Observing the formation of zero-mean circular Gaussian statistics in two-dimensional random media

Zero-mean circular Gaussian statistics is a well-known model for coherent electromagnetic wave scattered by random media. Applying Kullback-Leibler Divergence to measure the deviation of the simulation scattering field probability distribution from this model, the formation of zero-mean circular Gaussian statistics is investigated quantitatively in two-dimensional random media based on finite element method. Increasing the scattering and randomness in the media, the transmission electric field gradually approaches zero-mean circular Gaussian statistics, however, the deviation from a perfect statistics distribution has a limit which is only determined by the number of random electric field variables used for estimates the probability distribution; besides, field amplitude forming stable statistics faster than field phase.