Abstract

The sine–cosine single-frequency dithering technique for active phase locking of fiber amplifiers is presented for the first time to our knowledge. It has twice the phase control speed as the single-frequency dithering technique. Detailed theoretical development has been presented and the relevant experiment has been done. In the experiment, nine 10W level fiber amplifiers are tiled into 3×3 array and the total output power is about 100W. The sine–cosine single-frequency dithering algorithm is run on a signal processor based on a field-programmable gate array for phase control on the fiber amplifiers. When the phase control system is in a closed loop, the fringe contrast of far-field intensity pattern is improved by more than 90% from 21% in an open loop, and the residual phase error is less than λ/20.

© 2011 Optical Society of America

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2010

2009

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

2008

2007

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

2006

2005

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[CrossRef]

2004

T. M. Shay and V. Benham, “First experimental demonstration of phase locking of optical fiber arrays by RF phase modulation,” Proc. SPIE 5550, 313–319 (2004).
[CrossRef]

2003

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

1977

Anderegg, J.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Baker, J. T.

Benham, V.

Bennaï, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Beresnev, L. A.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Bourdon, P.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Broanan, S.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Canat, G.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Culpepper, M. A.

Goular, D.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Guo, S.

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Hou, J.

Jaouën, Y.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Jiang, Z. F.

Jolivet, V.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Komine, H.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Liu, L.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[CrossRef]

Liu, M.

Liu, Z.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Lombard, L.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Lu, L. C. A.

Ma, H.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Ma, Y.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Moreau, B.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Nelson, L. D. J.

O’Meara, T. R.

Pillkington, S. D.

Polnau, E.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Pourtal, E.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Sanchez, A. D.

Shay, T. M.

Si, L.

Spring, L. J.

Vasseur, O.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

Vorontsov, M. A.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[CrossRef]

Wang, X.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Ward, C. B.

Weber, M.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Weyrauch, T.

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

Wickham, M.

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

Xiao, R.

Xu, X.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

Zhao, Y.

Zhou, P.

Y. Ma, P. Zhou, X. Wang, H. Ma, X. Xu, L. Si, Z. Liu, and Y. Zhao, “Coherent beam combination with single frequency dithering technique,” Opt. Lett. 35, 1308–1310(2010).
[CrossRef] [PubMed]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

V. Jolivet, P. Bourdon, B. Bennaï, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouën, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15, 257–268(2009).
[CrossRef]

P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15, 248–256 (2009).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

Proc. SPIE

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[CrossRef]

L. Liu, M. A. Vorontsov, E. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Proc. SPIE 6708, 67080K (2007).
[CrossRef]

T. M. Shay and V. Benham, “First experimental demonstration of phase locking of optical fiber arrays by RF phase modulation,” Proc. SPIE 5550, 313–319 (2004).
[CrossRef]

J. Anderegg, S. Broanan, M. Weber, H. Komine, and M. Wickham, “8-watt coherently phased 4-element fiber array,” Proc. SPIE 4974, 1–6 (2003).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Scheme of the sine–cosine single-dithering technique.

Fig. 2
Fig. 2

Experimental setup of CBC of nine beams. Iso, isolator; PA, preamplifier.

Fig. 3
Fig. 3

Long-exposure far-field intensity pattern of the combined laser beam: (a) open loop, (b) closed loop, (c) theoretical pattern.

Fig. 4
Fig. 4

Time series signals of energy collected by the pinhole in an open loop and a closed loop.

Fig. 5
Fig. 5

Evolution in time from when the algorithm is turned on until the amplifiers are phase locked (a) for the single-frequency dithering technique and the (b) sine–cosine single- frequency dithering technique.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

