Quantized topological phase of ultrasonic guided wave with spin orbit interaction

Acoustic and ultrasonic waves have recently been described to have quantifiable spin states. Polarization vectors that evolve over time carry information of the spin state of wave propagates in a media, that is generally non observable. Quantum analogous spin state of ultrasonic guided wave is primarily manifest nonzero spin angular momentum (SAM) and its integration over the wave path gives the topological phase acquired due to the modified polarity. The topological geometric phase gives a new opportunity to quantify damage state in materials using ultrasonic guided wave that were usually considered difficult. In this article it is shown that ultrasonic guided waves must demonstrate quantifiable topological phenomena, naturally, if specific spin orbit interaction (SOI) driven actuation is activated. By inducing artificially created SOI, SAM density can be calculated from the fundamental conserved quantity. They reveal material independent but polarity dependent behavior of wave propagation and manifest as a topological phenomenon. In this article SAM density of ultrasonic guided waves is found from the fundamentals of Noether current and three-dimensional SOI. It is shown that polarity driven manifestation of SAM can be quantified, and topological geometric phase can be calculated. Utilizing two mirrored damages in different quadrants in an isotropic media that are equivalent to each other and are indistinguishable, it is shown that SOI induced SAM and polarity driven topological phase have qualitative and quantitative differences and could be used as a parameter for ultrasonic NDE.