Abstract

A new scalable fiber laser approach to phase locking of multiple gain cores in an antiguided structure is described and modeled. In essence, the waveguide comprises a periodic sequence of gain-loaded and no-gain segments that has a uniform refractive index (referred to as the ribbon) encapsulated within a reduced-index cladding region. Our calculations reveal that the constant-index profile within the ribbon structure provides optimal mode discrimination; the refractive index must be constant within ±0.001 to ensure single-mode operation for a five-core design. One-dimensional and two-dimensional calculations are pursued to support the design criteria. Slight periodic variation in the refractive index of the ribbon laser leads to the emergence of a photonic bandgap, in analogy to so-called holey fibers. Our constant-index design, together with the periodic gain profile, may be described as a photonic metal.

© 2002 Optical Society of America

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  2. W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
    [CrossRef]
  3. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” in Conference on Lasers and Electro-Optics (CLEO/US) (Optical Society of America, Washington, D.C., 1999), paper CPD11–1.
  4. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
    [CrossRef]
  5. M. Muendal, B. Engstrom, D. Kea, B. Lalierte, R. Minns, R. Robinson, B. Rockney, Y. Zhang, R. Collins, P. Gavrolovic, and A. Rowley, “35-watt cw singlemode ytterbium fiber laser at 1.1 micron,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CPD30–1.
  6. H. Zeller, U. Willamowski, A. Tunnermann, H. Welling, S. Unger, V. Reichel, H.-R. Muller, J. Kirchof, and P. Albers, “High-power cw neodymium-doped fiber laser operating at 9.2 W with high beam quality,” Opt. Lett. 20, 578–560 (1995).
    [CrossRef]
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    [CrossRef]
  8. P. Glas, M. Naumann, A. Schirrmacher, and Th. Pertsch, “A cw diode-pumped single-silica fiber comprising 40 cores used as active elements for a high power fiber laser at 1050 nm,” in Conference on Lasers and Electro-Optics (CLEO/US), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper CtuK 5.
  9. M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
    [CrossRef]
  10. P. L. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
    [CrossRef]
  11. 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]
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  14. E. K. Gorton and R. M. Jenkins, “Theory of 1-N-way phase-locked resonators,” Appl. Opt. 40, 916–920 (2001).
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    [CrossRef]
  20. A. P. Napartovich and D. Botez, “Analytic theory of phase-locked arrays of antiguided diode lasers,” in Physics and Simulation of Optoelectronic Devices, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 600–610 (1997).
    [CrossRef]
  21. E. Yablonovitch, “Inhibited spontaneous emission solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  22. J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
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2001 (2)

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

E. K. Gorton and R. M. Jenkins, “Theory of 1-N-way phase-locked resonators,” Appl. Opt. 40, 916–920 (2001).
[CrossRef]

2000 (3)

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]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

1999 (3)

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

T. M. Monro, D. J. Richardson, N. G. R. Broderick, and P. J. Bennet, “Holey optical fibers: an efficient modal model,” J. Lightwave Technol. 17, 1093–1102 (1999).
[CrossRef]

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

1997 (2)

J. Banerji, A. R. Davies, and R. M. Jenkins, “Comparison of Talbot and 1-to-N-way phase-locked array resonators,” Appl. Opt. 36, 1604–1609 (1997).
[CrossRef] [PubMed]

A. P. Napartovich and D. Botez, “Analytic theory of phase-locked arrays of antiguided diode lasers,” in Physics and Simulation of Optoelectronic Devices, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 600–610 (1997).
[CrossRef]

1996 (1)

A. P. Napartovich and D. Botez, “Analytic theory of the structure of collective modes in antiguided semiconductors,” Quantum Electron. 26, 670–675 (1996).
[CrossRef]

1995 (2)

1994 (1)

D. Botez and A. P. Napartovich, “Phase-locked arrays of antiguides: analytical theory,” IEEE J. Quantum Electron. 30, 975–980 (1994).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

1981 (2)

1980 (1)

Albers, P.

Arriaga, J.

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

Banerji, J.

Barbeito, P. M.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

Barkou, S. E.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

Bennet, P. J.

Bjarklev, A.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

Botez, D.

A. P. Napartovich and D. Botez, “Analytic theory of phase-locked arrays of antiguided diode lasers,” in Physics and Simulation of Optoelectronic Devices, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 600–610 (1997).
[CrossRef]

A. P. Napartovich and D. Botez, “Analytic theory of the structure of collective modes in antiguided semiconductors,” Quantum Electron. 26, 670–675 (1996).
[CrossRef]

D. Botez, A. P. Napartovich, and C. A. Zmudzinski, “Phase-locked arrays of antiguides: analytic theory II,” IEEE J. Quantum Electron. 31, 244–253 (1995).
[CrossRef]

D. Botez and A. P. Napartovich, “Phase-locked arrays of antiguides: analytical theory,” IEEE J. Quantum Electron. 30, 975–980 (1994).
[CrossRef]

Bricknese, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Broderick, N. G. R.

