8. (15 pts) Consider a uniaxial medium with the

permittivity tensor given by:

(4 0 0

0 4 0

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€

0 0 9/

Waveplates are used in

optics to control the

polarization of light. In this problem, you will use the

uniaxial medium to design waveplates for operation

with green light (wavelength of green light in free-

space is equal to 0.5 x 10-6m). For the following

parts, assume that the waveplate can be rotated around the y-axis to suitably and optimally

orient the principal axes of the waveplate with regard to the polarization of the incident wave

as desired by the application. The diagram above shows the principal axes of the waveplate

(the y-z-x directions). All waves will be assumed to be traveling in the +y direction in the

medium. z-axis is called the extraordinary axis (slow since 9>4), and x- and y-axes are called

the ordinary (fast) axes of the medium.

a. What is the minimum thickness L of the waveplate (in meters) that will let one convert

any linearly polarized incident wave into a right-hand circularly polarized output wave?

Explain your answer in detail. How would you orient the axis of the waveplate with

regard to the incident polarization direction to get a right-hand circularly polarized

output wave for the minimum thickness you calculated? Include a diagram that shows

the orientation of the principal axes of the waveplate with regard to the polarization of

the incident wave as desired by the application.

b. What is the minimum thickness L of the waveplate (in meters) that will let one convert

any linearly polarized incident wave into a left-hand circularly polarized output wave?

How would you orient the axis of the waveplate with regard to the incident polarization

direction to get a left-hand circularly polarized output wave for the minimum thickness

you calculated?

c. What is the minimum thickness L of the waveplate (in meters) that will let one convert a

right-hand circularly polarized incident wave into a left-hand circularly polarized output

wave and vice-versa?

d. What is the minimum thickness L of the waveplate (in meters) that will let one rotate the

polarization direction of any linearly polarized incident wave through an arbitrary angle

at the output? How would you orient the axis of the waveplate w.r.t. the incident

polarization direction to get the desired rotation angle for the output wave for the