Metamaterials provide a versatile platform for realizing topological phases and exploring non-Hermitian physics. However, the design of metamaterials exhibiting such rich physics is challenging because conventional design approaches require constant iterative optimization, which unfortunately is both time-intensive and computationally expensive. Here, a noniterative reverse design strategy based on tight-binding models is proposed. Our design starts with topolectrical circuits; by exploring the equivalence of scattering properties between circuits and waveguides, we demonstrate that a lumped-element circuit can be directly translated to its metamaterial counterpart. As a proof of concept, we design electromagnetic metamaterials based on three representative models. For the Hermitian case, a honeycomb lattice that preserves time-reversal symmetry ($T$), and the Haldane model with $T$-breaking nonreciprocal hoppings are implemented; whereas for the non-Hermitian case, a topological heterojunction exhibiting non-Hermitian skin effect is constructed. Given the widespread use of scattering parameters, the proposed strategy can be generalized to the design of metamaterials in systems beyond electromagnetics. Our work reveals an efficient and straightforward approach for realizing topological phenomena in classical wave systems, offering a deterministic alternative for the design of topological devices.

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• Metamaterials
• Topological effects in photonic systems
• Topological materials
• Tight-binding model