Broeng, J.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

Cheo, P. L.

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

Davies, A. R.

Dohle, R.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Dominic, V.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Elkin, N. N.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Eng, L.

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Feit, M. D.

Fischer, D.

Fleck, J. A.

Fleck Jr., J. A.

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]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Gorton, E. K.

Jenkins, R. M.

King, G. G.

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

Kirchof, J.

Knight, J. C.

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

Leitner, M.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[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. L. Cheo, A. Liu, and G. G. King, “A high-brightness laser beam from a phase-locked multicore Yb-doped fiber laser array,” IEEE Photon. Technol. Lett. 13, 439–441 (2001).
[CrossRef]

MacCormack, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Marshall, W. K.

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Mehuys, D.

Meyhuys, D.

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Mitsunaga, K.

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Monro, T. M.

Muller, H.-R.

Napartovich, A. P.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[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]

A. P. Napartovich and D. Botez, “Analytic theory of phase-locked arrays of antiguided diode lasers,” in Physics and Simulation of Optoelectronic Devices, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 600–610 (1997).
[CrossRef]

A. P. Napartovich and D. Botez, “Analytic theory of the structure of collective modes in antiguided semiconductors,” Quantum Electron. 26, 670–675 (1996).
[CrossRef]

D. Botez, A. P. Napartovich, and C. A. Zmudzinski, “Phase-locked arrays of antiguides: analytic theory II,” IEEE J. Quantum Electron. 31, 244–253 (1995).
[CrossRef]

D. Botez and A. P. Napartovich, “Phase-locked arrays of antiguides: analytical theory,” IEEE J. Quantum Electron. 30, 975–980 (1994).
[CrossRef]

Reeves, W. H.

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

Reichel, V.

Richardson, D. J.

Russell, P. St. J.

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

Sanders, S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Sandrock, T.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Sondergaard, T.

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

Streifer, W.

Sukharev, A. G.

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Tunnermann, A.

Unger, S.

Vysotsky, D. V.

Waarts, R.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Waarts, R. G.

Wadsworth, W. J.

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

Welch, D. F.

Welling, H.

Willamowski, U.

Wolak, E.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

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]

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Yariv, A.

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Yeh, P. S.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Zeller, H.

Zmudzinski, C. A.

D. Botez, A. P. Napartovich, and C. A. Zmudzinski, “Phase-locked arrays of antiguides: analytic theory II,” IEEE J. Quantum Electron. 31, 244–253 (1995).
[CrossRef]

Zucker, E.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

D. Meyhuys, K. Mitsunaga, L. Eng, W. K. Marshall, and A. Yariv, “Supermode control in diffraction-coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1165–1167 (1988).
[CrossRef]

Electron. Lett. (2)

W. J. Wadsworth, J. C. Knight, W. H. Reeves, P. St. J. Russell, and J. Arriaga, “Yb3+-doped photonic crystal fibre laser,” Electron. Lett. 36, 1452–1454 (2000).
[CrossRef]

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

D. Botez and A. P. Napartovich, “Phase-locked arrays of antiguides: analytical theory,” IEEE J. Quantum Electron. 30, 975–980 (1994).
[CrossRef]

D. Botez, A. P. Napartovich, and C. A. Zmudzinski, “Phase-locked arrays of antiguides: analytic theory II,” IEEE J. Quantum Electron. 31, 244–253 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

J. Lightwave Technol. (1)

J. Opt. A (1)

J. Broeng, T. Sondergaard, S. E. Barkou, P. M. Barbeito, and A. Bjarklev, “Waveguidance by the photonic bandgap effect in optical fibres,” J. Opt. A 1, 477–482 (1999).
[CrossRef]

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

Opt. Commun. (1)

M. Wrage, P. Glas, M. Leitner, T. Sandrock, N. N. Elkin, A. P. Napartovich, and A. G. Sukharev, “Experimental and numerical determination of coupling constant in multicore fiber,” Opt. Commun. 175, 97–102 (2000).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

E. Yablonovitch, “Inhibited spontaneous emission solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Proc. SPIE (1)

A. P. Napartovich and D. Botez, “Analytic theory of phase-locked arrays of antiguided diode lasers,” in Physics and Simulation of Optoelectronic Devices, W. W. Chow and M. Osinski, eds., Proc. SPIE 2994, 600–610 (1997).
[CrossRef]

Quantum Electron. (1)

A. P. Napartovich and D. Botez, “Analytic theory of the structure of collective modes in antiguided semiconductors,” Quantum Electron. 26, 670–675 (1996).
[CrossRef]

Other (5)

D. Marcuse, Theory of Dielectric and Optical Waveguides, 2nd ed. (Academic, New York, 1991).

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge U. Press, Cambridge, 1994), Chap. 1.

