Resonant freak microwaves

The Helmholtz equation describing transverse magnetic modes in a closed flat microwave resonator with 60 randomly distributed discs is numerically solved. At lower frequencies, the calculated wave intensity spatially distributed obeys the universal Porter-Thomas form if localized modes are excluded. A superposition of resonant modes is shown to lead to rare events of extreme intensities (freak waves) at localized “hot spots”. The temporally distributed intensity of such a superposition at the center of a hot spot also follows the Porter-Thomas form. Branched modes are found at higher frequencies. The results bear resemblance to recent experiments reported in an open cavity.