Permittivity Gradient Induced Depolarization: Electromagnetic Propagation with the Maxwell Vector Wave Equation

Stephen Shaffer, Alex Mahalov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Recent interest in 3-D vectorial sensors requires the development of vectorial propagation methods, rather than scalar wave equation approaches. We derive a vector wave equation from Maxwell's equations for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension. It is well known that the electric field components decouple for homogeneous media. However, 1-D permittivity variations yield an upper triangular system of scalar wave equations with the wave polarization component parallel to the inhomogeneous direction/axis acting as a forcing term for the orthogonal components. The main implication is that waves with polarization oriented parallel to the permittivity gradient will act as a forcing term and excite other polarization components and, thus, induce depolarization. Contemporary studies treat the permittivity as a constant when deriving a wave equation or paraxial approximation, and then re-introduce via inhomogeneous wave speed, variable permittivity, thus missing important terms and physical mechanisms in their resulting equations. Contemporary studies neglect the term in the Maxwell vector wave equation responsible for this effect. Application of the electromagnetic propagation depolarization effect is demonstrated numerically for an air-sea interface evaporation duct with a 500 MHz source.

Original languageEnglish (US)
Article number9171553
Pages (from-to)1553-1559
Number of pages7
JournalIEEE Transactions on Antennas and Propagation
Issue number3
StatePublished - Mar 2021


  • Electromagnetic (EM) propagation
  • nonhomogeneous media

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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