20 research outputs found
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 are illustrated, as
well as the typical local field distributions of localized and extended states.
Numerical calculations indicate that for a definite fraction the
distribution function of IPR has a scale invariant form. It is also shown
the scaling behavior of the ensemble averaged described by the
fractal dimension . To relate the eigenvectors correlations to resonance
level statistics, the axial symmetry between and the spectral
compressibility 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