  Degeneracies of non-Hermitian Hamiltonian i.e., exceptional points (EPs) of
parity-time (PT)-symmetric systems have received considerable research
attention due to their various possible applications in optical devices. At
EPs, at least two eigenvalues as well as their eigenvector coalesce. Recently,
the effect of the eigenfrequency splitting on transfer function near EP was
studied for an optical system consisting of two micro ring resonators, which
led to complex splitting in PT-symmetric and anti-PT-symmetric sensors. In
present work, we propose a simple system of three coupled ring resonators to
show real splitting in both PT-symmetric and anti-PT-symmetric parameter
domains by exploiting higher-order EPs. We indirectly couple two rings with
equal amount of gain and loss via an intermediate neutral ring. This system is
then tested for refractive index (RI) sensing by modulating the cladding index
and we numerically show a huge enhancement in sensitivity as compared to those
reported in previous studies of micro ring resonators. Importantly, the
enhancement is found to be of the order of 10^8. Further, we have found that
the order of EP can be tuned by perturbating the cladding. The outcomes of this
study may set up a wide range of applications in non-Hermitian triplet cavity
systems.
