  Coupled cavities are of interest as they expose qualitatively new effects,
such as non-Hermitian properties, that are beyond the possibilitie of
individual cavities. Here, we investigate the coupling between two dielectric
two-dimensional microdisk cavities and compare circular vs. deformed
(lima\c{c}on) resonator shapes as a function of their distance and address the
effect of coupling on the far-field emission properties. We find that the
asymmetric coupling characteristic for non-circular, deformed cavities induces
non-Hermitian properties prominently evident in a mode-dependent chirality of
the coupled cavity modes. We use an analytical model to explain our findings
and reveal the direct connection between coupling asymmetry and the resulting
sense of rotation of the coupled modes. While the overall far-field
directionality remains robust for intercavity distances larger than two
wavelengths, we observe enhanced and reversed emission for smaller distances
even for only two coupled cavities. Our findings could prove useful for future
applications such as far-field emission control and sensing .
