Dispersion relation for real-plane zeros as a solution of a special phase problem

A physical phenomenon of wave propagation has certain logarithmic threshold of complexity above which the conventional description of wave process is inadequate. For this reason the real-plane zeros of light wave are examined in the present paper. The probability of the real-plane zero occurrence is calculated by the numerical simulation of the lightwave propagation in an inhomogeneous medium. The functional relationship between the phase and the amplitude logarithm of the wave function near its real zero point has been found. This result takes the form of the dispersion relation, derived analytically and supported by numerical experiment.