Design and fabrication of stress-compensated optical coatings: Fabry&#x2013;Perot filters for astronomical applications

Marie-Maude de Denus-Baillargeon; Thomas Schmitt; Stéphane Larouche; Ludvik Martinu

doi:10.1364/AO.53.002616

Applied Optics
Vol. 53,
Issue 12,
pp. 2616-2624
(2014)
•https://doi.org/10.1364/AO.53.002616

Design and fabrication of stress-compensated optical coatings: Fabry–Perot filters for astronomical applications

Marie-Maude de Denus-Baillargeon, Thomas Schmitt, Stéphane Larouche, and Ludvik Martinu

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Marie-Maude de Denus-Baillargeon, Thomas Schmitt, Stéphane Larouche, and Ludvik Martinu, "Design and fabrication of stress-compensated optical coatings: Fabry–Perot filters for astronomical applications," Appl. Opt. 53, 2616-2624 (2014)

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Abstract

The performance of optical coatings may be negatively affected by the deleterious effects of mechanical stress. In this work, we propose an optimization tool for the design of optical filters taking into account both the optical and mechanical properties of the substrate and of the individual deposited layers. The proposed method has been implemented as a supplemental module in the OpenFilters open source design software. It has been experimentally validated by fabricating multilayer stacks using e-beam evaporation, in combination with their mechanical stress assessment performed as a function of temperature. Two different stress-compensation strategies were evaluated: (a) design of two complementary coatings on either side of the substrate and (b) implementing the mechanical properties of the individual materials in the design of the optical coating on one side only. This approach has been tested by the manufacture of a Fabry–Perot etalon used in astronomy while using evaporated ${SiO}_{2}$ and ${TiO}_{2}$ films. We found that the substrate curvature can be decreased by 85% and 49% for the first and second strategies, respectively.

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Properties	Fused Silica	Silicon $〈 100 〉$
CTE ( $α$ )	$0.55 \times 10^{- 6} ° C^{- 1}$	$2.6 \times 10^{- 6} ° C^{- 1}$
Young’s modulus (E)	72 GPa	130 GPa
Poisson’s ratio ( $ν$ )	0.16	0.28

Properties	${SiO}_{2}$	${TiO}_{2}$
n at 550 nm	1.47	2.24
k at 550 nm	0	$< 1 \times 10^{- 5}$
CTE ( $α$ )	$4.4 \times 10^{- 6} ° C^{- 1}$	$4.2 \times 10^{- 6} ° C^{- 1}$
Young’s modulus (E)	38 GPa	112 GPa
Poisson’s ratio ( $ν$ )	0.2	0.11
Intrinsic stress ( $σ_{i}$ )	$- 175 MPa$	190 MPa
Density ( $ρ$ )	$1.5 g / {cm}^{3}$	$3.8 g / {cm}^{3}$

Multilayer Stack	Number of Layers	Total Thickness in Stacks
Multilayer Stack	Number of Layers	${SiO}_{2} (nm)$	${TiO}_{2} (nm)$
Coating A	18	1218.1	514.5
Coating B	17	1055.6	499.0
Coating C	20	1104.0	622.2

Properties	Fused Silica	Silicon $〈 100 〉$
CTE ( $α$ )	$0.55 \times 10^{- 6} ° C^{- 1}$	$2.6 \times 10^{- 6} ° C^{- 1}$
Young’s modulus (E)	72 GPa	130 GPa
Poisson’s ratio ( $ν$ )	0.16	0.28

Properties	${SiO}_{2}$	${TiO}_{2}$
n at 550 nm	1.47	2.24
k at 550 nm	0	$< 1 \times 10^{- 5}$
CTE ( $α$ )	$4.4 \times 10^{- 6} ° C^{- 1}$	$4.2 \times 10^{- 6} ° C^{- 1}$
Young’s modulus (E)	38 GPa	112 GPa
Poisson’s ratio ( $ν$ )	0.2	0.11
Intrinsic stress ( $σ_{i}$ )	$- 175 MPa$	190 MPa
Density ( $ρ$ )	$1.5 g / {cm}^{3}$	$3.8 g / {cm}^{3}$

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