Abstract

We demonstrate phase locking of a linear array of seven fiber lasers via diffractive coupling. Coupling between the lasers is achieved by a common output coupler positioned at a quarter Talbot distance from the lasers. The output beams are anti-phase locked with a measured far-field fringe contrast of 82%, and their total output power is higher than that obtained when the lasers operate individually. We measure an exponential phase decorrelation between distant lasers in the array, and discuss its fundamental limitation on scalability of this and similar local coupling methods.

© 2011 Optical Society of America

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  1. S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
    [CrossRef] [PubMed]
  2. 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, 331-333 (2003).
    [CrossRef] [PubMed]
  3. A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
    [CrossRef]
  4. J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
    [CrossRef] [PubMed]
  5. C. J. Corcoran, and F. Durville, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118 (2005).
  6. L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
    [CrossRef]
  7. E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
    [CrossRef] [PubMed]
  8. J. R. Leger, "Lateral mode control of an AlGaAs laser array in a Talbot cavity," Appl. Phys. Lett. 55, 334-336 (1989).
    [CrossRef]
  9. D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
    [CrossRef] [PubMed]
  10. M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
    [CrossRef]
  11. J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315 (2008).
    [CrossRef]
  12. R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).
  13. M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
    [CrossRef]
  14. W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
    [CrossRef] [PubMed]
  15. E. du Tremolet de Lacheisserie, D. Gignoux, and M. Schlenker, Magnetism: Fundamentals (Springer, 2005), 2nd ed.
  16. R. K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1996), 2nd ed.
  17. C. D. Nabros, "Effects of phase errors on coherent emitting arrays," Appl. Opt. 33, 2284-2289 (1994).
    [CrossRef]

2010

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

2009

A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
[CrossRef]

2008

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315 (2008).
[CrossRef]

2006

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

2005

C. J. Corcoran, and F. Durville, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118 (2005).

2004

S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
[CrossRef] [PubMed]

2003

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, 331-333 (2003).
[CrossRef] [PubMed]

2000

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

1994

C. D. Nabros, "Effects of phase errors on coherent emitting arrays," Appl. Opt. 33, 2284-2289 (1994).
[CrossRef]

1991

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

1989

J. R. Leger, "Lateral mode control of an AlGaAs laser array in a Talbot cavity," Appl. Phys. Lett. 55, 334-336 (1989).
[CrossRef]

1987

J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
[CrossRef] [PubMed]

1972

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Aggarwal, R. L.

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, 331-333 (2003).
[CrossRef] [PubMed]

Augst, S. J.

S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
[CrossRef] [PubMed]

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, 331-333 (2003).
[CrossRef] [PubMed]

Chang, W.

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

Corcoran, C. J.

C. J. Corcoran, and F. Durville, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118 (2005).

Davidson, N.

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Durville, F.

C. J. Corcoran, and F. Durville, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118 (2005).

Ekhouse, V.

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Fan, T. Y.

S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
[CrossRef] [PubMed]

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, 331-333 (2003).
[CrossRef] [PubMed]

Fischer, D.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Fridman, M.

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

Friesem, A.

A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
[CrossRef]

Friesem, A. A.

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Galvanauskas, A.

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

Gerchberg, R. W.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Glas, P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Goyal, A. K.

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, 331-333 (2003).
[CrossRef] [PubMed]

Ishaaya, A.

A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
[CrossRef]

Ishaaya, A. A.

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Leger, J. R.

J. R. Leger, "Lateral mode control of an AlGaAs laser array in a Talbot cavity," Appl. Phys. Lett. 55, 334-336 (1989).
[CrossRef]

J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
[CrossRef] [PubMed]

Leitner, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Mehuys, D.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

Nabros, C. D.

C. D. Nabros, "Effects of phase errors on coherent emitting arrays," Appl. Opt. 33, 2284-2289 (1994).
[CrossRef]

Napartovich, A. P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Nixon, M.

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

Ronen, E.

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

Rothenberg, J. E.

J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315 (2008).
[CrossRef]

Sanchez, A.

S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
[CrossRef] [PubMed]

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, 331-333 (2003).
[CrossRef] [PubMed]

Saxton, W. O.

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Shimshi, L.

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Streifer, W.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

Swanson, G. J.

J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
[CrossRef] [PubMed]

Veldkamp, W. B.

J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
[CrossRef] [PubMed]

Vysotsky, D. V.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Waarts, R. G.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

Welch, D. F.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

Winful, H. G.

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

Wrage, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Wu, T.

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

Appl. Opt.

J. R. Leger, G. J. Swanson, and W. B. Veldkamp, "Coherent laser addition using binary phase gratings," Appl. Opt. 26, 4391-4399 (1987).
[CrossRef] [PubMed]

C. D. Nabros, "Effects of phase errors on coherent emitting arrays," Appl. Opt. 33, 2284-2289 (1994).
[CrossRef]

Appl. Phys. Lett.

