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Heuristic Approach to Study the Optimal Path of the Light Emission in a Percolating Cluster

Commun. Math. Anal.
Volume 17, Number 2 (2014), 34 - 44

Heuristic Approach to Study the Optimal Path of the Light Emission in a Percolating Cluster

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Abstract

In this paper a porous 3D system wherein the material porosity forms a percolating spanning cluster is studied. It is considered that the light nanoemitters are randomly incorporated into such a cluster and are pumped to the exited state by an external light beam. To find the optimal optical path between the radiated nanoemitters the Fermat principle was used and it is implemented by means of well-known the travelling salesman (TSP) approach generalized to 3D geometry. With the use of undirected graph mapping the TSP approach is applied for optimizing optical path (for principle of Fermat) to calculate the optimal light paths in such a percolation structure. The convergence of the algorithm for 3D incipient cluster is studied with details to exploit the space of feasible solutions when a collective light radiation of the internal nanoemitters becomes. Finally, the field correlations of the light emission that penetrates the entire 3D percolation cluster is discussed.