Optical phase of inhomogeneous Jones matrices: retardance and ortho-transmission states.

We determine the optical phase $ \psi $ψ (dynamic and geometric) introduced by a system described by an inhomogeneous Jones matrix. We show that there are two possible scenarios: (a) $ \psi $ψ has a finite range of $ \psi \in [{\psi _{\min }},{\psi _{\max }}] $ψ∈[ψ _min ,ψ _max ]. We calculate both limits and their corresponding polarization states analytically. (b) $ \psi $ψ spans the full range of $ \psi \in ( - \pi ,\pi ] $ψ∈(-π,π]. This scenario leads to the existence of two input polarization states whose output states are orthogonal. We call these states ortho-transmission states (OTSs) and find them analytically. We study the inverse problem of designing an optical system with OTSs given by the user.