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

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  • Blumenfeld, Raphael
  • Bergman, David J.

Abstract

We study nonlinear dielectrics obeying D = ϵ(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, ϵeff, are shown to coincide. For the case where ϵ 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 ϵeff. Finally we formulate the explicit time dependent equations that describe the dynamic behavior of the magnetic and electric fields in such materials.

Suggested Citation

  • Blumenfeld, Raphael & Bergman, David J., 1989. "Nonlinear dielectrics: Electrostatics of random media and propagation of electromagnetic waves in a homogeneous slab," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(1), pages 428-436.
    • Handle: RePEc:eee:phsmap:v:157:y:1989:i:1:p:428-436
    DOI: 10.1016/0378-4371(89)90339-7
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    Cited by:

    1. Kuzovkov, V. & Kotomin, E., 1992. "Self-organization in the A + B → 0 reaction of charged particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 172-176.

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