Nonlinear dielectrics: Electrostatics of random media and propagation of electromagnetic waves in a homogeneous slab

Raphael Blumenfeld, David J. Bergman

Research output: Contribution to journalArticlepeer-review

Abstract

We study nonlinear dielectrics obeying D = ε{lunate}(E2)β/2E. The solution to the eletrostatic equations is found to be unique for ∞ α = 1/(β + 1) 1/(d - 1). We find the electrostatic fields produced by a point charge and by an infinite charged slab in such a medium. Two definitions of the effective dielectric constant, ε{lunate}eff, are shown to coincide. For the case where ε{lunate} varies in space we show that the differential equation for the first correction to the potential field is dipolar in scaled coordinates. We use the first correction to bound ε{lunate}eff. Finally we formulate the explicit time dependent equations that describe the dynamic behavior of the magnetic and electric fields in such materials.

Original languageEnglish
Pages (from-to)428-436
Number of pages9
JournalPhysica A: Statistical Mechanics and its Applications
Volume157
Issue number1
DOIs
StatePublished - 1 May 1989

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