Planar Layered Media : A Part from the Book Chapter : Exact Solution of Far-Region Scattering Electromagnetic Fields by a Dipole Antenna Located on a Planar Multi-Layered Earth

An attempt to derive field expressions that are not subject to restrictive assumptions has been made by Chew, where an analytical procedure has been presented that allows to derived simple formula for SIs. Long et al., advanced the Chew’s technique and derived the far-field approximation of the SIs rapidly depending on the stationary phase-point. Bishay et al. and Shoeib used the technique (2001) with numerous approximation and transformations, to get closed-form expressions for the far-field due to a VMD in a rough/planar layered media. Recently, Shoeib used the technique (2001) without any approximation and she gets fast and more accurate closed-form expressions for the far-field due to a VMD in the sea (planar layered media).

Lately, Wang H. and Ren Y. study the EMW propagation produced by horizontal magnetic dipole (HMD) and VMD located both in seawater, based on vector potential. Their studies are useful in EM communications near the sea. Also, Hu et al. introduced a quasi-static approximation method to solve the SIs challenge within the near-field region, employing the horizontal electric dipole (HED) as a model.

Author(s) Details:

Sh. Shoeib
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt and El-Gazeera Higher Institute for Engineering and Technology, Egypt.

Also See : Reconstructing Aqueous Paleoenvironments Based : A Part from the Book Chapter : Foraminifera Proxy of Short Core Samples: A Retrospective Study of Ecological Development of Surabaya and Bali Semi-enclosed Bay, Indonesia

Recent global research developments in Exact Far-Region EM Scattering by a Dipole on Multi-Layered Earth

“Electromagnetic Scattering by Arbitrary-Shaped Magnetic Particles and Multipole Decomposition: Analytical and Numerical Approaches” [1]:

  • This paper, published in Physical Review B, discusses the role of multipole contributions in the scattering spectra of arbitrarily shaped magnetic particles.
  • The method for calculating exact multipole moments, including induced electric polarization and magnetization, is suggested and applied for dipole and quadrupole terms.
  • The derived expressions for dipole and quadrupole moments can be easily implemented in numerical solvers.
  • The study expands the capabilities for modeling metamaterial properties in spectral ranges where natural materials have a relative permeability different from unity.

“Fast and Accurate Solution for the Surface Fields Scattering of a Dipole Antenna on a Planar Multi-Layered Earth”  [2]:

  • In this research, a fast and accurate solution is derived for EM scattering from a dipole antenna placed on a planar multi-layered earth.
  • The derivation involves three steps:
  • Reducing field integrals to combinations of recognized Sommerfeld integrals (SIs).
  • Expressing the solution as an infinite series.
  • This approach is applicable irrespective of the operating frequency and saves computation time compared to other techniques.

“Exact Solution of Electromagnetic Scattering From a Dipole Antenna Inside a Two-Layered Cavity”[3] :

  • Although not directly related to multi-layered earth, this study provides an exact analytical solution for electric and magnetic dipoles radiating inside a two-layered cavity involving anti-isorefractive materials.
  • It serves as an additional benchmark for validating computational software.

“Electromagnetic Scattering” :

  • This resource discusses scattering processes, where particles continuously remove energy from incident electromagnetic waves and re-radiate it into the total solid angle centered at the particle.
  • The study focuses on the far-field solution for a single homogeneous sphere.


  1. Evlyukhin, A. B., & Tuz, V. R. (2023). Electromagnetic scattering by arbitrary-shaped magnetic particles and multipole decomposition: Analytical and numerical approaches. Physical Review B, 107(15), 155425.
  2. Shoeib, H. S. (2021). Fast and accurate solution for the surface fields scattering of a dipole antenna placed on planar multi-layered earth. Radio Science, 56(7), 1-7.
  3. Liu, Y., Negishi, T., & Erricolo, D. (2021). Exact solution of electromagnetic scattering from a dipole antenna located inside a multilayer metamaterial oblate spheroidal cavity. alR, 1(2lž1šĄicŽN1), 2lž1šĄicŽ.

To Read the Complete Chapter See Here

Related Posts

Coastal erosion

Beach Morphology Observed in Sindhudurg : A Part from the Book Chapter : Morphological Uniqueness of Beach Sindhudurg District, Maharashtra, India

The coast of Sindhudurg presents a hilly aspect with low lateritic plateaus and basaltic bluffs descending right into the sea, through steep slopes and cliff faces. There…

Remote Sensing

Mine Exploration by Using Remote Sensing Techniques : A Part from the Book Chapter : Identification of Iron Ore Mine and Structural Lineaments Extraction by Using Remote Sensing Technique, Iran: A Case Study of the Sangan Khaf Iron Ore Mine

There are a lot of research related to mine exploration by using remote sensing techniques. Somaieh Afshari and his colleagues in 2015 investigated the extraction of geological…

Groundwater Exploration

Aquifers in a Granite Terrain : A Part from the Book Chapter : Delineation of Fractured Aquifer Using Numerical Analysis (Factor) of Resistivity Data in a Granite Terrain

The resistivity investigations in hard rock regions by and large reflect in A, H or HA type of sounding curves. In hard rock terrains especially granites and…

ionospheric slab thickness

Diurnal Variation of the Ionospheric Slab Thickness : A Part from the Book Chapter : Estimation of foF2 Using Global Model of Ionospheric Slab Thickness (GMIST) During January 15, 2022 Tonga Eruption

Ma and Maruyama, based on GPS TEC data and Kokubunji ionosonde foF2 data, reported that seasonal variations of ionospheric slab thickness during a daytime exhibits opposite phase…

Southward IMF : A Part from the Book Chapter : The Solar Wind Impact on Magnetosphere and Identification of the IMF by Component with Use of the Ground-Based Magnetic Data

Since magnetic storms, produced by ring currents in magnetosphere (Ring Disturbances – DR) and magnetic substorms, produced by currents in polar ionosphere (Polar Disturbances – DP) are…

Aqueous Paleoenvironments

Reconstructing Aqueous Paleoenvironments Based : A Part from the Book Chapter : Foraminifera Proxy of Short Core Samples: A Retrospective Study of Ecological Development of Surabaya and Bali Semi-enclosed Bay, Indonesia

Sediment material in the coastal waters was transported through river streams and/or eroded materials from the surrounding area, therefore vertical stratification of the substratum sediments in this…

Leave a Reply