Reflection of light from a random amplifying medium with disorder in the complex refractive index: Statistics of fluctuations

The probability distribution of the reflection coefficient for light reflected from a one-dimensional random amplifying medium with cross-correlated spatial disorder in the real and the imaginary parts of the refractive index is derived using the method of invariant imbedding. The statistics of fluctuations have been obtained for both the correlated telegraph noise and the Gaussian white-noise models for the disorder. In both cases, an enhanced backscattering (with a reflection coefficient greater than unity) results because of coherent feedback due to Anderson localization and coherent amplification in the medium. The results show that the effect of randomness in the imaginary part of the refractive index on localization and reflection is qualitatively different.