Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings

Gérard Granet

doi:10.1364/JOSAA.15.001121

Journal of the Optical Society of America A
Vol. 15,
Issue 5,
pp. 1121-1131
(1998)
•https://doi.org/10.1364/JOSAA.15.001121

Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings

Gérard Granet

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Gérard Granet, "Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings," J. Opt. Soc. Am. A 15, 1121-1131 (1998)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A new formulation of the Chandezon method for crossed gratings is presented. In the nonorthogonal translation coordinate system, an arbitrary field in a homogeneous source-free region can be expressed as the sum of a TE field and a TM field. It is shown that the whole solution can be derived from the eigensolutions of an operator independent of the polarization. In addition, use is made of the $S$ -matrix formalism to include multilayer coated crossed gratings with parallel faces. Numerical results are given for sinusoidal crossed gratings and pyramidal gratings.

Full Article | PDF Article

Corrections

Gérard Granet, "Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings: errata," J. Opt. Soc. Am. A 15, 2444-2444 (1998)
https://opg.optica.org/josaa/abstract.cfm?uri=josaa-15-9-2444

More Like This

Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings: errata

Gérard Granet
J. Opt. Soc. Am. A 15(9) 2444-2444 (1998)

Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited

Lifeng Li
J. Opt. Soc. Am. A 11(11) 2816-2828 (1994)

Generalization of the coordinate transformation method with application to surface-relief gratings

J. P. Plumey and G. Granet
J. Opt. Soc. Am. A 16(3) 508-516 (1999)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (10)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (6)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (91)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

$M, N$	Present Formulation					Previous Formulation
$M, N$	$e_{(- 1, 0)}^{r}$	$e_{(0, - 1)}^{r}$	$e_{(0, 0)}^{r}$	∊	Time (s)	$e_{(- 1, 0)}^{r}$	$e_{(0, - 1)}^{r}$	$e_{(0, 0)}^{r}$	∊	Time (s)
5	0.18318308	0.04441311	0.54480306	$4.68 \times 10^{- 6}$	31	0.18317513	0.04441197	0.54482602	$2.39 \times 10^{- 7}$	103
6	0.18318536	0.04441384	0.54480149	$1.09 \times 10^{- 7}$	81	0.18318483	0.04441374	0.544803	$1.42 \times 10^{- 7}$	274
7	0.18318539	0.04441385	0.54480151	$2.17 \times 10^{- 9}$	207	0.18318535	0.04441385	0.5448016	$4.56 \times 10^{- 9}$	673
8	0.18318538	0.04441385	0.54480152	$1.3 \times 10^{- 11}$	472	0.18318538	0.04441385	0.54480153	$9 \times 10^{- 11}$	1225

$h / d$	Ref. 2				Present Method $(M = N = 5)$
$h / d$	$e_{(- 1, 0)}^{r}$	$e_{(0, - 1)}^{r}$	$e_{(0, 0)}^{r}$	∊	$e_{(- 1, 0)}^{r}$	$e_{(0, - 1)}^{r}$	$e_{(0, 0)}^{r}$	∊
0.1	0.01881	0.059691	0.842996	$- 6.6 \times 10^{- 16}$	0.01881	0.05969	0.842996	$2.22 \times 10^{- 16}$
0.2	0.063551	0.192968	0.486961	$- 2.5 \times 10^{- 15}$	0.063551	0.192968	0.486961	$2.72 \times 10^{- 13}$
0.3	0.110711	0.308565	0.161448	$- 6.0 \times 10^{- 13}$	0.110711	0.308564	0.161448	$4.18 \times 10^{- 11}$
0.4	0.139786	0.342547	0.035335	$- 9.2 \times 10^{- 10}$	0.139786	0.342547	0.035336	$1.31 \times 10^{- 9}$
0.5	0.134627	0.283651	0.163443	$- 1.6 \times 10^{- 7}$	0.134627	0.283651	0.163443	$1.57 \times 10^{- 8}$
0.6	0.089612	0.168376	0.484016	$- 7.1 \times 10^{- 6}$	0.089612	0.16838	0.484016	$8.59 \times 10^{- 8}$
0.7	0.036325	0.068458	0.790359	$- 7.1 \times 10^{- 5}$	0.036319	0.068512	0.790338	$1.92 \times 10^{- 7}$
0.8	0.035293	0.033719	0.862052	$7.8 \times 10^{- 5}$	0.033869	0.035333	0.861597	$4.59 \times 10^{- 8}$
0.9	0.097266	0.04057	0.727476	$3.1 \times 10^{- 3}$	0.097905	0.039988	0.724214	$1.15 \times 10^{- 7}$
1	0.180165	0.048574	0.557739	$1.5 \times 10^{- 2}$	0.183183	0.044413	0.544803	$4.68 \times 10^{- 6}$

