Scalar versus vectorial impedance-angle formalisms for optical fibers

Modeling strategies for weakly-guiding optical fibres often rely on the weak-guidance approximation. We revisit the vectorial modal field equations in the guise of a modal impedance-angle formalism, and discover that three distinct levels of weak-guidance approximations lead to propagation coefficient solutions that are O(Δⁿ), n = 1,2,3 with respect tot the weak-guidance parameter Δ.