Scattering of electromagnetic waves by a grating: a numerical evaluation of the iterative-series solution

Jean-Jacques Greffet and Z. Maassarani

Author Affiliations

Jean-Jacques Greffet and Z. Maassarani

^{}Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion Ecole Centrale de Paris, Centre National de la Recherche Scientifique, Châtenay-Malabry 92295 Cedex,
France

Jean-Jacques Greffet and Z. Maassarani, "Scattering of electromagnetic waves by a grating: a numerical evaluation of the iterative-series solution," J. Opt. Soc. Am. A 7, 1483-1493 (1990)

Iterative-series solutions have been recently developed for the scattering of p-polarized waves by a grating and for three-dimensional surfaces. However, their numerical behavior has not been investigated. We study the scattering by both dielectric and metallic sinusoidal gratings. We show that this kind of solution yields an accurate and efficient solution in the dielectric case. This solution may also be applied in conical-diffraction problems. Although some resonances have been successfully studied, the algorithm diverges for low values of the amplitude–period ratio in the case of metallic gratings.

Jean-Jacques Greffet, C. Baylard, and P. Versaevel Opt. Lett. 17(24) 1740-1742 (1992)

References

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Comparison between the Iterative-Series Solution, the Rearranged Iterative-Series Solution, and the Rayleigh Fourier Solution^{a}

ISS

RISS

RFS

n = l

n = 4

n = 8

n = 4

n = 8

P = 9

ρ_{0}

0.384 × 10^{−1}

0.716 × 10^{−2}

0.669 × 10^{−2}

0.712 × 10^{−2}

0.669 × 10^{−2}

0.689 × 10^{−2}

ρ_{−1}

0.294 × 10^{−1}

0.154 × 10^{−1}

0.160 × 10^{−1}

0.156 × 10^{−1}

0.160 × 10^{−1}

0.159 × 10^{−1}

E

1.09

0.997

1.000

0.997

1.000

1.001

t(s)

0.05

0.72

9.17

5.52

13.06

38.18

n is the number of orders used in the series, and P is the number of orders retained in the truncation of the linear system in the RFS; t is the computation time, and E is the sum of the efficiencies. The parameters are ∊ = 2.25, h/λ = 0.125, d/λ = 1.

Table 2

Convergence Domain of the Iterative-Series Solution for θ_{i} = 0°, ϕ_{i} = 0°, ∊ = 2.25, Polarization p^{a}

Comparison between the Iterative-Series Solution, the Rearranged Iterative-Series Solution, and the Rayleigh Fourier Solution^{a}

ISS

RISS

RFS

n = l

n = 4

n = 8

n = 4

n = 8

P = 9

ρ_{0}

0.384 × 10^{−1}

0.716 × 10^{−2}

0.669 × 10^{−2}

0.712 × 10^{−2}

0.669 × 10^{−2}

0.689 × 10^{−2}

ρ_{−1}

0.294 × 10^{−1}

0.154 × 10^{−1}

0.160 × 10^{−1}

0.156 × 10^{−1}

0.160 × 10^{−1}

0.159 × 10^{−1}

E

1.09

0.997

1.000

0.997

1.000

1.001

t(s)

0.05

0.72

9.17

5.52

13.06

38.18

n is the number of orders used in the series, and P is the number of orders retained in the truncation of the linear system in the RFS; t is the computation time, and E is the sum of the efficiencies. The parameters are ∊ = 2.25, h/λ = 0.125, d/λ = 1.

Table 2

Convergence Domain of the Iterative-Series Solution for θ_{i} = 0°, ϕ_{i} = 0°, ∊ = 2.25, Polarization p^{a}