Semi major and minor axis of polarization ellipse

In summary, the conversation is about deriving equations for the semi major and minor axes of the polarization ellipse. The equations are derived from the result by using a rotation matrix and squaring each component. However, there is uncertainty about the inclusion of cos(delta) in the final answer.
  • #1
henil
18
0
how can he we derive equations for semi major and minor axes of the polarization ellipse?
 
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  • #2
From what?
 
  • #3
Use these equations
6YrzuF7.jpg

to derive this equations
T7YUkpL.jpg

I just thought of one delta as dy-dx so only one of the first 2 equations actually has a delta in it
Rearranged one of the first equations, the one that no longer has a delta in it, for Ex/Ax=cos(wt-kz)

I then used a few trig identities on the second equation
oqrQ6j7.jpg
SKSqITC.jpg

squared the result then substituted the rearranged equation 1 into the cos(wt-kz) spot and the cos2(wt-kz) spot to get equation 3

Now to derive these equations from the result which are the semi major axis and semi minor axis
5dFsnjb.jpg

just use a rotation martix
3UDrLYX.jpg

where x'=a, y'=b, x=Ax, y=Ay and square each component

This is where I am stuck as I do not have the cos(delta) in the final answer so anyone that knows better can help you (and me) with the correct answer
 

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What is the definition of semi major and minor axis of polarization ellipse?

The semi major and minor axis of polarization ellipse refer to the two perpendicular axes of an ellipse that represent the maximum and minimum distances from the center of the ellipse to its boundary. In the context of polarization, these axes are used to describe the orientation and shape of an elliptical polarization state.

How are semi major and minor axis of polarization ellipse related to the polarization angle?

The semi major and minor axis of polarization ellipse are directly related to the polarization angle, also known as the angle of rotation or azimuth angle. The polarization angle is the angle between the semi major axis of the polarization ellipse and the horizontal axis, typically measured in degrees or radians.

What is the significance of the semi major and minor axis of polarization ellipse in light polarization?

The semi major and minor axis of polarization ellipse are important for understanding the polarization state of light. They provide information about the degree of elliptical polarization, the direction of polarization, and the relative amplitudes of the electric field components. These parameters can be used to characterize and analyze polarized light.

How are the semi major and minor axis of polarization ellipse calculated?

The semi major and minor axis of polarization ellipse can be calculated from the polarization parameters, which include the degree of elliptical polarization, the polarization angle, and the relative amplitudes of the electric field components. These parameters can be obtained through various measurement techniques, such as polarimetry or ellipsometry.

Can the semi major and minor axis of polarization ellipse change?

Yes, the semi major and minor axis of polarization ellipse can change depending on the properties of the incident light and the medium through which it is propagating. For example, if the incident light is unpolarized, the polarization ellipse will have equal semi major and minor axes. However, if the incident light is partially or fully polarized, the polarization ellipse can have different semi major and minor axes, indicating a change in the polarization state.

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