A retarder has retardance (it delays the slow component by a quarter cycle) and its…

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

A retarder has retardance Γ=π/2\Gamma = \pi/2 (it delays the slow component by a quarter cycle) and its fast axis lies at θ=30∘\theta = 30^\circ to the xx axis. Horizontally polarised light, Jones vector (1,0)(1,0), falls on it. ((a)) Starting from J(0)=diag(1,eiΓ)\mathbf{J}(0) = \mathrm{diag}(1, e^{i\Gamma}) for a fast axis along xx, and the rotation matrix R(θ)\mathbf{R}(\theta) defined in the text, write down J(θ)=R(θ)J(0)R(−θ)\mathbf{J}(\theta) = \mathbf{R}(\theta)\mathbf{J}(0)\mathbf{R}(-\theta) for general θ\theta and Γ\Gamma, then evaluate it at θ=30∘\theta = 30^\circ, Γ=π/2\Gamma = \pi/2. ((b)) Find the Jones vector of the light leaving the retarder. ((c)) Classify the output state (linear, circular or elliptical) and check that the output irradiance equals the input irradiance.

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