Estimation of first-passage lengths and Levy exponents in nanophotonic amplifying random media

摘要

We estimate the parameters of intensity fluctuations in amplifying nanophotonic random media, based on analytical and numerical methods. The statistics of such media belong to the Levy domain due to underlying power-law distributions. The power-law exponent is determined by the gain length and the mean first-passage length of the photon in the system. We employ a Monte-Carlo simulation to accurately estimate the excitation region of the medium, which yields the gain length and the geometric features of this region. The aspect ratio of this pumped region allows to further analytically calculate the mean first-passage length of a photon diffusing out of the amplifying region. Our calculations are in excellent agreement with experimental trends regarding the Gaussian to Levy transition.