  In this paper, one of the major shortcomings of the conventional numerical
approaches is alleviated by introducing the probabilistic nature of molecular
transitions into the framework of classical computational electrodynamics. The
main aim is to develop a numerical method, which is capable of capturing the
statistical attributes caused by the interactions between a group of
spontaneous as well as stimulated emitters and the surrounding electromagnetic
field. The electromagnetic field is governed by classical Maxwell's equations,
while energy is absorbed from and emitted to the (surrounding) field according
to the transitions occurring for the emitters, which are governed by
time-dependent probability functions. These probabilities are principally
consistent with quantum mechanics. In order to validate the proposed method, it
is applied to three different test-cases; directionality of fluorescent
emission in a corrugated single-hole gold nano-disk, spatial and temporal
coherence of fluorescent emission in a hybrid photonic-plasmonic crystal, and
stimulated emission of a core-shell SPASER. The results are shown to be closely
comparable to the experimental results reported in the literature.
