{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Assign4s

# Assign4s - ECSE 527 Optical Engineering Assignments 4...

This preview shows pages 1–3. Sign up to view the full content.

ECSE 527 Optical Engineering: Assignments 4 Solutions Question 1 i) For propagation over a distance z the electric field evolves according to E( z )=E 0 exp(-j k z ) Since for x -directed polarization k x =2 π n 0 / λ and for y -directed polarization k y =2 π n e / λ, and the propagation distance is d we can write: ( ) ( ) ( ) ( ) ( ) ( ) ( ) λ π λ π λ π / 2 exp / 2 exp / 2 exp 0 0 0 0 d n n j d E d n j E d E d n j E d E e x e y x = = = So we can write in matrix-vector form: ( ) ( ) ( ) ( ) ( ) ( ) = 0 0 / 2 exp 0 0 1 0 y x e y x E E d n n j d E d E λ π and where we have omitted the phase term that is common to both. So the Jones matrix is given as above. ii) For an m th half-wave plate designed for wavelength λ 0 we have thickness: d |(n 0 -n e )|=(2 m +1) λ 0 /2 ( ) + λ λ π 0 1 2 exp 0 0 1 m j So we just have to substitute this value of d into the matrix to obtain: iii) A linear polarizer at -45° has a Jones matrix: 1 1 1 1 2 1 So the combination of the HWP and linear polarizer is ( ) ( ) ( ) + + = + = λ λ π λ λ π λ λ π 0 0 0 1 2 exp 1 1 2 exp 1 2 1 1 2 exp 0 0 1 1 1 1 1 2 1 m j m j m j M iv) We have +45° polarized incident light, so the output electric field is given by

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document