Abstract

We theoretically investigated the effect of the spatial distribution of the active-ion concentration in multimode step-index waveguides on transverse-mode selection for continuous-wave laser operation. We found that uniform doping of a central portion of as much as 60% of the full waveguide core width is highly effective for the selection of fundamental-mode operation, even under highly saturated, high-power conditions. Profiling the dopant distribution to match that of the particular mode desired was also found to be effective, especially if it is the saturated inversion profile that is matched to the shape of the mode.

© 2002 Optical Society of America

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  1. V. Dominic, S. MacCormack, R. Waarts, S. Sanders, S. Bicknese, R. Dohle, E. Wolak, P. S. Yeh, and E. Zucker, “110W fibre laser,” Electron. Lett. 35, 1158–1160 (1999).
    [CrossRef]
  2. J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilsson, P. W. Turner, W. A. Clarkson, and D. J. Richardson, “High-energy, high-power, ytterbium-doped Q-switched fiber laser,” Opt. Lett. 25, 37–39 (2000).
    [CrossRef]
  3. R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
    [CrossRef]
  4. J. R. Lee, G. J. Friel, H. J. Baker, G. J. Hilton, and D. R. Hall, “A Nd:YAG planar waveguide laser operated at 121 W output with face pumping by diode bars, and its use as a power amplifier,” in Advanced Solid State Lasers, Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper TuC3–1.
  5. E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset core Nd fiber laser,” in Optical Fiber Communication, Vol. 1 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.
  6. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23, 1683–1685 (1998).
    [CrossRef]
  7. C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
    [CrossRef]
  8. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B 5, 1412–1423 (1988).
    [CrossRef]
  9. J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
    [CrossRef]
  10. A. Lucianetti, R. Weber, W. Hodel, H. P. Weber, A. Papashvili, V. A. Konyushkin, and T. T. Basiev, “Beam-quality improvement of a passively Q-switched Nd:YAG laser with a core-doped rod,” Appl. Opt. 38, 1777–1783 (1999).
    [CrossRef]
  11. D. L. Lee, Electromagnetic Principles of Integrated Optics (Wiley, New York, 1986), Chap. 4.

2001

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
[CrossRef]

2000

J. A. Alvarez-Chavez, H. L. Offerhaus, J. Nilsson, P. W. Turner, W. A. Clarkson, and D. J. Richardson, “High-energy, high-power, ytterbium-doped Q-switched fiber laser,” Opt. Lett. 25, 37–39 (2000).
[CrossRef]

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

1999

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

A. Lucianetti, R. Weber, W. Hodel, H. P. Weber, A. Papashvili, V. A. Konyushkin, and T. T. Basiev, “Beam-quality improvement of a passively Q-switched Nd:YAG laser with a core-doped rod,” Appl. Opt. 38, 1777–1783 (1999).
[CrossRef]

1998

1988

Alvarez-Chavez, J. A.

Basiev, T. T.

Beach, R. J.

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
[CrossRef]

Bennett, W. J.

Bhutta, T.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Bicknese, S.

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

Bonner, C. L.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Broderick, N. G.

Caplen, J.

Clarkson, W. A.

Dohle, R.

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

Dominic, V.

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

Dong, L.

Hodel, W.

Konyushkin, V. A.

Krupke, W. F.

Lucianetti, A.

MacCormack, S.

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

Mackenzie, J. I.

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

McMahon, J. M.

Meissner, H. E.

R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
[CrossRef]

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

Meissner, O. R.

Mitchell, S. C.

R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
[CrossRef]

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

Nilsson, J.

Offerhaus, H. L.

Papashvili, A.

Richardson, D. J.

Risk, W. P.

Sammut, R.

Sanders, S.

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

Shepherd, D. P.

R. J. Beach, S. C. Mitchell, H. E. Meissner, O. R. Meissner, W. F. Krupke, J. M. McMahon, W. J. Bennett, and D. P. Shepherd, “Continuous-wave and passively Q-switched cladding-pumped planar waveguide devices,” Opt. Lett. 26, 881–883 (2001).
[CrossRef]

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Tropper, A. C.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

Turner, P. W.

