Spectral properties of plasmon resonances in a random impedance network model of binary nanocomposites

One of the methods for the description of plasmon resonances in disordered metal-dielectric nanocomposites represents an initial composite as an electric network in the form of a lattice whose bonds are randomly arranged complex impedances. In this work, a general method is used to describe resonances in binary networks consisting of two types of impedances, which are arbitrary functions of the frequency [Th. Jonckheere and J.M. Luck, J. Phys. A $\mathbf{31}$, 3687 (1998)]. The generalization of the low-frequency $L$-$C$ model where metal and dielectric regions in the lattice are replaced by inductive bonds $L$ and capacitive bonds $C_{\mathrm{d}}$, respectively, has been considered. To analyze the spectrum of resonances in the entire optical region, a more accurate model involves the replacement of the metal regions by bonds in the form of parallel $LC$ circuits with the resonant frequency equal to the plasma frequency of the metal $\omega_{\mathrm{p}}$. The spectral properties of this model, as well as the model of a nanocomposite consisting of two metals with different plasma frequencies, have been considered. Analytical relations between the spectra of all such systems and the spectra of the initial $L$-$C$ model have been established in the matrix representation. General expressions describing the dependence of the resonance spectrum of composites with arbitrary geometry on the permittivity of the matrix have been obtained.