Vector and matrix states for Mueller matrices of nondepolarizing optical media

Abstract

Nondepolarizing Mueller matrices contain up to seven independent parameters. However, these seven parameters typically do not appear explicitly among the measured 16 parameters of a Mueller matrix, so that they are not directly accessible for physical interpretation. This work shows that all the information contained in a nondepolarizing Mueller matrix can be conveniently expressed in terms of a four component covariance vector state or a generating 4×4 matrix, which can be understood as a matrix state. The generating matrix, besides being directly related to the nondepolarizing Mueller matrix, mimics all properties of the Jones matrix and provides a powerful mathematical tool for formulating all properties of nondepolarizing systems, including the Mueller symmetries and the anisotropy coefficients.

Formalism of optical coherence and polarization based on material media states

“…The observable corresponding to the optical phenomena occurring in light-matter interactions is the 4×4 scattering matrix with sixteen real elements also known as the Mueller matrix that describes the linear transformation of the Stokes parameters of a light beam upon interaction with a linear medium. In this work, we first demonstrate how alternative representations of nondepolarizing (deterministic) optical systems that were recently presented [2] can be used to make the analogy between the scattering matrix states of optical systems and the quantum mechanical wavefuction. We also show that quantum coherence in material media can be represented by a coherent linear superposition of matrix (or vector) states associated to non-depolarizing Mueller matrices.…”

“…In a suitable basis that we have defined in a previous work [2], the dimensionless components of |h are τ , α, β and γ:…”

“…A deterministic state can be alternatively given by a Jones matrix J, a Mueller-Jones matrix M J , covariance vector |h or a 4 × 4 complex matrix, Z, defined as [2]:…”

“…By means of definition Z = A(I ⊗ J)A −1 (where A is a constant unitary matrix [2]), this coherent linear combination can be directly translated to the Z matrix states with the same complex coefficients:…”

Quaternion algebra for Stokes–Mueller formalism

“…In our previous works [1,2], we have introduced two different representations of Mueller-Jones states: the covariance vector |h and the Z matrix. Covariance vector, |h , can be defined in terms of the covariance matrix H associated to the Mueller matrix M:…”