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

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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 λπ / 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 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 + 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 + + = + = 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
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() + + = + + = λ λπ 0 0 0 0 0 0 0 1 2 exp 1 1 2 exp 1 2 2 2 1 1 2 exp 1 1 2 exp 1 2 1 ) ( ) ( m j m j E E E m j m j d E d E y x
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This note was uploaded on 09/28/2010 for the course ECSE ECSE 527 taught by Professor Kirk during the Winter '10 term at McGill.

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

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