On an asymptotic theory of diffraction gratings used in the scalar domain

Erwin G. Loewen; Michel Nevière; Daniel Maystre

doi:10.1364/JOSA.68.000496

Journal of the Optical Society of America
Vol. 68,
Issue 4,
pp. 496-502
(1978)
•https://doi.org/10.1364/JOSA.68.000496

On an asymptotic theory of diffraction gratings used in the scalar domain

Erwin G. Loewen, Michel Nevière, and Daniel Maystre

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Erwin G. Loewen, Michel Nevière, and Daniel Maystre, "On an asymptotic theory of diffraction gratings used in the scalar domain," J. Opt. Soc. Am. 68, 496-502 (1978)

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Abstract

Starting from the electromagnetic theory, we derive an asymptotic formalism to investigate the behavior of perfectly conducting gratings used at small wavelengths to groove pitch ratios and near normal incidence. The theory is applied to study three classical types of profiles: sinusoidal, lamellar, and blazed gratings. Results are given for both −1 and −2 Littrow (or near Littrow) mounts. The accuracy of the theory and the limits of the domain where it applies are studied by the use of rigorous electromagnetic computations. The role of a finite conductivity of the surface is also investigated.

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Equations (33)

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θ (d°)	P polarization			S polarization
θ (d°)	ξ₋₁	ξ₀	ξ	ξ₋₁	ξ₀	ξ
0	0.0332	0.0864	0.1633	0.0326	0.0856	0.1597
10	0.0332	0.0913	0.1680	0.0323	0.0850	0.1553
15	0.0334	0.0975	0.1740	0.0309	0.0839	0.1494
20	0.0336	0.1066	0.1830	0.0287	0.0818	0.1407
30	0.0340	0.1356	0.2109	0.0229	0.0760	0.1204
40	0.0336	0.1839	0.2544	0.0160	0.0662	0.0950
50	0.0321	0.2588	0.3201	0.0101	0.0576	0.0757
60	0.0280	0.3777	0.4105	0.0061	0.0662	0.0744
70	0.0210	0.5220	0.5468	0.0043	0.1304	0.1365
80	0.0118	0.7228	0.7369	0.0030	0.3526	0.3566
85	0.0063	0.8503	0.8578	0.0019	0.5935	0.5961

θ (d°)	Efficiency ξ₋₁		Reflectivity of the metal (gold)
θ (d°)	P plane	S plane	P plane	S plane
0	0.1966	0.2031	0.1668	0.1668
10	0.1961	0.1991	0.1719	0.1618
15	0.1922	0.1974	0.1784	0.1556
20	0.1854	0.1919	0.1879	0.1472
30	0.1670	0.1724	0.2168	0.1247
40	0.1404	0.1499	0.2624	0.0982
50	0.1103	0.1177	0.3299	0.0762
55	0.0945	0.1075	0.3740	0.0718
60	0.0778	0.0809	0.4265	0.0766
70	0.0467	0.0780	0.5617	0.1395
80	0.0214	0.0833	0.7477	0.3620
85	0.0104	0.1136	0.8645	0.6009

θ	P polarization		S polarization
(d°)	$\underset{\infty}{ξ_{- 1, σ \times R (θ)}}$		$\underset{\infty}{ξ_{- 1, σ \times R (θ)}}$
	Au	ξ_−1,Au	Au	ξ_−1,Au
0	0.0328	0.0332	0.0339	0.0326
10	0.0337	0.0332	0.0322	0.0323
20	0.0348	0.0336	0.0282	0.0287
30	0.0362	0.0340	0.0215	0.0229
40	0.0368	0.0336	0.0147	0.0160
45	0.0367	0.0330	0.0101	0.0129
50	0.0364	0.0321	0.0090	0.0101
60	0.0332	0.0280	0.0062	0.0061
70	0.0262	0.0210	0.0109	0.0043
80	0.0160	0.0118	0.0302	0.0030
85	0.0090	0.0063	0.0683	0.0019

θ (d°)	P polarization			S polarization
θ (d°)	ξ₋₁	ξ₀	ξ	ξ₋₁	ξ₀	ξ
0	0.0332	0.0864	0.1633	0.0326	0.0856	0.1597
10	0.0332	0.0913	0.1680	0.0323	0.0850	0.1553
15	0.0334	0.0975	0.1740	0.0309	0.0839	0.1494
20	0.0336	0.1066	0.1830	0.0287	0.0818	0.1407
30	0.0340	0.1356	0.2109	0.0229	0.0760	0.1204
40	0.0336	0.1839	0.2544	0.0160	0.0662	0.0950
50	0.0321	0.2588	0.3201	0.0101	0.0576	0.0757
60	0.0280	0.3777	0.4105	0.0061	0.0662	0.0744
70	0.0210	0.5220	0.5468	0.0043	0.1304	0.1365
80	0.0118	0.7228	0.7369	0.0030	0.3526	0.3566
85	0.0063	0.8503	0.8578	0.0019	0.5935	0.5961

θ (d°)	Efficiency ξ₋₁		Reflectivity of the metal (gold)
θ (d°)	P plane	S plane	P plane	S plane
0	0.1966	0.2031	0.1668	0.1668
10	0.1961	0.1991	0.1719	0.1618
15	0.1922	0.1974	0.1784	0.1556
20	0.1854	0.1919	0.1879	0.1472
30	0.1670	0.1724	0.2168	0.1247
40	0.1404	0.1499	0.2624	0.0982
50	0.1103	0.1177	0.3299	0.0762
55	0.0945	0.1075	0.3740	0.0718
60	0.0778	0.0809	0.4265	0.0766
70	0.0467	0.0780	0.5617	0.1395
80	0.0214	0.0833	0.7477	0.3620
85	0.0104	0.1136	0.8645	0.6009

Abstract

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Figures (6)

Tables (3)

Equations (33)

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