P. Glas, M. Naumann, A. Schirrmacher, and Th. Pertsch, “A cw diode-pumped single-silica fiber comprising 40 cores used as active elements for a high power fiber laser at 1050 nm,” in Conference on Lasers and Electro-Optics (CLEO/US), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), paper CtuK 5.

M. Muendal, B. Engstrom, D. Kea, B. Lalierte, R. Minns, R. Robinson, B. Rockney, Y. Zhang, R. Collins, P. Gavrolovic, and A. Rowley, “35-watt cw singlemode ytterbium fiber laser at 1.1 micron,” in Conference on Lasers and Electro-Optics, Vol. 11 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), paper CPD30–1.

V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bricknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110 W fibre laser,” in Conference on Lasers and Electro-Optics (CLEO/US) (Optical Society of America, Washington, D.C., 1999), paper CPD11–1.

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Figures (19)

Fig. 1
Fig. 1

Cross-sectional view of a five-core ribbon fiber.

Fig. 2
Fig. 2

(a) Refractive-index profile as a function of transverse position in the one-dimensional approximation to the ribbon waveguide structure shown in Fig. 1. The gain regions coincide with the lower index segments in the waveguide region. (b) Coordinate system used in our analysis for the TE-polarized wave (TE with respect to the refractive index boundaries) as shown. The E-vector is assumed to point in the y direction. Assuming that fused silica is the base optical material, the pump cladding index is 1.45, the gain regions have index 1.4585, and the no-gain regions within the waveguide have index 1.4614. The central segments within the waveguide are each 6 µm wide, and the end segments within the waveguide are 3 µm wide.

Fig. 3
Fig. 3

Electric field calculations for three values of β for the one-dimensional ribbon fiber structure described by the refractive-index profile in Fig. 2. The three profiles represent the fields calculated for the β values described in the text. Also shown is the refractive-index profile.

Fig. 4
Fig. 4

Eigenmode overlap with the gain region plotted versus effective index. Mode #5 (counting from the right) was designed to have a single intensity lobe for each of the gain-loaded segments in the waveguide region.

Fig. 5
Fig. 5

Intensity envelope of the eigenmode for which the ribbon structure was designed (Mode #5 in Fig. 4). The widths of the individual index segments are adjusted such that each gain region (shaded) sees a single intensity lobe. Superimposed is the refractive-index profile of the structure. The gain is located in the lower index regions within the waveguide structure.

Fig. 6
Fig. 6

Eigenmode overlap with the gain region plotted versus effective index. Mode #5 (counting from the right) was designed to have a single intensity lobe for each of the gain-loaded segments in the waveguide region.

Fig. 7
Fig. 7

Intensity envelope of the eigenmode for which the ribbon structure was designed (Mode #5 in Fig. 6). The widths of the individual index segments are adjusted such that each gain region (shaded) sees a single intensity lobe. Superimposed is the refractive-index profile of the structure, which is constant across the waveguide region.

Fig. 8
Fig. 8

Same structure as in Fig. 7 but with the gain-loaded segments’ refractive index increased by 0.001 above that of the no-gain segments. Gain-loaded regions are shaded.

Fig. 9
Fig. 9

Same structure as in Fig. 7 but with the gain-loaded segments’ refractive index decreased by 0.001 below that of the no-gain segments. Gain-loaded regions are shaded.

Fig. 10
Fig. 10

Cross sectional view of the ribbon structure with two transverse dimensions that is analyzed in the text. The dark regions in the upper picture indicate the gain-loaded portions of the waveguide. The refractive index is constant throughout the waveguide region and equals 1.4585. The waveguide region is 6 µm high, the end pieces are 4.5 µm wide, and the central segments are 4 µm wide.

Fig. 11
Fig. 11

Spectral power of modes excited by a Gaussian beam inserted into the structure described in Fig. 10.

Fig. 12
Fig. 12

Comparison of gain overlap and effective mode index for one-dimensional (1-D) and two-dimensional (2-D) calculations.

Fig. 13
Fig. 13

(a) Uncorrected far field of the ribbon structure of Fig. 10. Far-field lines are separated by 132 mrad. (b) Far field after correction with a simple phase plate. Approximately two thirds of the total energy is contained in the central peak.

