Kin-Wah Yu

Enhancement of optical nonlinearity through anisotropic microstructures

Abstract We investigate the polarization dependence of optical nonlinearity enhancement for a uniaxial anisotropic composite of metal nanocrystals in a dielectric host. Three cases are distinguished depending on whether the polarization is parallel, perpendicular or unpolarized with respect to the axis of anisotropy. For parallel polarization, the results show that the 3D results are qualitatively similar to the 2D case reported recently. For perpendicular polarization, the results are markedly different from the parallel counterpart: In contrast to the absorption, the enhancement factor actually increases with the anisotropy. Thus the separation of the absorption and enhancement peaks becomes even more pronounced than in the parallel polarization case. These results indicate a strong polarization dependence of the nonlinear optical response.

A theory of nonlinear AC response in nonlinear composites

Abstract A perturbative approach, which has previously been applied to study the effective nonlinear response in random nonlinear composites consisting of Kerr materials, is extended to treat random composites with components having nonlinear response at finite frequencies. For a sinusoidal applied field, the field in the composite generally includes components with frequencies at the higher harmonics. Using the potential in the absence of nonlinearity as the unperturbed potential, nonlinear response can be studied perturbatively. Expression for the effective nonlinear susceptibility at the third harmonic is derived in the dilute limit of one of the nonlinear components.

Hierarchy of critical exponents on a Sierpinski honeycomb

Abstract By solving exactly the electrical conductivity problem in a Sierpinski honeycomb lattice, we find a simple algorithm which enables us to obtain the complete set of currents by inspection. The moments of the current distribution and the associated multifractal spectrum are obtained. We also compute the multifractal spectrum for the resistance jumps, resulting from short-circuiting the current-carrying bonds of the lattice. We find that the two spectra are related as predicted by the Tellegen theorem. We compare the resistance jump spectrum with that of percolation backbone of a random resistor network at the percolation threshold and an excellent agreement between the two spectra is found.

Many-Particle Problems of Thermal Conduction in Two Dimensions*

A general scheme is developed to solve many-particle problems of thermal conduction in two dimensions. Based on the Greens function formalism, heat sources induced by discontinuity of temperature fields and temperature potentials on inclusion boundaries are explicitly taken into account, and analytical expressions for temperature distributions in granular systems are established. The unknown coefficients in the analytical expressions for temperature field are determined by a matrix equation whose elements are all monomials of the distances between particle centers. Decomposition of the matrix equation for the systems containing a chain of particles is discussed. Illustrative calculations are presented for granular systems with two and three particles.

NEW METHOD FOR EFFECTIVE VISCOSITY OF COLLOIDAL DISPERSIONS WITH PERIODIC MICROSTRUCTURES

Abstract One of the central theoretical problems in the colloid field is to determine the rheological relation between the macroscopic properties of colloidal suspensions and the microstructures of the systems. In this work, the authors develop a method of transformation field by which one can calculate the effective viscosity of an incompressible viscous fluid containing colloidal particles (either solid particles or liquid drops) fixed at the points of a periodic lattice. The effective viscosity of a colloidal dispersion of spherical particles is calculated. The predictions of the theory are in good agreement with the Einstein’s formula for suspensions and the Taylor’s formula for emulsions at low particle concentrations. At higher particle concentrations, the theory reproduces the results of Nunan and Keller. The method is also applicable to the viscosity of colloidal systems with non-spherical particles.

Calculation of energy subband structures of corrugated lateral-surface superlattices based on variational principles

A theoretical method is developed for calculating energy subbands of carriers in lateral-surface superlattices with corrugated interfaces (CLSSLs). Based on the variational principle and a coordinate transformation, the method overcomes difficulties in constructing wave functions which must satisfy complicated boundary conditions on corrugated interfaces. The method is tested numerically via calculations of electron subbands, probability distributions and intersubband optical absorptions of CLSSLs with periodic variations of well thicknesses. Sensitive dependencies of electron subbands, probability distributions and intersubband optical absorptions on structural parameters of CLSSLs are predicted.

Properties of a Magneto-Exciton in a Quantum Well

The ground state energies of an exciton in a quantum well structure for perpendicular magnetic field of arbitrary strength are studied. The results show that the energy of the magneto exciton will be increased with the increase of quantum well width and magnetic field strength.

Fractal networks with a wide distribution of conductances

Abstract We have studied the current distribution in a Sierpinski honeycomb network with an exponentially wide distribution of bond conductances. We extended the generalized multifractal spectrum in the two-dimensional square lattice of Roux et al.; we want to see how the spectrum is modified when the underlying lattice is not translational invariant but fractal. We regard the problem as a crossover behavior between the competing effects of the size of the network and the width of the distribution of conductances. We also discuss the possible crossover behaviors from fractal to Euclidean by considering the whole family of Sierpinski honeycombs parametrized by b (2⩽