Abstract

Spectral beam combination is a promising method for high-radiance lasers with a good beam quality. With the increase of the combination power, the temperature of the multilayer dielectric grating (MDG) unavoidably increases, leading to surface heat distortion of the MDG. In this study, the temperature field equation of the MDG is derived, and the key factors influencing the MDG temperature are investigated. Furthermore, experiments are performed to confirm the calculation results. The results reveal that the increase of the thickness of the substrate can improve the power tolerance of the MDG but delays the stable output of beam laser; use of a substrate material with a large thermal conductivity can greatly reduce the temperature of the MDG.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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2017 (4)

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

X. Hui and C. Yu, “Photonic bandgap structure and long-range periodicity of a cumulative Fibonacci lattice,” Photon. Res. 5(1), 11–14 (2017).
[Crossref]

L. Li, Y. Jin, F. Kong, L. Wang, J. Chen, and J. Shao, “Beam modulation due to thermal deformation of grating in a spectral beam combining system,” Appl. Opt. 56(19), 5511–5519 (2017).
[Crossref] [PubMed]

2016 (2)

2014 (1)

2013 (1)

2011 (2)

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. ten Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36(16), 3118–3120 (2011).
[Crossref] [PubMed]

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

2010 (1)

2007 (2)

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

2004 (2)

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

2003 (1)

1999 (1)

C. C. Cook and T. Y. Fan, “Spectral beam combining of yb-doped fiber lasers in an external cavity,” Opt. Photonics News 10(10), 411 (1999).

1994 (1)

J. Hue, J. DiJon, and P. Lyan, “Damage of mirrors under high-power continuous-wave CO2 laser irradiation: threshold and aging,” Proc. SPIE 2253, 751–763 (1994).
[Crossref]

Aggarwal, R. L.

Augst, S. J.

Ben, W. U.

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

Bercegol, H.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Bouchut, P.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Chen, J.

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

L. Li, Y. Jin, F. Kong, L. Wang, J. Chen, and J. Shao, “Beam modulation due to thermal deformation of grating in a spectral beam combining system,” Appl. Opt. 56(19), 5511–5519 (2017).
[Crossref] [PubMed]

Chen, X.

Chun, L. I. U.

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

Cook, C. C.

C. C. Cook and T. Y. Fan, “Spectral beam combining of yb-doped fiber lasers in an external cavity,” Opt. Photonics News 10(10), 411 (1999).

DiJon, J.

J. Hue, J. DiJon, and P. Lyan, “Damage of mirrors under high-power continuous-wave CO2 laser irradiation: threshold and aging,” Proc. SPIE 2253, 751–763 (1994).
[Crossref]

Divliansky, I.

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

Drachenberg, D.

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

During, A.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Eberhardt, R.

Fan, T. Y.

S. J. Augst, A. K. Goyal, R. L. Aggarwal, T. Y. Fan, and A. Sanchez, “Wavelength beam combining of ytterbium fiber lasers,” Opt. Lett. 28(5), 331–333 (2003).
[Crossref] [PubMed]

C. C. Cook and T. Y. Fan, “Spectral beam combining of yb-doped fiber lasers in an external cavity,” Opt. Photonics News 10(10), 411 (1999).

Fan, Z.

Fu, X.

Glebov, L.

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

Gou, L.

Gowin, M.

Goyal, A. K.

Hao, R. E. N.

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

He, B.

Henderson, A.

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

Hoffman, P. R.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

Honea, E.

Honea, E. C.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

Hu, M.

Hue, J.

J. Hue, J. DiJon, and P. Lyan, “Damage of mirrors under high-power continuous-wave CO2 laser irradiation: threshold and aging,” Proc. SPIE 2253, 751–763 (1994).
[Crossref]

Hui, X.

Hui, Y.

Jiang, M.

Jin, Y.

Jung, M.

Kong, F.

Lamaignere, L.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Lei, H.

Li, L.

