Non-Hermitian periodic wave systems display unusual behaviors that are not accounted for by traditional Bloch band theory, including the localization of entire bands of eigenstates near the edges of finite-size samples (the non-Hermitian skin effect). Recent theoretical work, mostly focused on discrete lattice models, has introduced the notion of a generalized Brillouin zone (GBZ) in complex reciprocal space to explain these phenomena. Here we extend this description to the case of photonic crystals, which hold great promise for the investigation of non-Hermitian effects in continuous lattices and their exploitation for practical device applications. Our approach is based on a tight-binding model that can be applied to any given photonic crystal to provide a direct and computationally efficient connection to non-Bloch band theory. As an illustration, we use this model to compute the complex frequency spectrum and GBZ of a finite two-dimensional lattice of lossy triangular building blocks. The results highlight a rich localization behavior for the skin modes and an intricate evolution of the GBZ controlled by the crystal wave vector parallel to the open boundaries. The framework developed in this work is attractive for the design and modeling of non-Hermitian photonic crystals of high structural complexity, where traditional electromagnetic simulations can become prohibitively expensive in terms of the required computational resources to handle finite-size systems. Furthermore, it introduces a powerful tool for theoretical studies where knowledge of the GBZ is required, including the investigation of topological phase transitions in photonic non-Hermitian settings.

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• Edge states
• Photonic crystals
• Topological effects in photonic systems
• Non-Hermitian systems