  Optical systems obeying non-Hermitian dynamics have been the subject of
intense and concerted investigation over the last two decades owing to their
broad implications in photonics, acoustics, electronics as well as atomic
physics. A vast majority of such investigations rely on a dissipative, balanced
loss-gain system which introduces unavoidable noise and consequently, this
limits the coherent control of propagation dynamics. Here, we show that an
all-dielectric, non-dissipative photonic crystal (PC) could host, at least two
exceptional points in its eigenvalue spectrum. By introducing optimum
apodization in the PC architecture, namely 1D-APC, we show that such a
configuration supports a spectrum of exceptional points which distinctly
demarcates the PT-symmetric region from the region where PT -symmetry is broken
in the parameter space. The analytical framework allows us to estimate the
geometric phase of the reflected beam and derive the constraint that governs
the excitation of topologically-protected optical Tamm-plasmon modes in
1D-APCs.
