Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

Abstract

We assess the degree of coherence of vectorial electromagnetic fields in the space-frequency domain as the distance between the cross-spectral density matrix and the identity matrix representing completely incoherent light. This definition is compared with previous approaches. It is shown that this distance provides an upper bound for the degree of coherence and visibility for any pair of scalar waves obtained by linear combinations of the original fields. This same approach emerges when applying a previous definition of global coherence to a Young interferometer.

Classical distinguishability as an operational measure of polarization

“…In polarization, it has been suggested to take unpolarized states as the reference set, both in the quantum [46] and the classical domain [47]. Such a set is very well characterized [48][49][50] and this provides sensible results.…”

Coherence for vectorial waves and majorization

“…Accordingly, different definitions have been proposed as different generalizations of Eq. (2.3), such as [2][3][4]: 6) and, when the corresponding inverses exist,…”

“…where λ is a four-dimensional vector containing the eigenvalues of Γ/trΓ [6]. An alternative assessment along this line can be found in Ref.…”

Fisher information as a generalized measure of coherence in classical and quantum optics

“…(13). Accordingly, a suitable estimation of the degree of coherence conveyed by the field state under phase shifts generated byĜ in the quantum sector is…”

“…(13). To simplify notation let us consider discrete indices instead of continuous variables so that the measured statistics P j of the j variable can be expressed in terms of the joint statistics of the j and k variables W j,k as …”