Abstract
We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1621-1634 |
| Number of pages | 14 |
| Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |
| Volume | 21 |
| Issue number | 9 |
| DOIs | |
| State | Published - 2004 |
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ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Computer Vision and Pattern Recognition
Cite this
Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces. / Falco, Frank; Tamir, Theodor; Leung, Kok-Ming.
In: Journal of the Optical Society of America A: Optics and Image Science, and Vision, Vol. 21, No. 9, 2004, p. 1621-1634.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Grating diffraction and Wood's anomalies at two-dimensionally periodic impedance surfaces
AU - Falco, Frank
AU - Tamir, Theodor
AU - Leung, Kok-Ming
PY - 2004
Y1 - 2004
N2 - We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.
AB - We address the problem of plane-wave scattering and Wood's anomalies at two-dimensional (2-D) periodic surfaces by employing a simplified grating model given by a planar surface whose impedance varies sinusoidally along two orthogonal directions. We obtain a rigorous solution to the corresponding boundary-value problem in terms of an infinite set of coupled recurrence equations. When truncated for computational purposes, this solution is in the form of a banded matrix, which we solve by direct methods and also by a highly efficient iterated matrix procedure. Numerical results are presented for symmetric and nonsymmetric incidence cases, and we show that certain diffracted fields do not depolarize in the former case. The expected Wood's anomalies of both Rayleigh and leaky-wave types are confirmed, and their location in wavelength space is numerically demonstrated for 2-D periodic configurations.
UR - http://www.scopus.com/inward/record.url?scp=4544286518&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=4544286518&partnerID=8YFLogxK
U2 - 10.1364/JOSAA.21.001621
DO - 10.1364/JOSAA.21.001621
M3 - Article
C2 - 15384428
AN - SCOPUS:4544286518
VL - 21
SP - 1621
EP - 1634
JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision
JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision
SN - 0740-3232
IS - 9
ER -