Mean power transmission for one-dimensional random wave propagation using a cumulant expansion

In this paper the problem of the mean power transmission for one-dimensional wave propagation in a random medium is studied. We use a cumulant technique valid for small k₀L_c where measures the size of the fluctuations, L_c is the correlation length of the random wave number, and k₀ is the undisturbed wave number. We obtain an integral expression for the mean transmitted power. It shows exponential decay for large width, and linear decay for small width. The relevant scale to measure the width of the slab is ²k²₀∫^∞₀C(x)cos(2k₀x)dx where C(x) is the autocorrelation of the random wave number.