  A lattice of optical ring resonators can exhibit a topological insulator
phase, with the role of spin played by the direction of propagation of light
within each ring. Unlike the system studied by Hafezi et al., topological
protection is achieved without fine-tuning the inter-resonator couplings, which
are given the same periodicity as the underlying lattice. The topological
insulator phase occurs for strong couplings, when the tight-binding method is
inapplicable. Using the transfer matrix method, we derive the bandstructure and
phase diagram, and demonstrate the existence of robust edge states. When gain
and loss are introduced, the system functions as a diode for coupled resonator
modes.
