Abstract

We present an analysis of the transverse supermode competition mechanism in multicore fiber lasers based on rate equations extended to fibers with multiple cores. The model is used to analyze 7-core and 19-core fiber lasers with three commonly used feedback mechanisms as boundary conditions: butt-contact mirror or fiber Bragg grating, Talbot cavity, and collimating lens plus mirror. For the two last-named cases, different feedback (reflection) factors for different modes result from the diffraction effect. The diffraction effect favors the in-phase supermode. Because of mode mixing, a pure in-phase supermode is not obtained. However, for the 7-core fiber laser the in-phase mode can dominate the output.

© 2005 Optical Society of America

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References

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  1. Y. Huo and P. K. Cheo, “Thermo-mechanical properties of high power and high energy Yb-doped fiber lasers,” IEEE Photonics Technol. Lett.  16, 759–761 (2004).
    [CrossRef]
  2. 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]
  3. M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
    [CrossRef]
  4. P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett.  13, 439–441 (2001).
    [CrossRef]
  5. Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier,” Opt. Express  12, 6230–6239 (2004).
    [CrossRef] [PubMed]
  6. A. Mafi and J. V. Molony, “Phase locking in a passive multicore photonic crystal fiber,” J. Opt. Soc. Am. B  21, 897–902 (2004).
    [CrossRef]
  7. E. K. Bochov, P. K. Cheo, and G. G. King, “Self-organization in a multicore fiber laser array,” Opt. Lett.  28, 1200–1202 (2003).
    [CrossRef]
  8. F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, 2000).
  9. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
    [CrossRef]
  10. C. J. Corcoran and K. A. Pasch, “Self-Fourier function and coherent laser combination,” J. Phys. A  37, L461–L469 (2004).
    [CrossRef]

2004 (4)

Y. Huo and P. K. Cheo, “Thermo-mechanical properties of high power and high energy Yb-doped fiber lasers,” IEEE Photonics Technol. Lett.  16, 759–761 (2004).
[CrossRef]

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier,” Opt. Express  12, 6230–6239 (2004).
[CrossRef] [PubMed]

A. Mafi and J. V. Molony, “Phase locking in a passive multicore photonic crystal fiber,” J. Opt. Soc. Am. B  21, 897–902 (2004).
[CrossRef]

C. J. Corcoran and K. A. Pasch, “Self-Fourier function and coherent laser combination,” J. Phys. A  37, L461–L469 (2004).
[CrossRef]

2003 (1)

2002 (1)

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

2001 (1)

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett.  13, 439–441 (2001).
[CrossRef]

2000 (1)

Bochov, E. K.

Cheo, P. K.

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier,” Opt. Express  12, 6230–6239 (2004).
[CrossRef] [PubMed]

Y. Huo and P. K. Cheo, “Thermo-mechanical properties of high power and high energy Yb-doped fiber lasers,” IEEE Photonics Technol. Lett.  16, 759–761 (2004).
[CrossRef]

E. K. Bochov, P. K. Cheo, and G. G. King, “Self-organization in a multicore fiber laser array,” Opt. Lett.  28, 1200–1202 (2003).
[CrossRef]

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett.  13, 439–441 (2001).
[CrossRef]

Corcoran, C. J.

C. J. Corcoran and K. A. Pasch, “Self-Fourier function and coherent laser combination,” J. Phys. A  37, L461–L469 (2004).
[CrossRef]

Elkin, N. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

Fischer, D.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

Glas, P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

Huo, Y.

Y. Huo and P. K. Cheo, “Thermo-mechanical properties of high power and high energy Yb-doped fiber lasers,” IEEE Photonics Technol. Lett.  16, 759–761 (2004).
[CrossRef]

Y. Huo, P. K. Cheo, and G. G. King, “Fundamental mode operation of a 19-core phase-locked Yb-doped fiber amplifier,” Opt. Express  12, 6230–6239 (2004).
[CrossRef] [PubMed]

King, G. G.