Waarts, R.

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

Weber, H. P.

Weber, R.

Wolak, E.

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

Yeh, P. S.

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

Zucker, E.

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

Appl. Opt.

Electron. Lett.

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

J. I. Mackenzie, S. C. Mitchell, R. J. Beach, H. E. Meissner, and D. P. Shepherd, “15 W diode-side-pumped Tm:YAG waveguide laser at 2 μm,” Electron. Lett. 37, 898–899 (2001).
[CrossRef]

IEEE J. Quantum Electron.

C. L. Bonner, T. Bhutta, D. P. Shepherd, and A. C. Tropper, “Double-clad structures and proximity coupling for diode-bar-pumped planar waveguide lasers,” IEEE J. Quantum Electron. 36, 236–242 (2000).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Other

D. L. Lee, Electromagnetic Principles of Integrated Optics (Wiley, New York, 1986), Chap. 4.

J. R. Lee, G. J. Friel, H. J. Baker, G. J. Hilton, and D. R. Hall, “A Nd:YAG planar waveguide laser operated at 121 W output with face pumping by diode bars, and its use as a power amplifier,” in Advanced Solid State Lasers, Vol. 50 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2001), paper TuC3–1.

E. Snitzer, H. Po, F. Hakimi, R. Tumminelli, and B. C. McCollum, “Double-clad, offset core Nd fiber laser,” in Optical Fiber Communication, Vol. 1 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), paper PD5.

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Figures (8)

Fig. 1
Fig. 1

Energy-level diagram. N03 are the population densities of the Stark levels involved, such that N2=f2NU and N1=f1NL, where NU and NL are the population densities of the upper and the lower laser level manifolds, respectively, and f1,2 are the fractional occupancies.

Fig. 2
Fig. 2

Step-function doping of the central region of the core, and the three lowest-order propagation modes of the highly multimode waveguide.

Fig. 3
Fig. 3

Relative gain for the ten lowest-order modes relative to doping fraction for I/Isat=0, where I is the intracavity lasing intensity and Isat=hv/στ is the saturation intensity.

Fig. 4
Fig. 4

Spatial distribution of the inversion for various levels of saturation by the fundamental mode for doping fractions (a) 1, (b) 0.6, and (c) 0.3.

Fig. 5
Fig. 5

Relative gain for the ten lowest-order modes relative to doping fraction for a heavily saturated gain region.

Fig. 6
Fig. 6

Doping fraction at which high-order-mode oscillation occurs relative to value of I/Isat.

Fig. 7
Fig. 7

Spatial distribution of the inversion for various levels of saturation by the fundamental mode for an original doping profile that is the square of the fundamental-mode profile.

Fig. 8
Fig. 8

Relative gain for the ten lowest-order modes relative to doping fraction when the heavily saturated doping profile is matched to the fundamental-mode profile.

Equations (10)

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dΔN(x, y, z)dt=fRd(x, y, z)-ΔN(x, y, z)+n10d(x, y, z)τ-fcσΔN(x, y, z)nΦϕ(x, y, z)=0,
 d(x, y, z)dV=1.
 ϕ(x, y, z)dV=1.
 ΔN(x, y, z)ϕ(x, y, z)dV=L+T2σl,
ΔN(x, y, z)=τfRd(x, y, z)-n10d(x, y, z)1+cστnfΦϕ(x, y, z).
ΔN(x, y, z)=d(x, y, z)(L+T)2σl[1+Sϕ(x, y, z)]d(x, y, z)ϕ(x, y, z)1+Sϕ(x, y, z) dV,
Gp=2σl  ΔN(x, y, z)ϕp(x, y, z)dV.
Grel=GpL+T=d(x, y, z)ϕp[1+Sϕ(x, y, z)]d(x, y, z)ϕ(x, y, z)1+Sϕ(x, y, z) dV dV.
ϕeven(x, y, z)=2WDLcos2(m+1)πxD,
ϕodd(x, y, z)=2WDLsin2(m+1)πxD,

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