Help needed with Polarisation (Rotated Waveplates)

[catedral3000]

Homework Statement

a) Plot, as a function of time, the horizontal and vertical components of
E(0,t) for 0 ≤ ωt ≤ 2π. Plot the trajectory of the point (Ex,Ey) for a constant z as a function of time.
A_H = 1, A_V = 1, ϕ_H = 0, ϕ_V = π/4
b) How would you convert the polarization pattern in part (a) to horizontal using
one half-and one quarter-wave plates? What should be the angles of both plates?

Relevant Equations

n/a

(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction.

(b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far.

I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more practice on these kinds of problems that'd be great!

 

[kuruman]

Can you plot the trajectory of point (Ex,Ey) as suggested in part (a)? What shape do you get?
If so, can you do the same for for part (b)? What shape do you get in this case?

Also, please provide the statement of the problem as was given to you. What comes before parts (a) and (b)?

 

[catedral3000]

Can you plot the trajectory of point (Ex,Ey) as suggested in part (a)? What shape do you get?
If so, can you do the same for for part (b)? What shape do you get in this case?

Also, please provide the statement of the problem as was given to you. What comes before parts (a) and (b)?

I've now edited the original problem so it is complete - that all the information given though!

For part (a) I get an elliptical shape with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction.

Part (b) is asking to convert this to horizontal polarisation using 1/2 and 1/4 wave plates.

 

[kuruman]

You know that the phase difference between the two components is $\frac{\pi}{4}.$

1. What phase difference do you need in order to get linear polarization?
2. What does a half-wave plate do to the phase difference? How would it change the trajectory?
3. What does a quarter-wave plate do to the phase difference? How would it change the trajectory?
4. What does combining the two plates do to the phase difference?