Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface
Summary :
As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E83-C No.3 pp.481-487
- Publication Date
- 2000/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Electromagnetic Theory
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Junichi NAKAYAMA, "Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface" in IEICE TRANSACTIONS on Electronics,
vol. E83-C, no. 3, pp. 481-487, March 2000, doi: .
Abstract: As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/e83-c_3_481/_p
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@ARTICLE{e83-c_3_481,
author={Junichi NAKAYAMA, },
journal={IEICE TRANSACTIONS on Electronics},
title={Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface},
year={2000},
volume={E83-C},
number={3},
pages={481-487},
abstract={As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.},
keywords={},
doi={},
ISSN={},
month={March},}
Copy
TY - JOUR
TI - Periodic Fourier Transform and Its Application to Wave Scattering from a Finite Periodic Surface
T2 - IEICE TRANSACTIONS on Electronics
SP - 481
EP - 487
AU - Junichi NAKAYAMA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Electronics
SN -
VL - E83-C
IS - 3
JA - IEICE TRANSACTIONS on Electronics
Y1 - March 2000
AB - As a new idea for analyzing the wave scattering and diffraction from a finite periodic surface, this paper proposes the periodic Fourier transform. By the periodic Fourier transform, the scattered wave is transformed into a periodic function which is further expanded into Fourier series. In terms of the inverse transformation, the scattered wave is shown to have an extended Floquet form, which is a 'Fourier series' with 'Fourier coefficients' given by band-limited Fourier integrals of amplitude functions. In case of the TE plane wave incident, an integral equation for the amplitude functions is obtained from the the boundary condition on the finite periodic surface. When the surface corrugation is small, in amplitude, compared with the wavelength, the integral equation is approximately solved by iteration to obtain the scattering cross section. Several properties and examples of the periodic Fourier transform are summarized in Appendix.
ER -
English
