Question

c) Unpolarised light with intensity \( I_{0} \) passes through a dichroic polariser with its transmission axis \( \hat{p} \) aligned with \( x \) and then a Quarter Wave Plate (QWP) whose fast axis is inclined from \( x \) by angle \( \theta \), as illustrated above. (i) What polarisation states are transmitted by the QWP for alignment angles: \( \theta=0, \theta=\pi / 4 \) and \( \theta=\pi / 2 \) ? (ii) Using the \( x y \) co-ordinate system, state the Jones matrix for the QWP when \( \theta=0 \). [1] (iii) Hence derive expressions for the transmitted Jones amplitude and the transmitted intensity for arbitrary \( \theta \). (iv) The QWP is now fixed at \( \theta=\pi / 4 \) and its transmitted light is passed through a Half Wave Plate (HWP) whose orientation is unknown. Find the polarisation state that emerges from the HWP, and explain why this does not depend upon its orientation. \( [4] \)

          c) Unpolarised light with intensity \( I_{0} \) passes through a dichroic polariser with its transmission axis \( \hat{p} \) aligned with \( x \) and then a Quarter Wave Plate (QWP) whose fast axis is inclined from \( x \) by angle \( \theta \), as illustrated above.
(i) What polarisation states are transmitted by the QWP for alignment angles: \( \theta=0, \theta=\pi / 4 \) and \( \theta=\pi / 2 \) ?
(ii) Using the \( x y \) co-ordinate system, state the Jones matrix for the QWP when \( \theta=0 \).
[1]
(iii) Hence derive expressions for the transmitted Jones amplitude and the transmitted intensity for arbitrary \( \theta \).
(iv) The QWP is now fixed at \( \theta=\pi / 4 \) and its transmitted light is passed through a Half Wave Plate (HWP) whose orientation is unknown. Find the polarisation state that emerges from the HWP, and explain why this does not depend upon its orientation.
\( [4] \)

c) Unpolarised light with intensity I0 passes through a dichroic polariser with its transmission axis p̂ aligned with x and then a Quarter Wave Plate (QWP) whose fast axis is inclined from x by angle θ, as illustrated above.
(i) What polarisation states are transmitted by the QWP for alignment angles: θ=0, θ=π / 4 and θ=π / 2 ?
(ii) Using the x y co-ordinate system, state the Jones matrix for the QWP when θ=0.
[1]
(iii) Hence derive expressions for the transmitted Jones amplitude and the transmitted intensity for arbitrary θ.
(iv) The QWP is now fixed at θ=π / 4 and its transmitted light is passed through a Half Wave Plate (HWP) whose orientation is unknown. Find the polarisation state that emerges from the HWP, and explain why this does not depend upon its orientation.
[4]

Added by Robert N.

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