  The H1 photonic crystal cavity supports two degenerate dipole modes of
orthogonal linear polarization which could give rise to circularly polarized
fields when driven with a $\pi$/$2$ phase difference. However, fabrication
errors tend to break the symmetry of the cavity which lifts the degeneracy of
the modes, rendering the cavity unsuitable for supporting circular
polarization. We demonstrate numerically, a scheme that induces chirality in
the cavity modes, thereby achieving a cavity that supports intrinsic circular
polarization. By selectively modifying two air holes around the cavity, the
dipole modes could interact via asymmetric coherent backscattering which is a
non-Hermitian process. With suitable air hole parameters, the cavity modes
approach the exceptional point, coalescing in frequencies and linewidths as
well as giving rise to significant circular polarization close to unity. The
handedness of the chirality can be selected depending on the choice of the
modified air holes. Our results highlight the prospect of using the H1 photonic
crystal cavity for chiral-light matter coupling in applications such as
valleytronics, spin-photon interfaces and the generation of single photons with
well-defined spins.
