A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves

Sautbekov, Seil; Bourgiotis, Sotiris; Chrysostomou, Ariadni; Frangos, Panayiotis

doi:10.2528/pierm17082806

Cited by 5 publications

(32 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the usual case, where σ ωε 0 , the field scattered by the plannar interface can be expressed as [30]…”

Section: Outline Of the Asymptotic Methodsmentioning

confidence: 99%

“…Then, in [30], the problem was re-examined, for the case where σ ωε 0 , which is valid for many practical cases of interest in terrestrial communications. As shown there, a special contour integral, called "Etalon integral", was used to deform the original contour of integration, through the application of the Saddle Point or Steepest Descent Method (SDP).…”

Section: Previous Contribution By Our Research Groupmentioning

confidence: 99%

“…Then, we return to the solution of [30] and elaborate on the derived expressions. Using small and large argument approximations, associated with the Fresnel integrals [37], pure analytic expressions are extracted that better describe the behavior of the EM field, close as well as far away from the ground interface, and provide useful information regarding the propagation mechanism.…”

Section: Scope Of This Researchmentioning

confidence: 99%

See 2 more Smart Citations

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

et al. 2021

View full text Add to dashboard Cite

A recently developed high-frequency asymptotic solution for the famous “Sommerfeld radiation problem” is revisited. The solution is based on an analysis performed in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. We first demonstrate an efficient technique for the accurate numerical calculation of the well-known Sommerfeld integrals. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the surface wave. In the second part, we introduce the asymptotic solution and investigate its performance; we compare the solution with the accurate numerical evaluation for the received EM field and with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method. Simulations for various frequencies, distances, altitudes, and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases leading to analytical field expressions close as well as far from the interface are examined.

show abstract

“…For the usual case, where σ ωε 0 , the field scattered by the plannar interface can be expressed as [30]…”

Section: Outline Of the Asymptotic Methodsmentioning

confidence: 99%

Section: Previous Contribution By Our Research Groupmentioning

confidence: 99%

Section: Scope Of This Researchmentioning

confidence: 99%

See 1 more Smart Citation

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

et al. 2021

View full text Add to dashboard Cite

show abstract

“…Then in [25], the mathematical formulation of the problem in the spectral domain was redefined for the usual case where σ ωε 0 , ie for a highly conductive interface, which is the case for most practical frequencies of interest in terrestrial communications. As shown there, a special contour integral, called "Etalon Integral", was used to deform the original contour of integration, associated with the Sommerfeld Integrals in the spectral domain, through the application of the Saddle Point Method (SDP).…”

Section: A Previous Contribution Of Our Research Groupmentioning

confidence: 99%

“…The analysis in [25] was constrained to the pure mathematical formulation of the problem. Simulations and related Fig.…”

Section: B Scope Of This Researchmentioning

confidence: 99%

The Evaluation of a Novel Asymptotic Solution to the Sommerfeld Radiation Problem using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

Bourgiotis¹,

Frangos²,

Sautbekov³

et al. 2019

Preprint

View full text Add to dashboard Cite

In this work, a recently developed novel solution of the famous "Sommerfeld Radiation Problem" is revisited. The solution is based on an analysis performed entirely in the spectral domain, through which a compact asymptotic formula describes the behavior of the EM field, which emanates from a vertical Hertzian radiating dipole, located above flat, lossy ground. The paper is divided into two parts. First, we demonstrate an efficient technique for the accurate numeric calculation of the wellknown Sommerfeld integrals, required for the evaluation of the field. The results are compared against alternative calculation approaches and validated with the corresponding Norton figures for the Surface Wave. Then, in the second part, we briefly introduce the asymptotic solution of interest and investigate its performance; we contrast the solution versus the accurate numerical evaluation for the total received EM field and also with a more basic asymptotic solution to the given problem, obtained via the application of the Stationary Phase Method (SPM). Simulations for various frequencies, distances, altitudes and ground characteristics are illustrated and inferences for the applicability of the solution are made. Finally, special cases, leading to analytic field expressions, close as well as far from the interface, are examined.

show abstract

Efficient generation of hydrogen by two-step thermochemical cycles: Successive thermal reduction and water splitting reactions using equal-power microwave irradiation and a high entropy material

et al. 2020

View full text Add to dashboard Cite

A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves

Cited by 5 publications

References 18 publications

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

The Evaluation of an Asymptotic Solution to the Sommerfeld Radiation Problem Using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

The Evaluation of a Novel Asymptotic Solution to the Sommerfeld Radiation Problem using an Efficient Method for the Calculation of Sommerfeld Integrals in the Spectral Domain

Efficient generation of hydrogen by two-step thermochemical cycles: Successive thermal reduction and water splitting reactions using equal-power microwave irradiation and a high entropy material

Contact Info

Product

Resources

About