A beam has coherency matrix

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 beam has coherency matrix, measured in an (x,y)(x,y) basis, Jcoh=(4001) mW mm−2.\mathbf{J}_{\mathrm{coh}} = \begin{pmatrix}4 & 0\\0 & 1\end{pmatrix}\ \text{mW mm}^{-2}. ((a)) Confirm Jcoh\mathbf{J}_{\mathrm{coh}} is Hermitian and positive semi-definite. ((b)) Find its eigenvalues and the degree of polarisation PP. ((c)) Carry out the unique decomposition into a fully polarised matrix and an unpolarised matrix, quoting the power (in mW mm−2^{-2}) and polarisation state of each part.

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