Multistep reversible excitation transfer in a multicomponent rigid solution: I. Calculation of steady-state and time-resolved fluorescence intensities

Previously obtained expressions describing the intensity of stationary fluorescence emitted by a multicomponent solution were significantly improved by using matrix calculus. Then, using a similar technique, new expressions describing the decay of the fluorescence intensity of the multicomponent system after pulsed excitation were found. In both of these cases, the effects of the internal filter, the effects of multistep radiative transfer of excitation energy, the possibility of radiative back-transfer, as well as the possibility of changes in the quantum yield of individual components due to radiationless transfer of excitation energy were taken into account. The cases of one-, two- and three-component systems were discussed in detail.