Compute the polarization state

[brad sue]

Homework Statement

compute the polarization state for the following scenarios:
The input light is randomly propagated in the z direction (figure attached) and then passes through a linear polarizer oriented 45° from either the x or y axis.

1-After the linear polarizer, the light passes through a beam splitter, and quarter wave plate with the fast axis aligned with the x axis, and is reflected back by a mirror (M) (See attached figure).
The output is in the –x direction as depicted in the figure.

2-Similar to (1), but the beam splitter is now replaced with a polarization beam splitter.

Please on my proposed solution can you help me to see what is wrong and help me especially with the angles of polarization?
thank you

Homework Equations

The Attempt at a Solution

polarization state in term of angle:
1- the light is polarized at 45 degrees > after the beam splitter, the intensity is divided by 2 but the angle of polarization stays the same > after the quarter wave plate, the linear light become a polarized circular light (clockwise or counterclockwise??) > After the mirror the circular light is reversed > when the circular light pass through the quarter wave plane, it becomes linear again but with what angle? > light comes out

For question 2- I don't see how it will change from the previous question. Also, i don't understand the use of a polarized beam splitter on polarized light?

Homework Statement

Thank you

 

[jbsteele]

for your help.1- The input light is randomly propagated in the z direction and then passes through a linear polarizer oriented 45° from either the x or y axis. After the linear polarizer, the light passes through a beam splitter, and quarter wave plate with the fast axis aligned with the x axis, and is reflected back by a mirror (M) (See attached figure). The output is in the –x direction as depicted in the figure.The polarization state of the output light can be described as a linear polarization along the x-axis, with an angle of -45 degrees (relative to the x-axis). This is because the light first passes through a linear polarizer oriented at 45 degrees relative to the x-axis, which imparts a linear polarization along the x-axis. Then, it passes through a quarter wave plate, which transforms the linear polarization into a circular polarization. Finally, it reflects off the mirror and passes through the quarter wave plate again, transforming the circular polarization back into a linear polarization along the x-axis, but with an angle of -45 degrees relative to the x-axis. 2- Similar to (1), but the beam splitter is now replaced with a polarization beam splitter. The polarization state of the output light can be described as a linear polarization along the x-axis, with an angle of 0 degrees (relative to the x-axis). This is because the light first passes through a linear polarizer oriented at 45 degrees relative to the x-axis, which imparts a linear polarization along the x-axis. Then, it passes through a quarter wave plate, which transforms the linear polarization into a circular polarization. Finally, it reflects off the polarization beam splitter, which splits the circularly polarized light into two components: one with a linear polarization along the x-axis, and one with a linear polarization along the y-axis. Since the output is in the -x direction, the light that is transmitted through the polarization beam splitter has a linear polarization along the x-axis, with an angle of 0 degrees relative to the x-axis.