Critical-point level-crossing geometry in random wave fields

Computer simulations and analytical calculation are used to study the geometry of level crossings of the real and the imaginary parts of wave functions and their spatial derivatives at the critical points of these functions, the intensity, and the phase. Zero-crossing maps that locate these critical points are presented, and topological constraints that determine the ordering of the critical points along the zero crossings are reviewed. Available theoretical calculations of the critical point number densities are also reviewed and are compared with measured data from the simulations. Quantitative results are given for the directions of the level crossings, their radii and centers of curvature, and the structure of the bifurcation lines of saddle points. Correlations between these quantities are also discussed.