Abstract

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.

Highlights

  • DERIVATION OF Maxwell vector wave equation (MVWE) GOVERNING EQUATIONS FROM MAXWELL’S EQUATIONS∂t for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension

  • Recent interest in 3-D vectorial sensors requires the development of vectorial propagation methods, rather than scalar wave equation approaches

  • E LECTROMAGNETIC (EM) propagation in inhomogeneous media poses several challenges and there is a need to go beyond standard scalar propagation models based on scalar wave, Helmholtz, and paraxial equations and to incorporate vector wave propagation effects

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Summary

DERIVATION OF MVWE GOVERNING EQUATIONS FROM MAXWELL’S EQUATIONS

∂t for a medium which has an inhomogeneous dielectric permittivity dominated by variation along one dimension. We first derive the general vector wave equation and apply restrictions to a specific cause for our study. We consider an unpolarized medium (P = 0) without an applied magnetic field (M = 0) and no charges (ρ = 0) or current (J = 0). These restrictions yield the MVWE for E. With μ = μ0 a constant and allowing only one dominant dimension of permittivity variation, we begin restricting the general case given by (9) to our specific study. The operators for the gradient and Laplacian have their usual Cartesian form (see Appendix) Polarized sources could be handled by controlling the relative amplitudes and phases of FH () and FV (), but only a vertically polarized source will be considered in the present study

EVAPORATION DUCT APPLICATION
Antenna Forcing Function and Boundary Conditions
RESULTS AND DISCUSSION
CONCLUSION
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