Observations of non-Rayleigh statistics in the approach to photon localization

We measure the distribution of intensity of microwave radiation transmitted through absorbing random waveguides of lengths $L$ up to localization length $\xi$. For large intensity values the distribution is given by a negative stretched exponential to the $1/2$ power, in agreement with predictions by Nieuwenhuizen and van Rossum[Phys. Rev. Lett. 74, 2674 (1995)] for diffusing waves in nonabsorbing samples, as opposed to a negative exponential given by Rayleigh statistics. The intensity distribution is well described by a transform derived by Kogan and Kaveh [Phys. Rev. B 52, R3813 (1995)] of the measured distribution of total transmission.