  The realization of higher-order exceptional points (HOEPs) can lead to orders
of magnitude enhancement in light-matter interactions beyond the current
fundamental limits. Unfortunately, implementing HOEPs in the existing schemes
is a rather difficult task, due to the complexity and sensitivity to
fabrication imperfections. Here we introduce a hierarchical approach for
engineering photonic structures having HOEPs that are easier to build and more
resilient to experimental uncertainties. We demonstrate our technique by an
example that involves parity-time (PT) symmetric optical microring resonators
with chiral coupling among the internal optical modes of each resonator.
Interestingly, we find that the uniform coupling profile is not required to
achieve HOEPs in this system -- a feature that implies the emergence of HOEPs
from disorder and provides resilience against some fabrication errors. Our
results are confirmed by using full-wave simulations based on Maxwell's
equation in realistic optical material systems.
