Enhancement of Nonlinear Dielectric Effects in Composite Materials

                                   by

                      Ohad Levy, Courant Institute

                AEB 340, 2:15pm, Thursday, May 23, 1996

                                Abstract

  Nonlinear composite materials have attracted growing interest in
  recent years due to their potential applications in nonlinear optical
  devices. The basic motivation behind this research is the hope that by
  mixing a nonlinear dielectric with one or more linear materials a
  composite could be fabricated with nonlinear dielectric coefficients
  significantly larger than those of the pure nonlinear component. The
  theoretical study of such mixtures has been limited to certain classes
  of microgeometries, since most of the analytical tools developed for
  studying linear composites are not applicable to nonlinear systems.
  These include layered microgeometries and dilute mixtures of identical
  spheroidal inclusions in a homogeneous host.

  It was found that the nonlinear response of a composite medium to an
  external electric field can be greatly enhanced if the system is near
  a strong isolated quasistatic resonance or partial resonance, where
  the local electric field inside the nonlinear component obtains values
  that are much larger than the volume averaged field. This situation,
  achievable in metal-dielectric composites, can result in bistability
  of the bulk effective dielectric response. Close enough to the
  resonance, the bistability can occur in field intensities so low such
  that the local nonlinear behavior is weak everywhere inside the
  composite medium. This allows for the development of calculation
  methods for the nonlinear behavior based on a "zero virtual work"
  variational principal and a selection of trial fields of the form
  suggested by a corresponding linear system.

  In composites where the nonlinear component has a second harmonic
  generation capability, the enhancement can lead to induced third order
  nonlinearity, as well as bistability, at the fundamental frequency.
  The enhancement in this case can be achieved near a quasistatic
  resonance at either the fundamental or the harmonic frequencies.

 Courant Institute of Mathematical Sciences
 New York University, New York, NY 10012

Requests for preprints and reprints to: Ohad Levy <ohad@MATH15.CIMS.NYU.EDU>
This source can be found at http://www.math.utah.edu/research/