Collimation and finite-size effects in suspended resonant guided-mode gratings

Christian Toft-Vandborg; Alexios Parthenopoulos; Ali Akbar Darki; Aurélien Dantan

doi:10.1364/JOSAA.440215

Journal of the Optical Society of America A
Vol. 38,
Issue 11,
pp. 1714-1725
(2021)
•https://doi.org/10.1364/JOSAA.440215

Collimation and finite-size effects in suspended resonant guided-mode gratings

Christian Toft-Vandborg, Alexios Parthenopoulos, Ali Akbar Darki, and Aurélien Dantan

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Christian Toft-Vandborg, Alexios Parthenopoulos, Ali Akbar Darki, and Aurélien Dantan, "Collimation and finite-size effects in suspended resonant guided-mode gratings," J. Opt. Soc. Am. A 38, 1714-1725 (2021)

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Table of Contents Category
- Diffraction and Gratings
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About this Article
History
- Original Manuscript: August 10, 2021
- Revised Manuscript: September 22, 2021
- Manuscript Accepted: October 5, 2021
- Published: October 28, 2021

Abstract

The optical transmission of resonant guided-mode gratings patterned on suspended silicon nitride thin films and illuminated at normal incidence with a Gaussian beam is investigated both experimentally and theoretically. Effects due to the beam focusing and its finite size are accounted for by a phenomenological coupled-mode model whose predictions are found to be in very good agreement with the experimentally measured spectra for various grating structures and beam sizes, and which allow for a detailed analysis of the respective magnitude of these effects. These results are highly relevant for the design and optimization of such suspended structured films that are widely used for photonics, sensing, and optomechanics applications.

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Data Availability

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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Equations (26)

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Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	A	B	C	D	E
$λ_{0}$ [nm]	941.8	948.3	926.3	928.7	958.3
$λ_{2}$ [nm]	925.4	918.6	900.1	900.0	1002.0
$ν$ [ $n m^{- 2}$ ]	$2.9 10^{- 5}$	$2.2 10^{- 5}$	$2.4 10^{- 5}$	$2.8 10^{- 5}$	$2.4 10^{- 5}$
$ν_{θ}$ [ $n m^{- 2}$ ]	$1.6 10^{- 3}$	$6.8 10^{- 4}$	$8.2 10^{- 4}$	$8.7 10^{- 4}$	$- 5.5 10^{- 4}$
$δ_{λ}$ [nm]	2.9	2.6	3.6	3.3	5.8
$l$ [µm]	3.0	3.4	2.4	2.3	1.1
$η$ [%]	8.2	7.8	9.0	8.3	8.4
$A_{w}$ [µm]	37.0	43.1	26.7	29.2	12.6

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	A	B	C	D	E
$λ_{0}$ [nm]	941.8	948.3	926.3	928.7	958.3
$λ_{2}$ [nm]	925.4	918.6	900.1	900.0	1002.0
$ν$ [ $n m^{- 2}$ ]	$2.9 10^{- 5}$	$2.2 10^{- 5}$	$2.4 10^{- 5}$	$2.8 10^{- 5}$	$2.4 10^{- 5}$
$ν_{θ}$ [ $n m^{- 2}$ ]	$1.6 10^{- 3}$	$6.8 10^{- 4}$	$8.2 10^{- 4}$	$8.7 10^{- 4}$	$- 5.5 10^{- 4}$
$δ_{λ}$ [nm]	2.9	2.6	3.6	3.3	5.8
$l$ [µm]	3.0	3.4	2.4	2.3	1.1
$η$ [%]	8.2	7.8	9.0	8.3	8.4
$A_{w}$ [µm]	37.0	43.1	26.7	29.2	12.6

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Abstract

Data Availability

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Figures (12)

Tables (2)

Equations (26)

Journal of the Optical Society of America A

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE

Sample	$b$ [µm]	$Λ$ [nm]	$w_{t}$ [nm]	$w_{m}$ [nm]	$d$ [nm]	Polarization
A	200	848	340	355	114	TM
B	200	858	394	411	153	TM
C	200	801	416	434	90	TM
D	100	800	432	453	91	TM
E	200	646	474	474	88	TE