We develop a general theory for twisted bilayer photonic crystals that takes into account both far-field response and near-field coupling. The theory is based on the framework of a generalized Rayleigh-Schrödinger perturbation theory for non-Hermitian Hamiltonians. A universal form for interlayer coupling is derived, which relates the hopping strength to the Fourier transforms of the Wannier functions in the single layer photonic crystal. For low-energy states at the K point in hexagonal lattices, the interlayer coupling reduces to that in the Bistritzer-MacDonald model for graphene. As an example, we study a twisted bilayer photonic crystal slab with air holes arranged in a honeycomb lattice in each layer. The first-order solution of our model predicts a fourfold band splitting in the far-field spectrum compared to the single-layer case, which is confirmed by numerical simulations. Moreover, our theory reveals that for low-energy states at K points, scattering toward the $\mathrm{\Gamma }$ point via the moiré potential is suppressed. Based on our theory, we propose a wide-angle, high-$Q$ tunable flat band cavity by combining the bilayer at a large twist angle with a Brillouin-zone-folding perturbation within each layer. The cavity behaves like a collection of quasibound states in the continuum with a divergent density of states, with potential applications in nonlinear optics, lasing, and quantum optics.

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• Bound states in the continuum
• Nanophotonics
• Photonic crystals
• Bloch wave theory
• Finite-difference time-domain method