Polychromatic electric field knots

The polarization of a monochromatic optical beam lies in plane, and general, is described by an ellipse, known as the ellipse. ellipse tight focusing (non-paraxial) regime forms non-trivial three-dimensional topologies, such M\"obius ribbon strips, well knots. latter formed when dynamics specific states, e.g., circular are studied upon propagation. However, there alternative method to generate knots: electric field's tip can be made evolve along knot trajectory time locally. We propose intuitive technique engineer path traced field vector polychromatic beams form different In particular, we show examples how tightly focused with at least three frequency components spatial modes cause follow, locally, knotted trajectory. Furthermore, characterize generated knots explore densities free-space propagation focal volume. Our study may provide insight for designing current structured electromagnetic fields interact materials.