  Exceptional point (EP) degeneracies in coupled cavities with gain and loss
provide on-chip photonic devices with unconventional features and performance.
However, such systems with realistic structures often miss the exact EPs even
in simulation, and the mechanism of this EP disruption has yet to be thoroughly
identified. Here, we extend the coupled-mode theory of one-dimensional
non-Hermitian resonator arrays to study the effects of the imaginary part of
the inter-cavity coupling, which is a second-order term and attributed to
material amplification, absorption, and radiation. By taking an appropriate
gauge for the model, we clarify that the imaginary coupling components have a
symmetric form in the effective Hamiltonian and hence represent
non-Hermiticity. These additional factors can lift the gain- and loss-based EP
degeneracies. However, they are proportional to the sum of the imaginary
permittivities for involved cavity pairs. Thus, when the amplification and
absorption of adjacent cavities are balanced, their contribution to the
imaginary coupling is canceled, and the EP singularity can be restored.
Radiation-induced imaginary couplings measure the change in net radiation loss
by the interference between cavity modes. Their impact on the EP can also be
counteracted by small cavity resonance detuning even in loss-biased cases. We
show and analyze eligible simulation examples based on photonic crystal
nanocavities, and highlight design of an ideal EP degeneracy that is protected
by generalized PT symmetry and induced by radiation.
