Question

b) The right circular polarisation state can be represented by \( \mathcal{R}=\frac{1}{\sqrt{2}}\left(\begin{array}{c}1 \\ -i\end{array}\right) \) in an \( x y \) Cartesian system. Find \( \mathcal{R}^{\prime} \), the Jones vector of this state expressed in the \( x^{\prime} y^{\prime} \) frame which is rotated anti-clockwise from \( x y \) by angle \( \theta \), as illustrated below left. You should express your answers in terms of \( \mathcal{R} \). [3] [ Hint: You will find it useful to recall that the matrix \( R(\theta) \) converts a vector whose components are expressed in the \( x^{\prime} y^{\prime} \) frame to the \( x y \) representation.]

          b) The right circular polarisation state can be represented by \( \mathcal{R}=\frac{1}{\sqrt{2}}\left(\begin{array}{c}1 \\ -i\end{array}\right) \) in an \( x y \) Cartesian system.

Find \( \mathcal{R}^{\prime} \), the Jones vector of this state expressed in the \( x^{\prime} y^{\prime} \) frame which is rotated anti-clockwise from \( x y \) by angle \( \theta \), as illustrated below left. You should express your answers in terms of \( \mathcal{R} \).
[3]
[ Hint: You will find it useful to recall that the matrix \( R(\theta) \) converts a vector whose components are expressed in the \( x^{\prime} y^{\prime} \) frame to the \( x y \) representation.]

b) The right circular polarisation state can be represented by ℛ=(1)/(√(2))(
1
-i
) in an x y Cartesian system.

Find ℛ^', the Jones vector of this state expressed in the x^' y^' frame which is rotated anti-clockwise from x y by angle θ, as illustrated below left. You should express your answers in terms of ℛ.
[3]
[ Hint: You will find it useful to recall that the matrix R(θ) converts a vector whose components are expressed in the x^' y^' frame to the x y representation.]

Added by Robert N.

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