  Non-orthogonal eigenstates are a fundamental feature of non-Hermitian systems
and are accompanied by the emergence of nontrivial features. However, the
platforms to explore non-Hermitian mode couplings mainly measure near-field
effects, and the far-field behaviour remain mostly unexplored. Here, we study
how a microcavity with non-Hermitian mode coupling exhibits eigenstate
non-orthogonality by investigating the spatial field and the far-field
polarization of cavity modes. The non-Hermiticity arises from asymmetric
backscattering, which is controlled by integrating two scatterers of different
size and location into a microdisk. We observe that the spatial field overlaps
of two modes increases abruptly to its maximum value, whilst different
far-field elliptical polarizations of two modes coalesce when approaching an
exceptional point. We demonstrate such features experimentally by measuring the
far-field polarization from the fabricated microdisks. Our work reveals the
non-orthogonality in the far-field degree of freedom, and the integrability of
the microdisks paves a way to integrate more non-Hermitian optical properties
into nanophotonic systems.