L. Li, Y. Jin, F. Kong, L. Wang, J. Chen, and J. Shao, “Beam modulation due to thermal deformation of grating in a spectral beam combining system,” Appl. Opt. 56(19), 5511–5519 (2017).
[Crossref] [PubMed]

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

Li, Q.

Limpert, J.

Liu, A.

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

Liu, G.

Liu, K.

Liu, Q.

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

Liu, Y.

Loftus, T. H.

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

Ludewigt, K.

Lyan, P.

J. Hue, J. DiJon, and P. Lyan, “Damage of mirrors under high-power continuous-wave CO2 laser irradiation: threshold and aging,” Proc. SPIE 2253, 751–763 (1994).
[Crossref]

Mead, R.

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

Miao, G.

Neauport, J.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Norsen, M.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

Peng, H.

Piombini, H.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Qin, L.

Raze, G.

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

Royse, R.

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

Sanchez, A.

Schmidt, O.

Schreiber, T.

Shao, J.

Smirnov, V.

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

Stafford, R.

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

ten Have, E.

Thomas, A. M.

T. H. Loftus, A. Liu, P. R. Hoffman, A. M. Thomas, M. Norsen, R. Royse, and E. Honea, “522 W average power, spectrally beam-combined fiber laser with near-diffraction-limited beam quality,” Opt. Lett. 32(4), 349–351 (2007).
[Crossref] [PubMed]

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

Tongqiang, X. I. A.

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

Tsybin, I.

Tünnermann, A.

Vatter, T.

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

Venus, G.

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

Wang, J.

Wang, L.

Wirth, C.

Wu, Z.

Yang, L.

Yang, Y.

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

Y. Zheng, Y. Yang, J. Wang, M. Hu, G. Liu, X. Zhao, X. Chen, K. Liu, C. Zhao, B. He, and J. Zhou, “10.8 kW spectral beam combination of eight all-fiber superfluorescent sources and their dispersion compensation,” Opt. Express 24(11), 12063–12071 (2016).
[Crossref] [PubMed]

Yu, C.

Zhang, B.

Zhang, J.

Zhao, C.

Zhao, X.

Zheng, Y.

Zhong, W.

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

Zhou, J.

Zhu, Z.

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

T. H. Loftus, A. M. Thomas, P. R. Hoffman, M. Norsen, R. Royse, A. Liu, and E. C. Honea, “Spectrally beam-combined fiber lasers for high-average-power applications,” IEEE J. Sel. Top. Quantum Electron. 13(3), 487–497 (2007).
[Crossref]

Opt. Commun. (1)

L. Li, Q. Liu, J. Chen, L. Wang, Y. Jin, Y. Yang, and J. Shao, “Polarization-independent broadband dielectric bilayer gratings for spectral beam combining system,” Opt. Commun. 385, 97–103 (2017).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Opt. Photonics News (1)

C. C. Cook and T. Y. Fan, “Spectral beam combining of yb-doped fiber lasers in an external cavity,” Opt. Photonics News 10(10), 411 (1999).

Photon. Res. (1)

Proc. SPIE (4)

L. Lamaignere, H. Bercegol, P. Bouchut, A. During, J. Neauport, H. Piombini, and G. Raze, “Enhanced optical damage resistance of fused silica surfaces using UV laser conditioning and CO2 laser treatment,” Proc. SPIE 5448, 952–961 (2004).
[Crossref]

J. Hue, J. DiJon, and P. Lyan, “Damage of mirrors under high-power continuous-wave CO2 laser irradiation: threshold and aging,” Proc. SPIE 2253, 751–763 (1994).
[Crossref]

A. Liu, R. Mead, T. Vatter, A. Henderson, and R. Stafford, “Spectral beam combining of high-power fiber lasers,” Proc. SPIE 5335, 81–88 (2004).
[Crossref]

D. Drachenberg, I. Divliansky, V. Smirnov, G. Venus, and L. Glebov, “High-power spectral beam combining of fiber lasers with ultra-high-spectral density by thermal tuning of volume Bragg gratings,” Proc. SPIE 7914, 79141F (2011).
[Crossref]

Therm. Sci. (1)

L. I. U. Chun, W. Zhong, R. E. N. Hao, W. U. Ben, and X. I. A. Tongqiang, “A differential-integral transform method for solving the 1-d heat diffusion equation,” Therm. Sci. 21, S89 (2017).

