Spin induced topological phase of ultrasonic guided wave in corrugated structure

Ultrasonic guided waves are widely used in structural health monitoring (SHM) and nondestructive evaluation (NDE). However, commonly used phase features, such as time-of-flight (TOF) shifts and single-channel phase measurements, are often sensitive to temperature variation, mechanical loading, and sensor coupling. This work introduces a geometry-based alternative: the geometric phase accumulated when guided-wave polarization slowly rotates while crossing a corrugated plate, and this phase is shown to be governed by the wave’s spin (local polarization rotation), making it less sensitive to absolute timing and amplitude variations than conventioanl phase-based methods. Starting from a continuum decomposition of total angular momentum, closed-form expressions for guided wave spin densities and spin field linked to energy transport by separating the Poynting vector into orbital and spin contributions are derived. Unlike bulk media, guided waves are shown to support multiple mixed spin states (similar and hybrid contributions), which provide additional pathways for geometry-driven polarization evolution and can enhance sensitivity to small boundary changes. Three practical geometric-phase estimation approaches are investigated: a k -space Berry-phase formulations, a field-space topological metric, and a real-space spin-trajectory construction. Among these the field-space metric is adopted because of its robustness to amplitude/timing drift. Time-domain finite-element simulations on corrugated aluminum plates (corrugation coefficient ∊ ∊ , periodicity P ; tone bursts 400–1200 kHz) show that near each tone-burst central frequncies the phase curves collapse across ∊ ∊ and P indicating low sensitivity. Away from that band they tilt and separate, while Δ ϕ approaching π and polarization flips relative to a flat-plate baseline. The full-field spin maps reveal counter-rotating layers through the thickness and localized repeating spin packets as P increases, coinciding with regions of highest Δ ϕ sensitivity. The time–marching 3D simulations also show that the spin field changes it shape over time, but keeps a clear mirror symmetry about the mid–plane due to symmetric geometry and loading scenario. The out–of–plane spin component s 3 can reverse between snapshots, indicating time–dependent switching of the local particle–rotation caused by wave mixing and scattering in the corrugated wave guide. Overall, a chain is demonstrated between geometric phase and spin, suggesting a robust geometry-linked feature for guided-wave propagation.