Green's-function formalism of dielectric resonance on binary networks: Application to optical properties

In this dissertation, Green's-function formalism (GFF) is developed to deal with the optical responses of arbitrary-shaped metallic clusters embedded in the infinite dielectric networks in the quasistatic limit. By the formalism, the resonance spectrum and the local field distribution for each eigenmode can be analytically obtained. We use the simple examples to describe the inhomogeneous local field in space around the metallic clusters due to the quasistatic resonance, which will be shown to give a large enhancement in the effective linear and nonlinear responses.; Then, the GFF is applied to two systems. First, the optical responses of the dilute anisotropic networks are investigated for various applied fields, parallel or perpendicular to the direction of anisotropy. The large third order nonlinear enhancements are found to arise from the geometric anisotropy. The peaks of absorption and nonlinear enhancement overlap when the applied field is parallel to the anisotropy. In contrast, the absorption peak is separated from the nonlinear enhancement peak when the applied field is perpendicular to the anisotropy. In terms of the distribution of inverse participation ratios (IPR) with q = 2 and of the spectral density of linear and nonlinear optical responses, the above results can be understood. Secondly, the optical responses of two interacting clusters in composites are studied. The GFF of two clusters with central symmetry is derived. Compared with the optical responses of the isolated cluster, the red shifts and blue shifts occur, respectively, when the applied field is parallel and perpendicular to the central line of two clusters. We can explain these shifts completely by means of the local field distribution of two interacting single bonds.; Finally, the statistics of the level spacing of resonance (or eigenvalues) and of the right eigenvectors of the Green's-matrix M of GFF is studied from the random matrix theory (RMT) for the disordered binary composites. In the level spacing statistics, the level spacing distribution P(t) and the level number variance Σ 2(L) are calculated on the unfolded scale for various concentration p. We find that both the short-range fluctuation P(t) and long-range spectral correlation Σ 2(L) lie between the profiles of the Poisson ensemble and Gaussion orthogonal ensemble (GOE). At the percolation threshold p_c, the crossover behavior of the functions P (t) and Σ2(L) is found, as well as the finite size scaling of the mean level spacing and the mean level number. In the statistics of eigenvectors of Green's-matrix M, we first investigate the properties of percolating systems. The local property of eigenvectors is illustrated by using the IPR with q = 2, giving the forms of 3D plots and contours of the typical localized, extended and intermediate states. In such systems, the large nonlinear enhancement and the separation between linear and nonlinear optical peaks are reported. It is also shown that the distribution function of IPR P_q has the scale invariant form for the fixed concentration p. The scaling behavior of the ensemble averaged ⟨P_q⟩, described by the fractal dimension D_q, is obtained. To link the level statistics with the eigenvectors correlations, the axial symmetry between D₂ and the spectral compressibility χ is found, where χ is defined as the slope of Σ2( L) with respect to L.