Elliptical Polarization (QM)

In summary, to understand the state of the photons, you can use Jones matrices and equations to find the axes, angle, and direction of the ellipse.
  • #1
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Homework Statement


The state of the photons is:
[tex]|\psi> = \frac{1}{\sqrt{1+r^2}}(|\psi_x> + r\exp{(i\alpha)}|\psi_y>)[/tex]
Where the [tex]|\psi_x>[/tex] and [tex]|\psi_y>[/tex] are the linear polarization states in the x and y direction, respectively.
They are elliptically polarized. I have to give the axes a,b of the ellipse, the angle of the major axis and the direction.

Homework Equations


I made a change of "axes" to the right and left circular polarization states:
[tex]|\psi_{R/L}> = \frac{1}{\sqrt{2}}(|\psi_x> \pm i|\psi_y>)[/tex]

The Attempt at a Solution


The result of the change is:
[tex]|\psi> = \frac{1}{\sqrt{2(1+r^2)}}(|\psi_R>(1-ir\exp{i\alpha}) + |\psi_L>(1+ir\exp{i\alpha}))[/tex]

I don't really know how to follow, I don't understand if I have to use the Jones matrices or if there's an other way. I think all the necessary information is there.
Could somebody give me some hints?
(It's the first time I write here, sorry if I've made any mistake).
 
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  • #2


Hi there! It looks like you are trying to understand the state of the photons given in the forum post. To do this, you can use the Jones matrices, which are commonly used in optics to describe the polarization state of light. In this case, the state of the photons can be represented by the following Jones vector:

|ψ> = [1/sqrt(1+r^2), r*exp(iα)/sqrt(1+r^2)]^T

To find the axes and angle of the ellipse, we can use the following equations:

a = |E_x|, b = |E_y|, θ = 0.5*tan^-1(|E_y/E_x|)

Where |E_x| and |E_y| are the magnitudes of the x and y components of the electric field vector, respectively. In this case, we have:

|E_x| = 1/sqrt(2(1+r^2))*(1-ir*exp(iα))
|E_y| = 1/sqrt(2(1+r^2))*(1+ir*exp(iα))

Using these values, we can find the axes and angle of the ellipse. The direction of the ellipse can be determined by the sign of r, where a positive r corresponds to a counterclockwise rotation and a negative r corresponds to a clockwise rotation.

I hope this helps! Let me know if you have any other questions.
 

1. What is elliptical polarization?

Elliptical polarization is a type of polarization of light where the electric field vector traces out an ellipse as the light propagates. This is in contrast to linear polarization, where the electric field vector oscillates in a straight line, or circular polarization, where the electric field vector rotates in a circle.

2. How is elliptical polarization different from linear and circular polarization?

In linear polarization, the electric field vector oscillates in a single plane, while in circular polarization, it rotates in a circle. Elliptical polarization is a combination of the two, with the electric field vector tracing out an ellipse.

3. What causes elliptical polarization?

Elliptical polarization can be caused by the superposition of two perpendicular linearly polarized waves with different amplitudes and phases. It can also occur when light passes through certain materials, such as crystals, that have different refractive indices for different polarization states.

4. What is the significance of elliptical polarization in quantum mechanics?

In quantum mechanics, the polarization state of a photon can be described by a wave function, which can be in a superposition of linear or circular polarization states. This allows for the possibility of elliptical polarization, which has important implications in quantum communication and quantum computing.

5. How is elliptical polarization measured?

Elliptical polarization can be measured using a polarimeter, which consists of a polarizer and an analyzer. The polarizer filters out light of a specific polarization state, while the analyzer measures the intensity of the light passing through. By rotating the analyzer, the ellipticity and orientation of the polarization can be determined.

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