Leitner, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

Liu, A.

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett.  13, 439–441 (2001).
[CrossRef]

Mafi, A.

Molony, J. V.

Napartovich, A. P.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

Pasch, K. A.

C. J. Corcoran and K. A. Pasch, “Self-Fourier function and coherent laser combination,” J. Phys. A  37, L461–L469 (2004).
[CrossRef]

Patel, F.

F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, 2000).

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

Troshchieva, V. N.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

Vysotsky, D. V.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

Wrage, M.

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

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]

IEEE Photonics Technol. Lett. (2)

Y. Huo and P. K. Cheo, “Thermo-mechanical properties of high power and high energy Yb-doped fiber lasers,” IEEE Photonics Technol. Lett.  16, 759–761 (2004).
[CrossRef]

P. K. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photonics Technol. Lett.  13, 439–441 (2001).
[CrossRef]

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

J. Phys. A (1)

C. J. Corcoran and K. A. Pasch, “Self-Fourier function and coherent laser combination,” J. Phys. A  37, L461–L469 (2004).
[CrossRef]

Opt. Commun. (1)

M. Wrage, P. Glas, D. Fischer, M. Leitner, N. N. Elkin, D. V. Vysotsky, A. P. Napartovich, and V. N. Troshchieva, “Phase locking in a multicore fiber laser by wave propagation through an annular waveguide,” Opt. Commun.  205, 367–375 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Other (2)

F. Patel, “Solid-state rare-earth doped media for applications in waveguide lasers,” Ph.D. dissertation (University of California, Davis, 2000).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Laser setup, showing three possible feedback mechanisms, (A)–(C); (b) configurations of cores in a 7-core and a 19-core fiber laser.

Fig. 2
Fig. 2

Some supermodes of the 7-core fiber. The mode numbers are (a) 1, (b) 2, (c) 5, (d) 6, and (e) 7 (in-phase mode).

Fig. 3
Fig. 3

Some supermodes of the 19-core fiber. The mode numbers are (a) 1, (b) 7, (c) 14, (d) 17, (e) 18, and (f) 19 (in-phase mode).

Fig. 4
Fig. 4

Amplitude coupling coefficients for the Talbot cavity: self-coupling factors of (a) 7 and (c) 19-cores, and coupling factors from the in-phase mode to all modes of (b) 7 and (d) 19-cores.

Fig. 5
Fig. 5

Output total power for (a) a 7-core and (b) a 19-core fiber for the Talbot cavity.

Fig. 6
Fig. 6

Amplitude coupling coefficients for the collimating lens plus mirror: self-coupling factors of (a) 7 and (c) 19-cores, and coupling factors from the in-phase mode to all modes of (b) 7 and (d) 19-cores.

Fig. 7
Fig. 7

Output total power for (a) a 7-core and (b) a 19-core fiber for the collimating lens ( f = 30 mm ) and mirror feedback.

Equations (7)

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{ Γ p σ ap [ P p + ( z ) + P p ( z ) ] A co h ν p + i Γ i j σ as [ P si + ( z ) + P si ( z ) ] A co h ν s } N 1 j ( z ) { Γ p σ ep [ P p + ( z ) + P p ( z ) ] A co h ν p + i Γ i j σ es [ P si + ( z ) + P si ( z ) ] A co h ν s + 1 τ } N 2 j ( z ) = 0 ,
± d P si ± ( z ) d z = j Γ i j [ σ es N 2 j ( z ) σ as N 1 j ( z ) ] P si ± α si P si ± ( z ) ,
± d P p ± ( z ) d z = j Γ p [ σ ep N 2 j ( z ) σ ap N 1 j ( z ) ] P p ± α p P p ± ( z ) ,
P si + ( 0 ) = 0.04 P si ( 0 ) .
P si ( L ) = j R i j P s j + ( L ) ,
P out = i 0.96 P si ( 0 ) .
η i j ( Z ) = A i * ( x , y , 0 ) A j ( x , y , Z ) ,

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