Abstract:

Metamaterial-based nonreciprocity has emerged as a promising frontier for novel wave manipulation, yet most realizations rely on external biasing or auxiliary mechanisms, restricting their robustness and applicability. Here, we investigate the inherent nonreciprocity in a nonlinear metamaterial without any external apparatus. Fundamentally, since structural asymmetry governs the internal mode distribution, amplitude-dependent nonlinearity inevitably creates distinct boundary-excitations for forward and backward waves, inherently leading to nonreciprocity. To effectively combine structural asymmetry with nonlinearity, we leverage a diatomic configuration as a robust baseline, and introduce alternating nonlinear stiffnesses. We develop a rigorous analytical framework based on the Rayleigh-Schrödinger perturbation to capture the amplitude-dependent dispersion of the asymmetric unit cell. The numerical simulations validate the analytical predictions, and demonstrate direction-specific bandgap modulation for forward and backward waves. This study advances the understanding of nonlinear dynamics by elucidating how the interplay between structural asymmetry and nonlinearity passively induces nonreciprocal transmission, offering a pathway toward self-adaptive wave control systems.

Key words: nonlinear metamaterial, nonreciprocity, amplitude-dependent, bandgap, perturbation