An application of Wright functions to the photon propagation

In a previous note a generalized Beer's law was discussed in relation to the space-fractional Poisson process to explain possible deviations from the exponential extinction law in spatially correlated media. Here a different point of view will be developed, applying a Wright type function to describe the probability of photon transmission in random media. We find the analytic form of the photon mean-free-path (MFP) related to such Wright law of extinction. We also give an estimate of the deviation from an exponential law, showing the utility of our approach and discussing a comparison with the predictions given by the classical Beer's law in uniform media. -- Highlights: •We show the utility of Wright-type special function in radiative transfer problem. •We suggest an interpretation of Wright law related to non-exponential extinction. •We compute the mean-free-path of this Wright-type transmission probability. •We show the deviations from the classical Beer–Lambert law