Symmetries of scattering factors and diffraction efficiencies in grating theory

Yasuhiko Tamura; Junichi Nakayama

doi:10.1364/JOSAA.35.001306

Journal of the Optical Society of America A
Vol. 35,
Issue 8,
pp. 1306-1314
(2018)
•https://doi.org/10.1364/JOSAA.35.001306

Symmetries of scattering factors and diffraction efficiencies in grating theory

Yasuhiko Tamura and Junichi Nakayama

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Yasuhiko Tamura and Junichi Nakayama, "Symmetries of scattering factors and diffraction efficiencies in grating theory," J. Opt. Soc. Am. A 35, 1306-1314 (2018)

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Abstract

This paper theoretically discusses basic topics on the reciprocity theorem and the optical theorem in the grating theory for plane wave reflection and transmission from a periodic rough interface between two-layered homogeneous media. Based on the shadow theory, symmetries of the scattering factors and diffraction efficiencies are newly presented in several formulas.

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$p$	TE	Calculation Value	${OPT}_{err}$	${REC}_{err}$
$3 k_{L}$	$U_{1}^{[0]} (3 k_{L})$ $U_{1}^{[0]} (- 3 k_{L})$	$0.000114485 - 0.000865287 i$ $0.000114480 - 0.000865289 i$	−4.04 −3.59	−5.52
$2 k_{L}$	$U_{2}^{[1]} (2 k_{L})$ $U_{2}^{[1]} (- 3 k_{L})$	$0.000841377 - 0.00630886 i$ $0.000840893 - 0.00630466 i$	−3.56 −4.80	−3.48
$- k_{L}$	$V_{1}^{[0]} (- k_{L})$ ${\bar{V}}_{2}^{[0]} (k_{L})$	$- 0.574297 - 0.225626 i$ $- 0.574280 - 0.225551 i$	−4.89 −4.77	−4.45
$2 k_{L}$	$V_{1}^{[- 2]} (2 k_{L})$ ${\bar{V}}_{2}^{[- 2]} (0)$	$- 0.00495447 + 0.0272806 i$ $- 0.00495425 + 0.0272872 i$	−3.68 −5.59	−3.94
$p$	TM	Calculation Value	${OPT}_{err}$	${REC}_{err}$
$3 k_{L}$	$U_{1}^{[0]} (3 k_{L})$ $U_{1}^{[0]} (- 3 k_{L})$	$0.000375899 - 0.0111885 i$ $0.000375876 - 0.0111885 i$	−3.66 −3.33	−5.61
$2 k_{L}$	$U_{2}^{[1]} (2 k_{L})$ $U_{2}^{[1]} (- 3 k_{L})$	$0.00424813 - 0.0287655 i$ $0.00424763 - 0.0287622 i$	−4.84 −4.25	−4.24
$- k_{L}$	$V_{1}^{[0]} (- k_{L})$ ${\bar{V}}_{2}^{[0]} (k_{L})$	$- 1.01361 - 0.288472 i$ $- 1.01366 - 0.288459 i$	−4.28 −4.33	−4.59
$2 k_{L}$	$V_{1}^{[- 2]} (2 k_{L})$ ${\bar{V}}_{2}^{[- 2]} (0)$	$- 0.0144754 + 0.0148320 i$ $- 0.0144722 + 0.0148354 i$	−3.54 −4.68	−3.96

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Journal of the Optical Society of America A