Normal form for Mueller matrices in polarization optics

Abstract

The normal (canonical) form for Mueller matrices in polarization optics is derived: it is shown that a non-singular real 4×4 matrix M qualifies to be the bona fide Mueller matrix of some physical system if and only if it has the canonical form M = L' λL, where L and L' are elements of the proper orthochronous Lorentz group L λ ₊, and where λ = diag (λ₀,λ₁,λ₂,λ₃) with λ₀ ≥|λ_j| > 0. It is further shown that λ1 andλ₂ can be taken to be positive so that the signature of λ₃ is the same as that of det M. Several experimentally measured Mueller matrices are analysed in the light of the normal form. The case of singular Mueller matrices is briefly discussed as a limiting case.