Analysis of Modified Luneberg Lens Using Exact Solutions

Haruo SAKURAI; Makoto OHKI; Shogo KOZAKI

Analysis of Modified Luneberg Lens Using Exact Solutions

Haruo SAKURAI, Makoto OHKI, Shogo KOZAKI

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Analytical solutions have been obtained for the electromagnetic scattering by a modified Luneberg lens with the permittivity of arbitrary parabolic function. They are expressed by four spherical vector wave functions for radially stratified medium which were introduced for the Luneberg lens by C. T. Tai. They consist of the confluent hypergeometric function and a "generalized" confluent hypergeometric function, in which the parameters for the permittivity of arbitrary parabolic function are involved. The characteristics of the modified Luneberg lens are numerically investigated using exact solutions in comparison with that of the conventional Luneberg lens. The bistatic cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in order to study the focal properties of the Luneberg lens. The focal shifts defined by the distance between the geometrical focal point and the electromagnetic focal point are obtained for various ka (k is the wave number and a is the radius of the lens). The focal shift normalized to the radius of the sphere becomes larger as ka is smaller. However it drops down rapidly for ka<2.5 because the power of convergence by the Luneberg lens becomes weak when ka is small. The permittivities of a modified Luneberg lens are found versus ka>5 when the peak of the electric field amplitude appears on the surface of sphere.

Publication: IEICE TRANSACTIONS on Electronics Vol.E82-C No.10 pp.1846-1852

Publication Date: 1999/10/25

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Type of Manuscript: PAPER

Category: Electromagnetic Theory

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Haruo SAKURAI, Makoto OHKI, Shogo KOZAKI, "Analysis of Modified Luneberg Lens Using Exact Solutions" in IEICE TRANSACTIONS on Electronics, vol. E82-C, no. 10, pp. 1846-1852, October 1999, doi: .
Abstract: Analytical solutions have been obtained for the electromagnetic scattering by a modified Luneberg lens with the permittivity of arbitrary parabolic function. They are expressed by four spherical vector wave functions for radially stratified medium which were introduced for the Luneberg lens by C. T. Tai. They consist of the confluent hypergeometric function and a "generalized" confluent hypergeometric function, in which the parameters for the permittivity of arbitrary parabolic function are involved. The characteristics of the modified Luneberg lens are numerically investigated using exact solutions in comparison with that of the conventional Luneberg lens. The bistatic cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in order to study the focal properties of the Luneberg lens. The focal shifts defined by the distance between the geometrical focal point and the electromagnetic focal point are obtained for various ka (k is the wave number and a is the radius of the lens). The focal shift normalized to the radius of the sphere becomes larger as ka is smaller. However it drops down rapidly for ka<2.5 because the power of convergence by the Luneberg lens becomes weak when ka is small. The permittivities of a modified Luneberg lens are found versus ka>5 when the peak of the electric field amplitude appears on the surface of sphere.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e82-c_10_1846/_p

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@ARTICLE{e82-c_10_1846,
author={Haruo SAKURAI, Makoto OHKI, Shogo KOZAKI, },
journal={IEICE TRANSACTIONS on Electronics},
title={Analysis of Modified Luneberg Lens Using Exact Solutions},
year={1999},
volume={E82-C},
number={10},
pages={1846-1852},
abstract={Analytical solutions have been obtained for the electromagnetic scattering by a modified Luneberg lens with the permittivity of arbitrary parabolic function. They are expressed by four spherical vector wave functions for radially stratified medium which were introduced for the Luneberg lens by C. T. Tai. They consist of the confluent hypergeometric function and a "generalized" confluent hypergeometric function, in which the parameters for the permittivity of arbitrary parabolic function are involved. The characteristics of the modified Luneberg lens are numerically investigated using exact solutions in comparison with that of the conventional Luneberg lens. The bistatic cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in order to study the focal properties of the Luneberg lens. The focal shifts defined by the distance between the geometrical focal point and the electromagnetic focal point are obtained for various ka (k is the wave number and a is the radius of the lens). The focal shift normalized to the radius of the sphere becomes larger as ka is smaller. However it drops down rapidly for ka<2.5 because the power of convergence by the Luneberg lens becomes weak when ka is small. The permittivities of a modified Luneberg lens are found versus ka>5 when the peak of the electric field amplitude appears on the surface of sphere.},
keywords={},
doi={},
ISSN={},
month={October},}

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TY - JOUR
TI - Analysis of Modified Luneberg Lens Using Exact Solutions
T2 - IEICE TRANSACTIONS on Electronics
SP - 1846
EP - 1852
AU - Haruo SAKURAI
AU - Makoto OHKI
AU - Shogo KOZAKI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E82-C
IS - 10
JA - IEICE TRANSACTIONS on Electronics
Y1 - October 1999
AB - Analytical solutions have been obtained for the electromagnetic scattering by a modified Luneberg lens with the permittivity of arbitrary parabolic function. They are expressed by four spherical vector wave functions for radially stratified medium which were introduced for the Luneberg lens by C. T. Tai. They consist of the confluent hypergeometric function and a "generalized" confluent hypergeometric function, in which the parameters for the permittivity of arbitrary parabolic function are involved. The characteristics of the modified Luneberg lens are numerically investigated using exact solutions in comparison with that of the conventional Luneberg lens. The bistatic cross section, the forward cross section and the radar cross section are studied in detail. The near-field distribution is also investigated in order to study the focal properties of the Luneberg lens. The focal shifts defined by the distance between the geometrical focal point and the electromagnetic focal point are obtained for various ka (k is the wave number and a is the radius of the lens). The focal shift normalized to the radius of the sphere becomes larger as ka is smaller. However it drops down rapidly for ka<2.5 because the power of convergence by the Luneberg lens becomes weak when ka is small. The permittivities of a modified Luneberg lens are found versus ka>5 when the peak of the electric field amplitude appears on the surface of sphere.
ER -