  Topological photonic edge states, protected by chiral symmetry, are
attractive for guiding wave energy as they can allow for more robust guiding
and greater control of light than alternatives; however, for photonics, chiral
symmetry is often broken by long-range interactions. We look to overcome this
difficulty by exploiting the topology of networks, consisting of voids and
narrow connecting channels, formed by the spaces between closely spaced perfect
conductors. In the limit of low frequencies and narrow channels, these
void-channel systems have a direct mapping to analogous discrete mass-spring
systems in an asymptotically rigorous manner and therefore only have
short-range interactions. We demonstrate that the photonic analogues of
topological tight-binding models that are protected by chiral symmetries, such
as the SSH model and square-root semimetals, are reproduced for these
void-channel networks with appropriate boundary conditions. We anticipate,
moving forward, that this paper provides a basis from which to explore
continuum photonic topological systems, in an asymptotically exact manner,
through the lens of a simplified tight-binding model.
