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