Characterization of a perfect sinusoidal grating profile using an artificial neural network for plasmonic-based sensors

Moustapha Godi Tchéré; Stéphane Robert; Stéphane Robert; Julie Dutems; Hugo Bruhier; Hugo Bruhier; Bernard Bayard; Yves Jourlin; Damien Jamon

doi:10.1364/AO.520109

Applied Optics
Vol. 63,
Issue 14,
pp. 3876-3884
(2024)
•https://doi.org/10.1364/AO.520109

Characterization of a perfect sinusoidal grating profile using an artificial neural network for plasmonic-based sensors

Moustapha Godi Tchéré, Stéphane Robert, Julie Dutems, Hugo Bruhier, Bernard Bayard, Yves Jourlin, and Damien Jamon

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Moustapha Godi Tchéré, Stéphane Robert, Julie Dutems, Hugo Bruhier, Bernard Bayard, Yves Jourlin, and Damien Jamon, "Characterization of a perfect sinusoidal grating profile using an artificial neural network for plasmonic-based sensors," Appl. Opt. 63, 3876-3884 (2024)

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Related Topics
Table of Contents Category
- Diffraction and Gratings
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: January 25, 2024
- Revised Manuscript: March 27, 2024
- Manuscript Accepted: April 14, 2024
- Published: May 7, 2024

Abstract

In this paper, we present a system intended to detect a targeted perfect sinusoidal profile of a diffraction grating during its manufactured process. Indeed, the sinusoidal nature of the periodic structure is essential to ensure optimal efficiency of specific applications as plasmonic sensors (surface plasmon resonance -based sensors). A neural network is implemented to characterize the geometrical shape of the structure under testing at the end of the laser interference lithography process. This decision tool operates in classifier mode prior to further processing. Then, the geometrical parameters of the structure can be reliably determined if necessary. Two solutions can be considered: the detection of a fixed geometrical shape operating on a binary mode and the identification of a geometrical shape from a limited number of profiles. These methods are validated in the context of plasmonic sensors on experimental sinusoidal grating structures with a grating period of 627 nm.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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$P_{s}$	$P_{g}$	$P_{s d}$	$P_{s t}$
	$40 < δ < \frac{Λ}{2}$	$- 0.25 < ρ < 2$	$0 < α < 1$
$100 n m < h < 200 n m$	$100 n m < h < 200 n m$	$100 n m < h < 200 n m$	$100 n m < b < 500 n m$
$300 n m < h_{r} < 400 n m$	$300 n m < h_{r} < 400 n m$	$300 n m < h_{r} < 400 n m$	$100 n m < h < 200 n m$
$300 n m < h_{r} < 400 n m$	$300 n m < h_{r} < 400 n m$	$300 n m < h_{r} < 400 n m$	$300 n m < h_{r} < 400 n m$

		Real Class
		$P_{s}$	$P_{fs}$	Precision
Predicted class	$P_{s}$	450	19	95.9%
	$P_{fs}$	0	431	100%
Sensitivity		100%	95.8%	Accuracy: 97.9%

		Real Class
		$P_{s}$	$P_{fs}$	Precision
Predicted class	$P_{s}$	450	15	96.7%
	$P_{fs}$	0	426	100%
	C.I	0	9
Sensitivity		100%	94.6%	Accuracy: 97.3%

		Real Class
		$P_{s}$	$P_{fs}$	Precision
Predicted class	$P_{s}$	426	10	97.7%
	$P_{fs}$	0	420	100%
	C.I	24	20
Sensitivity		94.6%	93.3%	Accuracy: 94.0%

	$P_{s}$	$P_{g}$	$P_{s d}$	$P_{s t}$
$E_{1}$	$h_{r} = 471.28 n m$	$h_{r} = 470.48 nm$	$h_{r} = 471.12 n m$	$h_{r} = 471.7 n m$
	$E_{I_{s}, I_{c}} = 0.05$	$E_{I_{s,} I_{c}} = 0.04$	$E_{I_{s,} I_{c}} = 0.04$	$E_{I_{s,} I_{c}} = 0.05$
	$E_{g e o n o r m} = 13.4 %$	$E_{geonorm} = 7.61\%$	$E_{g e o n o r m} = 10.2 %$	$E_{g e o n o r m} = 13.82 %$
$E_{2}$	$h_{r} = 410.8 n m$	$h_{r} = 411.07 n m$	$h_{r} = 411.51 n m$	$h_{r} = 411.48 nm$
	$E_{I_{s,} I_{c}} = 0.06$	$E_{I_{s,} I_{c}} = 0.08$	$E_{I_{s,} I_{c}} = 0.07$	$E_{I_{s,} I_{c}} = 0.05$
	$E_{g e o n o r m} = 13.29 %$	$E_{g e o n o r m} = 12.95 %$	$E_{g e o n o r m} = 7.91 %$	$E_{geonorm} = 7.74 %$
$E_{3}$	$h_{r} = 418.56 n m$	$h_{r} = 418.45 n m$	$h_{r} = 418.73 nm$	$h_{r} = 419.02 n m$
	$E_{I_{s,} I_{c}} = 0.08$	$E_{I_{s,} I_{c}} = 0.05$	$E_{I_{s,} I_{c}} = 0.04$	$E_{I_{s,} I_{c}} = 0.06$
	$E_{g e o n o r m} = 18.82 %$	$E_{g e o n o r m} = 9.83 %$	$E_{geonorm} = 8.22\%$	$E_{g e o n o r m} = 14.85 %$
$E_{4}$	$h_{r} = 392.47 n m$	$h_{r} = 392.36 n m$	$h_{r} = 393.14 n m$	$h_{r} = 393.41 nm$
	$E_{I_{s,} I_{c}} = 0.12$	$E_{I_{s,} I_{c}} = 0.13$	$E_{I_{s,} I_{c}} = 0.13$	$E_{I_{s,} I_{c}} = 0.10$
	$E_{g e o n o r m} = 14.82 %$	$E_{g e o n o r m} = 16.79 %$	$E_{g e o n o r m} = 14.18 %$	$E_{geonorm} = 12.42\%$
$E_{5}$	$h_{r} = 318.81 n m$	$h_{r} = 318.03 nm$	$h_{r} = 319.02 n m$	$h_{r} = 321.54 n m$
	$E_{I_{s,} I_{c}} = 0.19$	$E_{I_{s,} I_{c}} = 0.18$	$E_{I_{s,} I_{c}} = 0.19$	$E_{I_{s,} I_{c}} = 0.22$
	$E_{g e o n o r m} = 12.53 %$	$E_{geonorm} = 10.92 %$	$E_{g e o n o r m} = 12.32 %$	$E_{g e o n o r m} = 15.39 %$

	$E_{1}$	$E_{2}$	$E_{3}$	$E_{4}$	$E_{5}$
$P_{s}$	0.02	0.00	0.00	0.00	0.00
$P_{f s}$	0.98	1.00	1.00	1.00	1.00

	$E_{1}$	$E_{2}$	$E_{3}$	$E_{4}$	$E_{5}$
$P_{s}$	0.02	0.00	0.00	0.00	0.00
$P_{f s}$	0.98	1.00	1.00	1.00	1.00

Abstract

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Equations (14)

Applied Optics