such as the degree of polarization?

The degree of polarization (DOP) is related to the first and second Stokes parameters (S0 and S1) through the equation DOP = √(S1^2 + S2^2)/S0. This means that the DOP can be calculated from the Stokes parameters, but they provide additional information about the polarization state of the light.

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