A partially polarised LED beam has the following time-averaged field products

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

What an Instrument Can See, Ch Polarisation as a statistical object: coherency and Mueller matrices

Problem

A partially polarised LED beam has the following time-averaged field products, measured in an (x,y)(x,y) basis transverse to propagation: ⟨ExEx∗⟩=3 mW mm−2,⟨EyEy∗⟩=1 mW mm−2,⟨ExEy∗⟩=(0.5+0.5i) mW mm−2.\begin{aligned}\langle E_xE_x^*\rangle &= 3\ \text{mW mm}^{-2},\\\langle E_yE_y^*\rangle &= 1\ \text{mW mm}^{-2},\\\langle E_xE_y^*\rangle &= (0.5+0.5i)\ \text{mW mm}^{-2}.\end{aligned} ((a)) Write down the coherency matrix Jcoh\mathbf{J}_{\mathrm{coh}}, using ⟨EyEx∗⟩=⟨ExEy∗⟩∗\langle E_yE_x^*\rangle = \langle E_xE_y^*\rangle^*, and confirm it is Hermitian. ((b)) Compute its trace and determinant, and state whether the beam is a physically allowed partially polarised beam. ((c)) Find its eigenvalues, in mW mm−2^{-2}, to two decimal places.

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