Braided nodal lines in wave superpositions

Nodal lines ( phase singularities, optical vortices) are the generic interference fringes of complex scalar waves. Here, an exact complex solution of the time-independent wave equation ( Helmholtz equation) is considered, possessing nodal lines which are braided in the form of a borromean, or pigtail braid. The braid field is a superposition of counterpropagating, counterrotating, non-coaxial third-order Bessel beams and a plane wave whose propagation is perpendicular to that of the beams. The construction is structurally stable, and can be generalized to a limited class of other braids.