Abstract

Phase locking of two fiber lasers is obtained by mutual injection. The coherence properties of this composite laser are analyzed. In the most general case, the radiations at the two output mirrors of the laser are not mutually coherent. The cross-correlation of the two emitted beams shows that an extra-cavity delay line is required to get stable and high visibility interference fringes. Such a laser configuration is attractive for coherent beam combining in the far field provided the multiple output beams are properly time delayed.

© 2009 Optical Society of America

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References

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2008 (1)

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

2007 (3)

2005 (1)

J.C. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118–201118-3 (2005).
[Crossref]

2004 (1)

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

2003 (1)

2002 (2)

Barthélémy, A.

Bruesselbach, H.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Chen, Z.

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

Corcoran, J.C.

J.C. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118–201118-3 (2005).
[Crossref]

Desfarges-Berthelemot, A.

Dunning, G. J.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Durville, F.

J.C. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118–201118-3 (2005).
[Crossref]

Even, P.

Feng, Y.

Gavrielides, A.

Hammon, D. L.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Hou, J.

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

Jiang, Z.

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

Jones, D. C.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Kermène, V.

Lefort, L.

Lei, B.

Lhermite, J.

Li, H.

Li, L.

Mangir, M. S.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Minden, M. L.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Moloney, J. V.

Peterson, P.

Peyghambarian, N.

Pureur, D.

Rogers, J. L.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Sabourdy, D.

Saitou, T.

Saleh, B.E.A.

B.E.A. Saleh and M.C. Teich, Fundamental of photonics (Wiley Series in Pure and Applied Optics, 1991).
[Crossref]

Schülzgen, A.

Sekiguchi, T.

Shirakawa, A.

Simpson, T. B.

Solis, A. J.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Teich, M.C.

B.E.A. Saleh and M.C. Teich, Fundamental of photonics (Wiley Series in Pure and Applied Optics, 1991).
[Crossref]

Temyanko, V. L.

Ueda, K.

Vaughan, L.

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Zhou, P.

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

Appl. Phys. Lett. (1)

J.C. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118–201118-3 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

Z. Chen, J. Hou, P. Zhou, and Z. Jiang, “Mutual injection-locking and coherent combining of two individual fiber lasers,” IEEE J. Quantum Electron. 44, 515–519 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (1)

M. L. Minden, H. Bruesselbach, J. L. Rogers, M. S. Mangir, D. C. Jones, G. J. Dunning, D. L. Hammon, A. J. Solis, and L. Vaughan, “Self-organized coherence in fiber laser arrays,” Proc. SPIE 5335, 89–97 (2004).
[Crossref]

Other (1)

B.E.A. Saleh and M.C. Teich, Fundamental of photonics (Wiley Series in Pure and Applied Optics, 1991).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup of the mutual injection laser (FBG, fiber Bragg grating; FC, fiber combiner; UFC, unbalanced fiber coupler; YDF, Ytterbium doped fiber; AC, angle cleave; L1, L2 and LM, lengths of the three sub-cavities; P, plane including the laser outputs) and of the fringe analysis device (extra-cavity delay line, reflective prism and CCD camera).

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Fig. 2.
Fig. 2.

(a) Calculated product of the three resonance frequency combs of the MIL sub-cavities. (b) Measured electrical spectrum with the same sub-cavity lengths (L1=28.8 m, L2=36.56 m, LM=64.94 m).

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Fig. 3.
Fig. 3.

Visibility of the interference fringes between the MIL outputs as function of their relative delay Δz=c.τ, (a) calculated from the impulse response of the MIL, (b) measured from the cross-correlation of the output beams. The red and green stars mark the Δz values for which the fringe pattern of Fig. 4(a) and Fig. 4(b) were respectively recorded.

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Fig. 4.
Fig. 4.

Experimental fringe patterns between MIL outputs recorded for the two Δz values marked on Fig. 3(b): (a) into a mutual coherence area, (b) out of the mutual coherence areas.

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Equations (5)

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

ΔL=LM−(L1+L2)=q.λ⁄2withqanintegernumber
g12(τ)=G12(τ)I0
G12(τ)=∫−∞+∞U1(t)U2*(t+τ)dt
I(τ)=2I0[1+Re{g12(τ)}]
V(τ)=Imax(τ)−Imin(τ)Imax(τ)+Imin(τ)=∣g12(τ)∣

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