E i ( t ) = E i 0 cos ( ω L t + ϕ i ) ( where     i = 1 , 2 , 3 , , k ) ,
E 1 ( t ) = E 10 cos ( ω L t + ϕ 1 + β s sin ( ω t ) ) ,
E 2 ( t ) = E 20 cos ( ω L t + ϕ 2 + β c cos ( ω t ) ) ,
I ( t ) = ε 0 μ 0 ( m = 1 k E m ( t ) ) ( n = 1 k E j ( t ) ) = ε 0 μ 0 [ ( m = 3 k E m ( t ) ) ( n = 3 k E j ( t ) ) + 2 E 1 ( t ) m = 3 k E m ( t ) + 2 E 2 ( t ) n = 3 k E n ( t ) + E 1 2 ( t ) + E 2 2 ( t ) + 2 E 1 ( t ) E 2 ( t ) ] ,
i PD ( t ) = R PD S I ( t ) = R PD S ε 0 μ 0 [ ( m = 3 k E m ( t ) ) ( n = 3 k E j ( t ) ) + 2 E 1 ( t ) m = 3 k E m ( t ) + 2 E 2 ( t ) n = 3 k E n ( t ) + E 1 2 ( t ) + E 2 2 ( t ) + 2 E 1 ( t ) E 2 ( t ) ] ,
V 1 = 0 τ i PD ( t ) sin ( ω t ) d t ,
V 2 = 0 τ i PD ( t ) cos ( ω t ) d t .
V 1 = R PD S ε 0 μ 0 [ 2 m = 3 k 0 τ E 1 ( t ) E m ( t ) sin ( ω t ) d t + 2 n = 3 k 0 τ E 2 ( t ) E n ( t ) sin ( ω t ) d t + 2 0 τ E 1 ( t ) E 2 ( t ) sin ( ω t ) d t ] .
V 1 a = 2 R PD S ε 0 μ 0 m = 3 k 0 τ E 1 ( t ) E m ( t ) sin ( ω t ) d t ,
V 1 b = 2 R PD S ε 0 μ 0 n = 3 k 0 τ E 2 ( t ) E n ( t ) sin ( ω t ) d t ,
V 1 c = 2 R PD S ε 0 μ 0 0 τ E 1 ( t ) E 2 ( t ) sin ( ω t ) d t .
V 1 a = 2 R PD S ε 0 μ 0 m = 3 k 0 τ E 1 ( t ) E m ( t ) sin ( ω t ) d t = 2 R PD S ε 0 μ 0 m = 3 k 0 τ E 10 E m 0 cos ( ω L t + ϕ 1 + β s sin ( ω t ) ) cos ( ω L t + ϕ m ) sin ( ω t ) d t = R PD S ε 0 μ 0 m = 3 k 0 τ E 10 E m 0 { cos ( ϕ 1 ϕ m ) [ J 0 ( β s ) + 2 i = 1 J 2 i ( β s ) cos ( 2 i ω t ) ] sin ( ϕ 1 ϕ m ) [ 2 i = 1 J 2 i 1 ( β s ) sin ( ( 2 i 1 ) ω t ) ] } sin ( ω t ) d t = R PD S E 10 J 1 ( β s ) ε 0 μ 0 m = 3 k E m 0 sin ( ϕ m ϕ 1 ) .
V 1 b = 2 R PD S ε 0 μ 0 n = 3 k 0 τ E 2 ( t ) E n ( t ) sin ( ω t ) d t = R PD S ε 0 μ 0 n = 3 k 0 τ E 20 E n 0 { cos ( ϕ 2 ϕ n ) [ J 0 ( β c ) + 2 i = 1 ( 1 ) i J 2 i ( β c ) cos ( 2 i ω t ) ] sin ( ϕ 2 ϕ n ) [ 2 i = 0 ( 1 ) i J 2 i + 1 ( β c ) cos ( ( 2 i + 1 ) ω t ) ] } sin ( ω t ) d t = 0 ,
V 1 c = 2 R PD S ε 0 μ 0 0 τ E 1 ( t ) E 2 ( t ) sin ( ω t ) d t = 2 R PD S ε 0 μ 0 0 τ E 10 E 20 sin ( ω t ) { cos ( ϕ 1 ϕ 2 ) { J 0 ( β s ) + 2 i = 1 J 2 i ( β s ) cos [ 2 i ( ω t ) ] } { J 0 ( β c ) + 2 j = 1 ( 1 ) j J 2 j ( β c ) cos [ 2 j ( ω t ) ] } + cos ( ϕ 1 ϕ 2 ) { 2 i = 0 J 2 i + 1 ( β s ) sin [ ( 2 i + 1 ) ω t ] } { 2 j = 0 ( 1 ) j J 2 j + 1 ( β c ) cos [ ( 2 j + 1 ) ω t ] } sin ( ϕ 1 ϕ 2 ) { 2 n = 0 J 2 i + 1 ( β s ) sin [ ( 2 i + 1 ) ω t ] } { J 0 ( β c ) + 2 j = 1 ( 1 ) j J 2 j ( β c ) cos [ 2 j ( ω t ) ] } + sin ( ϕ 1 ϕ 2 ) { J 0 ( β s ) + 2 i = 1 J 2 i ( β s ) cos [ 2 i ( ω t ) ] } { 2 j = 0 ( 1 ) j J 2 j + 1 ( β c ) cos [ ( 2 j + 1 ) ω t ] } } d t = R PD S E 10 J 1 ( β s ) ε 0 μ 0 E 20 sin ( ϕ 2 ϕ 1 ) .
V 1 = V 1 a + V 1 b + V 1 c = R PD S E 10 J 1 ( β s ) ε 0 μ 0 [ m = 3 k E m 0 sin ( ϕ m ϕ 1 ) + 0 + E 20 sin ( ϕ 2 ϕ 1 ) ] = R PD S E 10 J 1 ( β s ) ε 0 μ 0 m = 2 k E m 0 sin ( ϕ m ϕ 1 ) .
V 2 = R PD S E 20 J 1 ( β c ) ε 0 μ 0 n = 1 k E n 0 sin ( ϕ n ϕ 2 ) .
V 2 i 1 = R PD S E ( 2 i 1 ) 0 J 1 ( β s ) ε 0 μ 0 m = 1 k E m 0 sin ( ϕ m = ϕ ( 2 i 1 ) ) ,
V 2 i = R PD S E ( 2 i ) 0 J 1 ( β c ) ε 0 μ 0 n = 1 k E n 0 sin ( ϕ n ϕ 2 i ) .

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