$h / d$	Previous Formulation
	$M = N = 5$		$M = N = 6$		$M = N = 7$		$M = N = 8$
	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊
1	0.544826	$- 2.3 \times 10^{- 7}$	0.544803	$- 1.4 \times 10^{- 7}$	0.544802	$- 4.5 \times 10^{- 9}$	0.544802	$9 \times 10^{- 11}$
1.1	0.41056	$3.35 \times 10^{- 5}$	0.410519	$4.6 \times 10^{- 7}$	0.410516	$9 \times 10^{- 10}$	0.410516	$1.1 \times 10^{- 12}$
1.2	0.32145	$1.5 \times 10^{- 4}$	0.321359	$3.5 \times 10^{- 6}$	0.321354	$6.2 \times 10^{- 8}$	0.321354	$7.2 \times 10^{- 10}$
1.3	0.24448	$3.8 \times 10^{- 4}$	0.244219	$1 \times 10^{- 5}$	0.244207	$2.3 \times 10^{- 7}$	0.244208	$3.2 \times 10^{- 9}$
1.4	0.15582	$6.8 \times 10^{- 4}$	0.155217	$1.8 \times 10^{- 5}$	0.15519	$3.4 \times 10^{- 7}$	0.155114	$6.6 \times 10^{- 10}$
1.5	0.77793	$1.12 \times 10^{- 3}$	0.77119	$2.8 \times 10^{- 5}$	0.77093	$1.7 \times 10^{- 7}$	0.077096	$2.4 \times 10^{- 8}$
1.6	0.05719	$2.28 \times 10^{- 3}$	0.0575	$8.9 \times 10^{- 5}$	0.05754	$1.6 \times 10^{- 6}$	0.05755	$1.9 \times 10^{- 8}$
1.7	0.09636	$5.2 \times 10^{- 3}$	0.09851	$3.3 \times 10^{- 4}$	0.09871	$1.2 \times 10^{- 5}$	0.098734	$3.4 \times 10^{- 7}$
1.8	0.16541	$1 \times 10^{- 2}$	0.169798	$9 \times 10^{- 4}$	0.170278	$4.8 \times 10^{- 5}$	0.17033	$2 \times 10^{- 6}$
1.9	0.248207	$2 \times 10^{- 2}$	0.255549	$2.2 \times 10^{- 3}$	0.256564	$1.4 \times 10^{- 4}$	0.256695	$7.2 \times 10^{- 6}$
2	0.350388	$3.5 \times 10^{- 2}$	0.362702	$4.5 \times 10^{- 3}$	0.364821	$3.4 \times 10^{- 4}$	0.365035	$2 \times 10^{- 5}$
	Present Formulation
	$M = N = 5$		$M = N = 6$		$M = N = 7$		$M = N = 8$
	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊	$e_{(0, 0)}^{r}$	∊

	0.544803	$4.68 \times 10^{- 6}$	0.544801	$1.09 \times 10^{- 7}$	0.544802	$2.17 \times 10^{- 9}$	0.544802	$1.3 \times 10^{- 11}$
	0.410517	$2.46 \times 10^{- 5}$	0.410516	$7.05 \times 10^{- 7}$	0.410516	$1.6 \times 10^{- 8}$	0.410516	$2.65 \times 10^{- 10}$
	0.321369	$7.7 \times 10^{- 5}$	0.321354	$2.7 \times 10^{- 6}$	0.321354	$7.2 \times 10^{- 8}$	0.321355	$1.5 \times 10^{- 9}$
	0.244292	$1.84 \times 10^{- 4}$	0.24421	$7.81 \times 10^{- 6}$	0.244208	$2.44 \times 10^{- 7}$	0.244208	$6.17 \times 10^{- 9}$
	0.155435	$4.05 \times 10^{- 4}$	0.155201	$2 \times 10^{- 5}$	0.155195	$7.34 \times 10^{- 7}$	0.155195	$2.04 \times 10^{- 8}$
	0.077402	$9.39 \times 10^{- 4}$	0.077106	$5.26 \times 10^{- 5}$	0.077099	$2.22 \times 10^{- 6}$	0.077099	$7.36 \times 10^{- 8}$
	0.0575	$2.19 \times 10^{- 3}$	0.057538	$1.38 \times 10^{- 4}$	0.057553	$6.66 \times 10^{- 6}$	0.057554	$2.43 \times 10^{- 7}$
	0.097901	$4.61 \times 10^{- 3}$	0.098667	$3.32 \times 10^{- 4}$	0.098738	$1.8 \times 10^{- 5}$	0.098742	$7.4 \times 10^{- 7}$
	0.168347	$8.68 \times 10^{- 3}$	0.170154	$7.17 \times 10^{- 4}$	0.170337	$4.38 \times 10^{- 5}$	0.170344	$2 \times 10^{- 6}$
	0.252754	$1.48 \times 10^{- 2}$	0.256267	$1.4 \times 10^{- 3}$	0.256667	$9.56 \times 10^{- 5}$	0.256695	$4.96 \times 10^{- 6}$
	0.357264	$2.3 \times 10^{- 2}$	0.364129	$2.48 \times 10^{- 3}$	0.36501	$1.87 \times 10^{- 4}$	0.36508	$1.1 \times 10^{- 5}$

