Use the same two general constructions as always: 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 as always: 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=60∘\Gamma = 60^\circ has its fast axis at θ=45∘\theta = 45^\circ to xx. Horizontal linearly polarised light, Jones vector (1,0)(1,0), is incident. Give the two output amplitudes and their phase difference, and classify the resulting state, saying in particular whether its axes are aligned with xx and yy. ((b)) Derive the general Mueller matrix MP(θ)\mathbf{M}_P(\theta) for an ideal polariser. Fully polarised horizontal light of irradiance 11, Stokes vector (1,1,0,0)(1,1,0,0), falls on a polariser with its axis at θ=45∘\theta = 45^\circ to xx. Find the output Stokes vector and its degree of polarisation, and check the total transmitted irradiance against Malus's law.

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