Dielectric resonances of lattice animals and other fractal clusters

Abstract

Abstract. Electrical and optical properties of binary inhomogeneous media are currently modelled by a random network of metallic bonds (conductance σ 0 , concentration p) and dielectric bonds (conductance σ 1 , concentration 1 − p). The macroscopic conductivity of this model is analytic in the complex plane of the dimensionless ratio h = σ 1 /σ 0 of the conductances of both phases, cut along the negative real axis. This cut originates in the accumulation of the resonances of clusters with any size and shape. We demonstrate that the dielectric response of an isolated cluster, or a finite set of clusters, is characterised by a finite spectrum of resonances, occurring at well-defined negative real values of h, and we define the cross-section which gives a measure of the strength of each resonance. These resonances show up as narrow peaks with Lorentzian line shapes, e.g. in the weakdissipation regime of the RL − C model. The resonance frequencies and the corresponding cross-sections only depend on the underlying lattice, on the geometry of the clusters, and on their relative positions. Our approach allows an exact determination of these characteristics. It is applied to several examples of clusters drawn on the square lattice. Scaling laws are derived analytically, and checked numerically, for the resonance spectra of linear clusters, of lattice animals, and of several examples of self-similar fractals.

Localized mode transfer and optical response in three-component composites

“…When dielectric resonance s"ϭ1/͓1Ϫ(⑀ 1 /⑀ 0 )͔… happens, ⑀ 1 /⑀ 0 has a branch cut with the number n in the negative real axis. 2,5 In GFF, Green's matrix M in the clusters subspace maps the geometry of the clusters. The element of M has the form M x,y ϭ ͚ zC(y) (G x,y ϪG x,z ), where zC(y) means that the jointing points z and y belong to the clusters subspace and are the nearest neighbors, and G x,y is Green's function of Laplace operator on the infinite square network, i.e., Ϫ⌬G x,y ϭ␦ x,y with G x,x ϭ0.…”

“…The correction of this relation is checked for various binary systems. 2,5 In our numerical calculations, this sum rule is always used to check the correction of Green's matrix and the rationality of the resonances. Now consider a three-component composite.…”

“…[1][2][3][4][5][6][7] When dielectric resonance takes place, the system exhibits various eigenmode localizations of local field, [8][9][10] including surface-plasmon modes in the disordered nanosystems, 1,11,12 localized dipolar excitations on the roughly nanostructured surfaces, 13 and selective photomodification in the fractal aggregates of colloidal particles. 14 The fluctuations of local field are reported to enhance strongly the effective linear and nonlinear optical responses in composites.…”

Avoiding crossing of dielectric resonances in three-component composites

“…The salient properties of G x,y were reviewed in the appendix of Ref. 13. By introducing a difference admittance ratio ϭ(⑀ 2 Ϫ⑀ 0 )/(⑀ 1 Ϫ⑀ 0 ), the matrix M can be written as…”

A theory of spectral properties of disordered metal-semiconductor nanocomposites

“…Thus, continuous heterogeneous medium is replaced by a discrete network with LC-and C-bonds. In literature the approximation when LC-bonds are replaced to L-bonds is extensively studied [1,2,3]. However, it is valid only for a low frequencies ω ω p and the properties of the general case remain unclear.…”