	$M = N = 5$	$M = N = 6$	$M = N = 7$	$M = N = 8$	$M = N = 9$	$M = N = 10$
$e_{(- 1, - 2)}^{r}$	0.027249	0.02727	0.027377	0.027393	0.027422	0.027428
$e_{(- 0, - 2)}^{r}$	0.037875	0.037428	0.037375	0.037287	0.037247	0.03721
$e_{(- 2, - 1)}^{r}$	0.028982	0.028708	0.028571	0.028477	0.02842	0.02838
$e_{(- 1, - 2)}^{r}$	0.005062	0.005115	0.005104	0.005115	0.005115	0.005118
$e_{(0, - 1)}^{r}$	0.152897	0.154705	0.15546	0.155939	0.156184	0.156363
$e_{(- 2 - 0)}^{r}$	0.036213	0.035908	0.035951	0.035922	0.035925	0.035916
$e_{(- 1,, 0)}^{r}$	0.139854	0.139041	0.138317	0.138054	0.137882	0.137798
$e_{(0, 0)}^{r}$	0.019859	0.020346	0.020814	0.021003	0.021148	0.021229
∊	0.001291	0.001121	0.000768	0.000649	0.000549	0.000493

	Ref. 1	Ref. 8	Ref. 4	Ref. 18	Present Method
	Ref. 1	Ref. 8	Ref. 4	Ref. 18	$M = 3$	$M = 5$	$M = 7$
$e_{(- 1, 0)}^{r}$	0.00259	0.00254	0.00207	0.00249	0.00246	0.00246	0.00246
$e_{(0, 0)}^{r}$	0.01948	0.01984	0.01928	0.01963	0.01962	0.01954	0.01951
$e_{(- 1, - 1)}^{t}$	0.00081	0.00092	0.00081	0.00086	0.00085	0.00086	0.00086
$e_{(0, - 1)}^{t}$	0.00683	0.00704	0.00767	0.00677	0.00678	0.00679	0.00679
$e_{(- 1, 0)}^{t}$	0.00321	0.00303	0.0037	0.00294	0.00292	0.00294	0.00294
$e_{(0, 0)}^{t}$	0.9643	0.96219	0.96316	0.96448	0.96493	0.96476	0.96472
$e_{(1, 0)}^{t}$	0.00276	0.00299	0.00332	0.00282	0.00282	0.00281	0.0028
∊	0.00002	0.0013	$- 0.00001$	0.00011	0.00019	0.00006	0.00009

	$M = N = 3$	$M = N = 4$	$M = N = 5$
TE Polarization
$e_{(- 1, - 1)}^{r}$	0.00371816	0.00379195	0.00379255
$e_{(0, - 1)}^{r}$	0.0174459	0.01763833	0.01763991
$e_{(0, 0)}^{r}$	0.79512396	0.79463043	0.79462637
∊	$- 7.4 \times 10^{- 7}$	$3.8 \times 10^{- 9}$	$- 1.3 \times 10^{- 11}$
TM Polarization
$e_{(- 1, - 1)}^{r}$	0.03900172	0.03888695	0.0388858
$e_{(0, - 1)}^{r}$	0.02094925	0.02104628	0.02104708
$e_{(0, 0)}^{r}$	0.05357425	0.05366466	0.05366555
∊	$2.6 \times 10^{- 5}$	$3.6 \times 10^{- 8}$	$3.6 \times 10^{- 10}$

Abstract

Corrections

Cited By

Figures (10)

Tables (6)

Equations (91)

Journal of the Optical Society of America A