Fig. 3: Non-Hermitian Rayleigh waves in half-space.
From: Non-Hermitian elastodynamics in gyro-odd continuum media
a Scatter plots showing the phase diagram and the complex velocity \({v}_{{{{{{{{\rm{R}}}}}}}}}^{+}\) for the forward propagating Rayleigh waves, and b corresponding to \({v}_{{{{{{{{\rm{R}}}}}}}}}^{-}\) in the backward direction. Beyond the stable solutions (red dots), we use gray dots and hollow circles to differentiate between no solution and instability, respectively. The red arrows indicate either a forward or backward propagating direction. The dashed lines mark the transition of one-way propagation reversal. c–e Numerically calculated modal fields with parameters highlighted in (a, b). In each simulation, a vibrating source (red stars, ω = 15π) is placed on the top surface to excite surface waves, and the modal fields are normalized with regard to their own maximum values. f, g Scatter maps rendering the penetration depth δ⊥ and the reciprocal propagation length 1/δ∥ (normalized to the wavelength) for the non-Hermitian Rayleigh waves. In here, we discriminate between forward and backward propagating waves. h A group of odd-elastic engine cycles at different depths for the Rayleigh waves studied in d. i Likewise for the scenario illustrated in e. In this study, we set material parameters μ = 0.5 and α = 1.