Other (1)

Lockheed Martin, “Lockheed Martin to deliver world recordsetting 60 kw laser to U.S. Army,” https://phys.org/news/2017-03-lockheed-martin-world-record-setting-60kw.html .

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Figures (8)

Fig. 1
Fig. 1 MDG diagram in rectangular coordinates.
Fig. 2
Fig. 2 (a) Maximum MDG temperature as a function of the time and corresponding normalization curves for different irradiation powers; (b) MDG maximum temperature variations with power in the steady state.
Fig. 3
Fig. 3 (a) Variations of the maximum MDG temperature as a function of the time and corresponding normalization curves for different laser radii; (b) MDG maximum temperature variations with laser radius in the steady state.
Fig. 4
Fig. 4 (a) Maximum temperature of the MDG as a function of the time and corresponding normalization curves for different substrate thicknesses; (b) MDG maximum temperature variations for different substrate thicknesses in the steady state; (c) Maximum temperature of the MDG as a function of the time and corresponding normalization curves for different substrate lengths; (d) MDG maximum temperature variations for different substrate lengths in the steady state.
Fig. 5
Fig. 5 Variations of the maximum temperatures of the MDGs with different substrate materials as a function of the time.
Fig. 6
Fig. 6 (a) Schematic of the MDG-temperature measurement. (b) Temperature of the MDG measured by the infrared thermal imager.
Fig. 7
Fig. 7 Variations of the maximum temperature of the MDG with time under different irradiation conditions.
Fig. 8
Fig. 8 Variations of the maximum temperature of the MDG with time for different substrate parameters.

Tables (2)

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Table 1 Physical parameters of quartz and yttrium aluminum garnet (YAG).

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Table 2 Parameters of the MDGs.

Equations (12)

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c p ρ T t =( kT )+ρ f 0
k( 2 T x 2 + 2 T y 2 + 2 T z 2 )=ρ c p T t
( k T Z +hT ) z=c =h T 0 +ηf( x,y )
( k T n ) S 2 =h( T T 0 )
f( x,y )= 9Pcosθ 2π r 2 exp[ 9 ( x a 2 ) 2 +9 cos 2 θ ( y a 2 ) 2 2 r 2 ]
T t=0 = T 0
T( x,y,z,t )= m=1 n=1 p=1 X( β m ,x )Y( γ n ,y )Z( η p ,z ) N( β m )N( γ n )N( η p ) { 1exp[ α( β m 2 + γ n 2 + η p 2 )t ] } α( β m 2 + γ n 2 + η p 2 ) A( β m , γ n , η p )+ T 0
A( β m , γ n , η p )= αη k [ η p cos( c η p )+Hsin( c η p ) ] 0 a 0 b X( β m , x ' )Y( γ n , y ' )f( x ' , y ' )dx'dy'
X( β m ,x )= β m cos( β m x )+Hsin( β m x ),N( β m )= 1 2 [ ( β m 2 + H 2 )( a+ H 2 β m 2 + H 2 )+H ]
Y( γ n ,y )= γ n cos( γ n y )+Hsin( γ n y ),N( γ n )= 1 2 [ ( γ n 2 + H 2 )( b+ H 2 γ n 2 + H 2 )+H ]
Z( η p ,z )= η p cos( η p z )+Hsin( η p z ),N( η p )= 1 2 [ ( η p 2 + H 2 )( b+ H 2 η p 2 + H 2 )+H ]
H= h k , α= k ρ c p

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