Polarization singularities and M\"{o}bius strips in sound and water-surface waves

TL;DR

This paper demonstrates the natural occurrence of polarization singularities and M"{o}bius strips in inhomogeneous monochromatic sound and water-surface waves, providing new insights into their topological features and interactions.

Contribution

It introduces polarization singularities and M"{o}bius strips in sound and water waves, expanding the study of topological features beyond electromagnetic fields.

Findings

Polarization singularities appear in sound and water waves.

Examples of C-points and M"{o}bius strips in wave fields.

Potential applications in wave-matter interaction studies.

Abstract

We show that polarization singularities, generic for any complex vector field but so far mostly studied for electromagnetic fields, appear naturally in inhomogeneous yet monochromatic sound and water-surface (e.g., gravity or capillary) wave fields in fluids or gases. The vector properties of these waves are described by the velocity or displacement fields characterizing the local oscillatory motion of the medium particles. We consider a number of examples revealing C-points of purely circular polarization and polarization M\"{o}bius strips (formed by major axes of polarization ellipses) around the C-points in sound and gravity wave fields. Our results (i) offer a new readily accessible platform for studies of polarization singularities and topological features of complex vector wavefields and (ii) can play an important role in characterizing vector (e.g., dipole) wave-matter interactions in acoustics and fluid mechanics.