Stochastic modeling of plasmonic field evolution propagating in non-uniform metallic strip arrays

The amplitude field distribution of surface plasmons propagating in an array of non-uniform metallic strips is analyzed. The study models the evolution of the amplitude function as a Markov chain, which is associated with a stochastic matrix. The plasmonic amplitude function is related to a probability vector whose entropy evolution enables the description of the plasmonic stability, which is governed by the structure of the matrix’s eigenvectors. The dominant eigenvector, also known as the steady-state vector, is of particular importance and corresponds to the largest eigenvalue. This dominant vector is obtained using the Perron–Frobenius theorem and provides the stable plasmonic amplitude function propagating across the entire array of metallic strips. From this vector, partial coherence effects are analyzed. Computer simulations are presented.