Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Lihh, Won-seok

doi:10.1109/tap.2007.905830

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…This failure of the saddle point method can be attributed to the fact that the radius of analyticity of the Maclaurin expansion reduces to zero when the saddle point θ approaches the branch point ξ b . To mitigate this break-down at the critical angle one has to resort to the uniform saddle-point method, but the solution is then expressed in terms of parabolic cylinder functions and does not lend itself to a ready physical interpretation [28]- [31].…”

Section: Asymptotic Transmitted Fieldmentioning

confidence: 99%

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

Michalski

Mosig

2021

IEEE J. Microw.

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The complete radiation field pattern of a vertical Hertzian dipole antenna on or above a lossless or low-loss dielectric half-space is studied using a rigorous Sommerfeld formalism. The reflected fields in the air above the interface and the subsurface fields transmitted into the dielectric are computed by numerical integration of the Sommerfeld integrals. Furthermore, to facilitate the physical interpretation of these results, a detailed asymptotic saddle-point integration method analysis is presented, which includes terms that vary in magnitude with the second power of the inverse distance from the dipole. It is shown that the secondorder field constituents are dominant at the interface, where the first-order geometrical fields vanish. These second-order terms comprise an evanescent wave propagating along the interface in the upper half-space and a lateral wave, also known as the head wave, which propagates in the subsurface along the direction of the critical angle. The two waves only exist between two cones whose half-angles are equal to the critical angle, and their interference with the geometrical-optics fields determines the radiation pattern for elevation angles near the horizon. The far zone surface fields on either side of the interface comprise two second order waves that propagate along the interface, one with the phase velocity in the air, and the other with the phase velocity in the dielectric. Away from the interface, the leading field components vary with the first power of the inverse distance, which explains the sharp dip in the field pattern at the interface-a phenomenon known as the interface pattern extinction. Another distinctive phenomenon, observed in the subsurface field pattern, is the rippling that occurs in the angular range between the critical angle cone and the interface. The asymptotic analysis has shown that this pattern scalloping results from the interference of the lateral wave with the geometrical-optics spherical wave.INDEX TERMS Dipole antennas, antenna radiation patterns, interface pattern extinction, dielectric halfspace, Sommerfeld integrals, saddle-point integration method, lateral waves.This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

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Section: Asymptotic Transmitted Fieldmentioning

confidence: 99%

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

Michalski

Mosig

2021

IEEE J. Microw.

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“…The square root of a complex quantity, say , is such that . By the decomposition of the TE and TM waves [7] (transverse-electric and -magnetic to the axis, respectively), the TE fields are expressed as (2) (3) and the TM fields are expressed as (4)…”

Section: Integral Representation Of Fieldsmentioning

confidence: 99%

A Second-Order Asymptotic Approximation for the Sommerfeld Half-Space Problem

Lihh¹

2012

IEEE Trans. Antennas Propagat.

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“…In the complex plane, the Sommerfeld integration path runs from the left extreme in the third quadrant to the right extreme in the first quadrant, through the origin. The six TM fields are given by [10] (3)…”

Section: Integral Representation Of Tm Fieldsmentioning

confidence: 99%

“…Dealing with the combined effect of the branch point and the stationary-phase point, in the presence of the pole, might yield more accurate description near the critical cone [10], but at the cost of simplicity and explicitness of the field expressions. This paper does not cover the fields near the critical cone.…”

Section: Introductionmentioning

confidence: 99%

A Correction to Head-Wave Fields for a Simple Planar Contrast of Permittivity

Lihh¹

2010

IEEE Trans. Antennas Propagat.

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When asymptotically describing the wave fields on the denser side of a planar permittivity interface, the canonical headwave fields of the tangential-magnetic (TM) set show discrepancies with the full-wave fields. This paper derives the correction fields that supplement the canonical TM head-wave fields, by taking into account the proximity between the head-wave branch point and an extraneous pole in the wavenumber domain. The validity of the correction is demonstrated in the time domain by comparing the waveforms of a corrected field and the full-wave field, for various ratios of permittivity and at various locations of observation. Consideration is also given to the case of a conducting medium.

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Asymptotic Fields in Frequency and Time Domains Generated by a Point Source at the Horizontal Interface Between Vertically Uniaxial Media

Cited by 6 publications

References 18 publications

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

On the Complete Radiation Pattern of a Vertical Hertzian Dipole Above a Low-Loss Ground

A Second-Order Asymptotic Approximation for the Sommerfeld Half-Space Problem

A Correction to Head-Wave Fields for a Simple Planar Contrast of Permittivity

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