Knotted Polarizations and Spin in 3D Polychromatic Waves

TL;DR

This paper explores how complex 3D polarizations in multi-frequency vector waves can form knotted structures, revealing new topological features and their observable effects in optical, acoustic, and water wave phenomena.

Contribution

It introduces the concept of knotted polarizations in multi-frequency wave interference and describes their properties, including spin and polarization parameters, across various wave types.

Findings

Knotted polarizations can be formed in multi-frequency wave interference.

Interfering three waves can generate various knot types.

Knotted water particle trajectories are observable in water wave experiments.

Abstract

We consider complex 3D polarizations in the interference of several vector wave fields with different commensurable frequencies and polarizations. We show that the resulting polarizations can form knots, and interfering three waves is sufficient to generate a variety of Lissajous, torus, and other knot types. We describe the spin angular momentum, generalized Stokes parameters and degree of polarization for such knotted polarizations, which can be regarded as partially-polarized. Our results are generic for any vector wave fields, including, e.g., optical and acoustic waves. As a directly-observable example, we consider knotted trajectories of water particles in the interference of surface water (gravity) waves with three different frequencies.