Use the same two general constructions once more: for a retarder of retardance with…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Polarisation and anisotropic media · Polarisation and anisotropic media

Optics and Photonics, Ch Polarisation states, polarisers and the Jones and Stokes calculus

Problem

Use the same two general constructions once more: J(θ)=R(θ)J(0)R(−θ)\mathbf{J}(\theta) = \mathbf{R}(\theta)\mathbf{J}(0)\mathbf{R}(-\theta) for a retarder of retardance Γ\Gamma with fast axis at θ\theta to xx, and MP(θ)=RS(2θ)MP(0)RS(−2θ)\mathbf{M}_P(\theta) = \mathbf{R}_S(2\theta)\mathbf{M}_P(0)\mathbf{R}_S(-2\theta) for an ideal polariser with its axis at θ\theta to xx, where MP(0)\mathbf{M}_P(0) is the horizontal-polariser matrix of Section 8.7 and RS(ϕ)\mathbf{R}_S(\phi) rotates (S1,S2)(S_1,S_2) through ϕ\phi. ((a)) Derive the general Jones matrix J(θ)\mathbf{J}(\theta) for a retarder of retardance Γ\Gamma. A retarder with Γ=120∘\Gamma = 120^\circ has its fast axis at θ=60∘\theta = 60^\circ to xx. Vertically polarised light, Jones vector (0,1)(0,1), is incident. Give the two output amplitudes and their phase difference, and classify the resulting state. ((b)) Derive the general Mueller matrix MP(θ)\mathbf{M}_P(\theta) for an ideal polariser. A laser beam of irradiance 11, linearly polarised at 45∘45^\circ to xx (Stokes vector (1,0,1,0)(1,0,1,0)), falls on a polariser with its axis at θ=15∘\theta = 15^\circ to xx. Find the output Stokes vector and its degree of polarisation, and check the transmitted irradiance against Malus's law.

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