Orientation of Major Axis for polarized light

AI Thread Summary
Case 1 successfully demonstrated linearly polarized light at an angle of π/4, while Case 2 presented challenges with an undefined angle α. The conclusion for Case 2 indicates circularly polarized light due to the relationship Eα = Eα±π/2 and the fact that cos(δ) equals zero. It is noted that circular polarization lacks a defined axis, explaining the undefined α. To determine the handedness of the circular polarization, further analysis is required, potentially involving the application of Euler's equation and additional resources like Jones calculus.
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Homework Statement
Consider the Jones vector: $$\begin{pmatrix}A \\Be^{i \delta}\end{pmatrix}$$ For the following cases, what is the orientation of the major axis, and
what is the ellipticity of the light? Case I: ##A = B = \frac{1}{\sqrt{2}}; \delta = 0;## Case II: ##A = B = \frac{1}{\sqrt{2}}; \delta = \frac{\pi}{2};## Case III: ##A = B = \frac{1}{\sqrt{2}}; \delta = \frac{\pi}{4}##
Relevant Equations
$$\alpha = \frac{1}{2}tan^{-1}(\frac{2 A B cos(\delta)}{A^2-B^2})$$
$$E_{\alpha}=|E_{eff}|\sqrt{A^2 cos^2(\alpha) + B^2 sin^2(\alpha) + 2 A B cos(\delta)sin(2 \alpha)}$$
$$E_{\alpha \pm \frac{pi}{2}}=|E_{eff}|\sqrt{A^2 cos^2(\alpha) + B^2 sin^2(\alpha) - 2 A B cos(\delta)sin(2 \alpha)}$$
Case 1 worked out great, I found it to be linearly polarized light at an angle ##\alpha = \frac{\pi}{4}##, but Case 2 is giving me trouble. As best I can tell, ##\alpha## is undefined in case 2. How do I solve case 2?
 
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I believe I figured it out, though I would love confirmation. Since ##cos(\delta) = cos(\frac{\pi}{2})=0## and ## A = B##, we end up with ## E_\alpha = E_{\alpha_\pm+\frac{pi}{2}}##. That means we have circularly polarized light! So of course ##\alpha## is undefined; a circle has no determined axes!
 
You are correct. Your professor might also want you to say if it is right-hand or left-hand circular polarized. More information can be found here https://en.wikipedia.org/wiki/Jones_calculus
And you can use euler's equation to make the exponential into trig functions and plug in the angle.
 
stephen8686 said:
You are correct. Your professor might also want you to say if it is right-hand or left-hand circular polarized. More information can be found here https://en.wikipedia.org/wiki/Jones_calculus
And you can use euler's equation to make the exponential into trig functions and plug in the angle.
How can I tell the handedness?
 
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