Abstract

This work extends the understanding of photon behavior in spherical diffusive gain-media that may inform random lasing. We assess the time-dependent photon fluence rate on the boundary of a spherical homogeneous diffusive gain-medium, when resulted from hypothetical synchronous impulsive photon generations distributed uniformly within. The combined temporal photon fluence rate at a boundary position is modeled by means of a geometric-distribution-probability (GDP) weighting of the pulse-spread-function, according to the line-of-sight distance between the boundary point and a model-source. The approach acts to transform between a time-dependent size issue and a size-dependent time issue. The integral manifests a bi-phasic pattern having a global minimum. The time of the onset of the phase-change multiplying with the speed of light equates to a line-of-sight length, which decreases monotonically as the size of the sphere increases. The line-of-sight length equaling the radius of the spherical medium is interpreted as the threshold-size of lasing. This threshold size associated with a spherical medium assessed over a gain/scattering ratio spanning seven orders of magnitude of [ 10 − 3 , 10 4 ] is in good agreement with the values given by the Letoknov's eigen-mode-decomposition in the diffusive regime and by the radiative transfer approach over the semi-ballistic regime.

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