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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

- Publicized

- Online ISSN

- DOI

- 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 -