Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line

Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is found to have a critical line which separates regions of saturating and non-saturating magnetoresistance. The percolation problem which describes this line is a generalization of anisotropic percolation. We locate the percolation threshold and determine the t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in two-constituent 2D isotropic percolation. We also determine the exponents which characterize the critical dependence on magnetic field, and confirm numerically that nu is independent of anisotropy. We propose and test a complete scaling description of the magnetoresistance in the vicinity of the critical line.Comment: Substantially revised version; description of behavior in finite magnetic fields added. 7 pages, 7 figures, submitted to PR

On random symmetric matrices with a constraint: the spectral density of random impedance networks

We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found recently for the average density of resonances in random impedance networks [Y.V. Fyodorov, J. Phys. A: Math. Gen. 32, 7429 (1999)]. In the case of banded matrices, the analytical results are compared with those extracted from the numerical solution of Kirchhoff equations for quasi one-dimensional random impedance networks.Comment: 4 pages, 5 figure

Fluctuations and scaling of inverse participation ratios in random binary resonant composites

We study the statistics of local field distribution solved by the Green's-function formalism (GFF) [Y. Gu et al., Phys. Rev. B {\bf 59} 12847 (1999)] in the disordered binary resonant composites. For a percolating network, the inverse participation ratios (IPR) with $q=2$ are illustrated, as well as the typical local field distributions of localized and extended states. Numerical calculations indicate that for a definite fraction $p$ the distribution function of IPR $P_q$ has a scale invariant form. It is also shown the scaling behavior of the ensemble averaged $$ described by the fractal dimension $D_q$. To relate the eigenvectors correlations to resonance level statistics, the axial symmetry between $D_2$ and the spectral compressibility $\chi$ is obtained.Comment: 7 pages, 6 figures, accepted by Physical Review

Effective nonlinear optical properties of composite media of graded spherical particles

We have developed a nonlinear differential effective dipole approximation (NDEDA), in an attempt to investigate the effective linear and third-order nonlinear susceptibility of composite media in which graded spherical inclusions with weak nonlinearity are randomly embedded in a linear host medium. Alternatively, based on a first-principles approach, we derived exactly the linear local field inside the graded particles having power-law dielectric gradation profiles. As a result, we obtain also the effective linear dielectric constant and third-order nonlinear susceptibility. Excellent agreement between the two methods is numerically demonstrated. As an application, we apply the NDEDA to investigate the surface plasma resonant effect on the optical absorption, optical nonlinearity enhancement, and figure of merit of metal-dielectric composites. It is found that the presence of gradation in metal particles yields a broad resonant band in the optical region, and further enhances the figure of merit.Comment: 20 pages, 5 figure

Dimensional Crossover in the Effective Second Harmonic Generation of Films of Random Dielectrics

The effective nonlinear response of films of random composites consisting of a binary composite with nonlinear particles randomly embedded in a linear host is theoretically and numerically studied. A theoretical expression for the effective second harmonic generation susceptibility, incorporating the thickness of the film, is obtained by combining a modified effective-medium approximation with the general expression for the effective second harmonic generation susceptibility in a composite. The validity of the thoretical results is tested against results obtained by numerical simulations on random resistor networks. Numerical results are found to be well described by our theory. The result implies that the effective-medium approximation provides a convenient way for the estimation of the nonlinear response in films of random dielectrics.Comment: 9 pages, 2 figures; accepted for publication in Phys. Rev.

Precise determination of the conductivity exponent of 3D percolation using exact numerical renormalization

PACS. 05.50.+q Lattice theory and statistics (Ising, Potts, etc.) - 05.70.-a Thermodynamics,

FDTD modeling of realistic semicontinuous metal films

We have employed a parallelized 3D FDTD (finite-difference time-domain) solver to study the electromagnetic properties of random, semicontinuous, metal films. The structural features of the simulated geometries are exact copies of the fabricated films and are obtained from SEM images of the films themselves. The simulation results show good agreement with the experimentally observed far-field spectra, allowing us to also study the nonlinear moments of the optical responses for these realistic nanostructures. These results help to further our understanding of the details of the electromagnetic response of randomly structured metal films. Our results can also be applied in the optimization of random metal nanostructures and in the design of surface-enhanced spectroscopies and other plasmonic applications