Beam modulation due to thermal deformation of grating in a spectral beam combining system

Linxin Li; Yunxia Jin; Fanyu Kong; Leilei Wang; Junming Chen; Jianda Shao

doi:10.1364/AO.56.005511

Applied Optics
Vol. 56,
Issue 19,
pp. 5511-5519
(2017)
•https://doi.org/10.1364/AO.56.005511

Beam modulation due to thermal deformation of grating in a spectral beam combining system

Linxin Li, Yunxia Jin, Fanyu Kong, Leilei Wang, Junming Chen, and Jianda Shao

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Linxin Li, Yunxia Jin, Fanyu Kong, Leilei Wang, Junming Chen, and Jianda Shao, "Beam modulation due to thermal deformation of grating in a spectral beam combining system," Appl. Opt. 56, 5511-5519 (2017)

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Abstract

As the power of a spectral beam combining (SBC) system increases, the temperature of the multilayer dielectric grating (MDG) inevitably rises under the influence of high-power continuous-wave (CW) laser irradiation. Hence, thermal deformation of the MDG occurs, along with degeneration of the combined beam properties. In this study, we experimentally and theoretically investigate the influence of the MDG thermal deformation on the combined beam properties. An experimental setup is first proposed, in which beam quality $M^{2}$ , beam profile, and MDG wavefront deformation are investigated. The experimental results indicate that the beam quality clearly degrades and the MDG wavefront deformation becomes more significant with increasing pump-CW power density. On this basis, a calculation model for MDG thermal deformation in SBC systems is proposed. The results indicate that MDG wavefront deformation becomes more significant, combined beam profile becomes deformed, and beam quality of the combined beam degrades with increasing power density. Further, thermal expansion of the substrate is a crucial factor that induces MDG wavefront deformation and far-field intensity modulation.

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Parameters	${SiO}_{2}$	${HfO}_{2}$	Fused Silica
$Density / kg \cdot m^{- 3}$	2100	10300	2200
Specific $heat / J \cdot {(kg \cdot K)}^{- 1}$	722	146	670
Heat $conductivity / W \cdot {(m \cdot K)}^{- 1}$	7.6	0.647	1.4
Thermal $expansion / 10^{- 6} K^{- 1}$	0.5	5.8	0.55
Young’s modulus/Gpa	73.1	170	72
Poisson’s ratio	0.17	0.27	0.17

Parameters	Deformation Height $h$ (nm)	Phase Modulation $ϕ$ ( $λ = 1058 nm$ 31°)
Substrate	136.9	$0.2576 λ$
High-index layer (H 11 layers)	1.490	$- 0.0074 λ$
Low-index layer (L 10 layers)	0.280	$- 0.0010 λ$
Matching layer (M)	0.049	$- 0.0004 λ$
Bottom grating relief (N)	0.053	$- 0.0004 λ$
Top grating relief (Q)	0.383	$- 0.0028 λ$
Sum	139.3	$0.2446 λ$

Deformation Height $h$ (nm)	0	50	100	150
Beam quality $M^{2}$	1.00	1.48	2.66	3.82

Parameters	${SiO}_{2}$	${HfO}_{2}$	Fused Silica
$Density / kg \cdot m^{- 3}$	2100	10300	2200
Specific $heat / J \cdot {(kg \cdot K)}^{- 1}$	722	146	670
Heat $conductivity / W \cdot {(m \cdot K)}^{- 1}$	7.6	0.647	1.4
Thermal $expansion / 10^{- 6} K^{- 1}$	0.5	5.8	0.55
Young’s modulus/Gpa	73.1	170	72
Poisson’s ratio	0.17	0.27	0.17

Parameters	Deformation Height $h$ (nm)	Phase Modulation $ϕ$ ( $λ = 1058 nm$ 31°)
Substrate	136.9	$0.2576 λ$
High-index layer (H 11 layers)	1.490	$- 0.0074 λ$
Low-index layer (L 10 layers)	0.280	$- 0.0010 λ$
Matching layer (M)	0.049	$- 0.0004 λ$
Bottom grating relief (N)	0.053	$- 0.0004 λ$
Top grating relief (Q)	0.383	$- 0.0028 λ$
Sum	139.3	$0.2446 λ$

Abstract

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Equations (6)

Applied Optics