Intensity fluctuation spectra in a multiply scattering medium

Abstract

Large intensity fluctuations arising in a wave which propagates through a medium containing weak random inhomogeneities of refractive index are studied. Physical arguments are used to show how and why these large fluctuations are produced, and also to derive expressions for the spectrum of spatial frequencies present in the intensity fluctuations. Their dispersion, i.e. the scintillation index, is also derived. It is shown that there are three distinct regions of intensity fluctuations: that of small intensity fluctuations but where the phase fluctuations can be large; a focusing region where the scintillation index has peaks greater than unity; and finally a far-field region where the scintillation index saturates to unity. These results and the accompanying expressions agree with certain analytical solutions of the fourth-moment parabolic equation. The same methods are then used to obtain the spectra of time-frequencies in the different regions when the medium fluctuates in time but does not drift. The behaviour of the spectrum is investigated and it is shown that in the focusing region it behaves like ω −1 over a large range of frequencies. In the far-field region it becomes a Gaussian spectrum.