Fig. 14
Fig. 14

Overlap versus index difference of the two highest overlap modes for one-dimensional (1-D) and two-dimensional (2-D) cases with systematic index variation between the gain and no-gain regions.

Fig. 15
Fig. 15

Gain overlap versus cell width variation of the two highest overlap modes for three values of cell Δn. All data points were calculated with the one-dimensional model.

Fig. 16
Fig. 16

Overlap versus index difference of the two highest overlap modes for one-dimensional structures that have a systematic index variation between the gain and the no-gain regions. Three structures are investigated here that consist of 5 (depicted by squares), 20 (depicted by circles), and 100 (depicted by triangles). For each structure investigated, the gain overlap of the highest overlap and the next-highest overlap mode are plotted against the systematic index variation.

Fig. 17
Fig. 17

Gain discrimination requirements versus number of mode cores taken from the data in Fig. 16. Additionally, data points are included for 10, 50, and 75-gain-core structures. The FWHM spread in index plotted here is defined by the two points at which the gain discrimination between the two highest overlap modes is just halved from its peak value at Δn=0. Straight line, linear least-squares fit to the data points that is constrained to pass through the origin.

Fig. 18
Fig. 18

Effects of random variations in cell refractive index illustrated with a 100-core structure in which gain overlaps of the structure’s eigenmodes are plotted against the various modes’ effective refractive indices. In each case the individual cells that constitute the waveguide have had their refractive indices randomly varied with a uniform spread about the design point. The magnitudes of the uniform random distributions were taken to be Δn=0, Δn=±0.00015, Δn=±0.00037, and Δn=±0.00073, as indicated.

Fig. 19
Fig. 19

Gain overlap for a 100-core ribbon fiber. The overlap of the two highest gain overlap modes from Fig. 18 is plotted as a function of the random error introduced in the individual cell refractive indices. Random errors in refractive indices are uniformly distributed with the indicated amplitudes.

Tables (2)

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Table 1 Details of Design of a One-Dimensional Ribbon Fiber Structure with a Step Index between Gain and No-Gain Segments

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Table 2 Detailed Design of a One-Dimensional Ribbon Fiber Structure with a Constant-Index Waveguide Region

Equations (37)

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2-nc2t2ε(r, t)=0.
ε(r, t)=uˆyE(x)exp[i(ωt-βz)],
d2E(x)dx2=-nωc2-β2E(x),
E(xi-)=E(xi+),
dEdx|x=xi-=dEdx|x=xi+,
E(x)0,x±,
E(x)=expβ2-n1ωc21/2x,
dEdx|x=0-=β2-n1ωc21/2.
Erhs=Elhs cos(αili)+dEdx|lhsαi sin(αili),
dEdx|rhs=-Elhsαi sin(αili)+dEdx|lhs cos(αili),
βniωc,
αi=niωc2-β21/2
Erhs=Elhs cosh(αˆili)+dEdx|lhsαˆ sinh(αˆili),
dEdx|rhs=Elhsαˆi sinh(αˆili)+dEdx|lhs cosh(αˆili),
β>niωc,
αˆi=β2-niωc21/2,
β=8.7167195×(0.99999),fielddivergesto-,
β=8.7167195,fieldconvergesto0,
β=8.7167195×(1.00001),fielddivergesto+.
Γ=|E(x)|2g(x)dx|E(x)|2dx,
β=neffωc.
ε(r, t)=E(x)exp[i(ωt-βz)]exp(ξΓz/2),
ε(r, t)=E(x)expiωt-β+i12ξΓz=E(x)expiωt-neffωcz.
Im(neff)=cξΓ2ω.
lgngωc2-β21/2+lngnngωc2-β21/2=π,
tanledgengωc2-β21/2
=-1+β2-ncladωc21/2nngωc2-β21/2tanlng2nngωc2-β21/2β2-ncladωc21/2ngωc2-β21/2-ngωc2-β21/2nngωc2-β21/2tanlng2nngωc2-β21/2,
2ε(x, y, z)+n(x, y)ωc2ε(x, y, z)=0.
2Ei(x, y)=-n(x, y)ωc2-βi2Ei(x, y),
ε(x, y, z)=E(x, y, z)exp(iKcz),
iEz=-12Kc2E+Kc21-n2(x, y)nc2E=HE,
HEi=βiEi,
βi=(Kc2-2Kcβi)1/2Kc-βi.
P(z)=E*(x, y, 0)E(x, y, z)dxdy.
P(z)=|An|2 exp(iβnz),
P(β)=|An|2δ(β-βn).
En(x, y)=E(x, y, z)exp(iβnz)dz.

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