C. J. Corcoran, and F. Durville, "Experimental demonstration of a phase-locked laser array using a self-Fourier cavity," Appl. Phys. Lett. 86, 201118 (2005).

J. R. Leger, "Lateral mode control of an AlGaAs laser array in a Talbot cavity," Appl. Phys. Lett. 55, 334-336 (1989).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Ishaaya, N. Davidson, and A. Friesem, "Passive laser beam combining with intracavity interferometric combiners," IEEE J. Sel. Top. Quantum Electron. 15, 301-311 (2009).
[CrossRef]

Opt. Commun.

L. Shimshi, A. A. Ishaaya, V. Ekhouse, N. Davidson, and A. A. Friesem, "Passive intra-cavity phase locking of laser channels," Opt. Commun. 263, 60-64 (2006).
[CrossRef]

Opt. Express

W. Chang, T. Wu, H. G. Winful, and A. Galvanauskas, "Array size scalability of passively coherently phased fiber laser arrays," Opt. Express 18, 9634-9642 (2010) (all other references are cited here.).
[CrossRef] [PubMed]

Opt. Lett.

M. Fridman, M. Nixon, N. Davidson, and A. A. Friesem, "Passive phase locking of 25 fiber lasers," Opt. Lett. 9, 1434-1436 (2010).
[CrossRef]

S. J. Augst, T. Y. Fan, and A. Sanchez, "Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers," Opt. Lett. 29, 474-476 (2004).
[CrossRef] [PubMed]

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, 331-333 (2003).
[CrossRef] [PubMed]

E. Ronen, M. Fridman, M. Nixon, A. A. Friesem, and N. Davidson, "Phase locking of lasers with intracavity polarization elements," Opt. Lett. 33, 2305-2307 (2008).
[CrossRef] [PubMed]

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, "Modal analysis of linear Talbot-cavity semiconductor lasers," Opt. Lett. 16, 823-825 (1991).
[CrossRef] [PubMed]

M. Wrage, P. Glas, D. Fischer, M. Leitner, D. V. Vysotsky, and A. P. Napartovich, "Phase locking in a multicore fiber laser by means of a Talbot resonator," Opt. Lett. 25, 1436-1438 (2000).
[CrossRef]

Optik (Stuttg.)

R. W. Gerchberg, and W. O. Saxton, "A practical algorithm for the determination of phase from image and diffraction plane pictures," Optik (Stuttg.) 35, 237-246 (1972).

Proc. SPIE

J. E. Rothenberg, "Passive coherent phasing of fiber laser arrays," Proc. SPIE 6873, 687315 (2008).
[CrossRef]

Other

E. du Tremolet de Lacheisserie, D. Gignoux, and M. Schlenker, Magnetism: Fundamentals (Springer, 2005), 2nd ed.

R. K. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1996), 2nd ed.

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Figures (5)

Fig. 1
Fig. 1

Basic configuration for phase locking a fiber laser array via diffractive coupling.

Fig. 2
Fig. 2

(a) Measured near field intensity distribution of an array of seven fiber lasers and (b) their far field intensity distribution. (c) The cross section of the far field intensity distribution of the supermode. Blue curve: measured far field intensity, fringe contrast of 82.3%. Green curve: retrieved far field intensity by Gerschberg Saxton algorithm. Red curve: calculated intensity distribution of the pure in phase supermode. Black curve: calculated (by Gerschberg Saxton algorithm) far field intensity distribution for the anti phase supermode after a π phase mask that changes it into an in phase mode.

Fig. 3
Fig. 3

(a) The spectrum of the individual lasers in the array, their mean spectrum, and the spectrum of the phase-locked array; (b) far field intensity fringe contrast as a function of the number of lasers in the array.

Fig. 4
Fig. 4

Measured far field intensity fringe contrast of two lasers in the phase locked array as a function of the distance between the two lasers. As evident, although all lasers operate with the same central wavelength, the fringe contrast between two distant lasers is deteriorated. Blue dots: measured fringe contrast. Green line: mean. Red line: linear fit.

Fig. 5
Fig. 5

The Strehl ratio as a function of the size of the array for different correlation lengthes. eα, blue curve: eα=0.99; green curve eα=0.9; red curve eα=0.54 (similar to our experimental results); turquoise curve: eα=0.1.

Equations (3)

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S = < | Σ i E i | 2 > E 0 2 N 2 = N + 2 Σ i , j i < cos ( ϕ i ϕ j ) > N 2
f c i , j < | E i + E j | 2 > < | E i E j | 2 > < | E i + E j | 2 > + < | E i E j | 2 > = < cos ( ϕ i ϕ j ) >
S = N + 2 ( Σ i , j i e α ( i j ) ) N 2 = N + 2 e α ( e N α e α ( e α 1 ) 2 N 1 e α 1 ) N 2

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