Question

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4. This problem deals with Jones calculus. An optical rotator is a polarization element that rotates the linear polarization state of an incident field by an angle φ. The Jones matrix for an optical rotator can be given like so cosφ sin φ -sin φ cos φ (a 1pt) Using the Jones calculus show that the linear polarization of a field initially polarized along the x-axis is rotated by the optical rotator. (b 1pt) Show that for an initial field which is circularly (left or right) polarized, the output polarization remains unchanged. This demosntrates that left and right circular polarizations are "eigen-vectors" of the rotator matrix, and that they are therefore natural polarization states to describe systems that include rotators. (c 1pt) Consider a device composed of the following sequence of elements along the z-axis: a polarizer with transmission angle α = 0 followed by an optical rotator with angle φ and completed by a second polarizer with α-π/4. Calculate the Jones matrices for passage in the forward direction along the z-axis through this optical device for a general angle φ. (d ipt) Show that for φ = π/4 horizontally linearly polarized light transmits without loss.

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