Topological Configurations of Optical Phase Singularities

Geometric and topological properties of phase singularity lines in three-dimensional complex scalar wavefields are discussed. In particular, their role as the intersections of the zero contour surfaces of the real and imagi-nary parts of the field gives numerous insights into 3D vortex topology. In addition, complex scalar wavefields (i.e. solutions of the three-dimensional Helmholtz and paraxial equations) are compared to more general complex scalar fields, including those arising naturally from algebraic geometry. 1