Abstract

Hermite-Gaussian modes in geometrically unconfined resonators with a four-level system saturable gain guide inside are experimentally observed and proved. The gain guide was formed with a polished cylindrical surface low-concentration Nd:YAG rod exposed to isotropic pump radiation. The connection of the mode scaling factor with the system parameters is compared with the theory. The abilities of the recently established gain-saturation guiding mechanism to support the generation of beams with wide tops and rapidly decreasing intensity in the wings are also experimentally proved. Application areas for saturable gain guiding are briefly discussed.

© 2002 Optical Society of America

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References

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  1. F. Salin, J. Squier, “Gain guiding in solid-state lasers,” Opt. Lett. 17, 1352–1354 (1992).
    [CrossRef] [PubMed]
  2. N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
    [CrossRef]
  3. P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
    [CrossRef] [PubMed]
  4. Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 790–795 (1996).
    [CrossRef]
  5. C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
    [CrossRef]
  6. O. Denchev, S. Kurtev, P. Petrov, “Modes of unstable resonators with a saturable gain guide,” Appl. Opt. 40, 921–929 (2001).
    [CrossRef]
  7. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 777–814.
  8. A. E. Siegman, “Hermite-Gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973).
    [CrossRef]
  9. W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), pp. 363–366.
  10. Ref. 7, pp. 695–697.
  11. R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World, January1993), pp. 123–130.
  12. J. M. Eggleston, G. Giuliani, R. L. Byer, “Radial intensity filters using radial birefringent elements,” J. Opt. Soc. Am. 71, 1264–1271 (1981).
    [CrossRef]
  13. Ref. 7, pp. 728–734.
  14. D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.
  15. J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
    [CrossRef]

2001 (1)

1999 (1)

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

1998 (1)

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

1996 (1)

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 790–795 (1996).
[CrossRef]

1993 (1)

P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
[CrossRef] [PubMed]

1992 (1)

1983 (1)

N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
[CrossRef]

1981 (1)

1973 (1)

Battle, P. R.

P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
[CrossRef] [PubMed]

Byer, R. L.

Carlsten, J. L.

P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
[CrossRef] [PubMed]

Denchev, O.

Eggleston, J. M.

Ernst, G.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Giuliani, G.

Golla, D.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Jones, R. D.

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World, January1993), pp. 123–130.

Knoke, S.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Koechner, W.

W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), pp. 363–366.

Kurtev, S.

Lin, A. P.

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

Newstein, M.

N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
[CrossRef]

Perry, N.

N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
[CrossRef]

Petrov, P.

Rabinowitz, P.

N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
[CrossRef]

Salin, F.

Schone, W.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Scott, T. R.

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World, January1993), pp. 123–130.

Serral, C.

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

Shen, D. Y.

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

Siegman, A. E.

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 790–795 (1996).
[CrossRef]

A. E. Siegman, “Hermite-Gaussian functions of complex argument as optical-beam eigenfunctions,” J. Opt. Soc. Am. 63, 1093–1094 (1973).
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 777–814.

Song, J.

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

Squier, J.

Sun, Y.

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 790–795 (1996).
[CrossRef]

Tunnermann, A.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Ueda, K.

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

van Druten, N. J.

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

van Exter, M. P.

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

Welling, H.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

Wessel, J. G.

P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
[CrossRef] [PubMed]

Woerdman, J. P.

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

J. Song, A. P. Lin, D. Y. Shen, K. Ueda, “High optical-to-optical efficiency of LD pumped CW Nd:YAG laser under pumping distribution control,” Appl. Phys. B 66, 539–542 (1998).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. Sun, A. E. Siegman, “Optical mode properties of laterally offset gain and index guiding structures,” IEEE J. Quantum Electron. 32, 790–795 (1996).
[CrossRef]

C. Serral, M. P. van Exter, N. J. van Druten, J. P. Woerdman, “Transverse mode formation in microlasers by combined gain- and index-guiding,” IEEE J. Quantum Electron. 35, 1314–1321 (1999).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (1)

Phys. Rev. A (2)

N. Perry, P. Rabinowitz, M. Newstein, “Wave propagation in media with focused gain,” Phys. Rev. A 27, 1989–2002 (1983).
[CrossRef]

P. R. Battle, J. G. Wessel, J. L. Carlsten, “Gain-guiding effects in an amplifier with focused gain,” Phys. Rev. A 48, 707–716 (1993).
[CrossRef] [PubMed]

Other (6)

W. Koechner, Solid-State Laser Engineering, 3rd ed. (Springer-Verlag, Berlin, 1992), pp. 363–366.

Ref. 7, pp. 695–697.

R. D. Jones, T. R. Scott, “Laser-beam analysis pinpoints critical parameters,” Laser Focus World, January1993), pp. 123–130.

Ref. 7, pp. 728–734.

D. Golla, S. Knoke, W. Schone, G. Ernst, A. Tunnermann, H. Welling, “Design and operation of a 250 W CW, diode laser side-pumped Nd:YAG rod laser,” in Advanced Solid-State Lasers, B. H. T. Chai, S. A. Payne, eds., Vol. 24 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1995), pp. 207–209.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), pp. 777–814.

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Figures (11)

Fig. 1
Fig. 1

Gaussian beam gain profile saturation for g 0 = 1 cm-1, α0 = 1 cm-1, and ω g b = 3. Curves 1, S = 0.01; 2, S = 0.4; S = 1.6; S = 5.

Fig. 2
Fig. 2

Twyman-Green interferograms of the polished surface rod at (a) zero idle difference adjustment of the interferometer, (b) strips of equal slope parallel to the parallel astigmatism direction; (c) strips parallel to the perpendicular astigmatic direction.

Fig. 3
Fig. 3

Rod cross-sectional fluorescence intensity distribution at λ = 1.06 µm: (a) polished cylindrical surface rod and (b) ground surface rod.

Fig. 4
Fig. 4

Illustration of the multimode beam generation at focused gain distribution. (L - lnR) represents the total loss in the resonator; R is the output reflectance; L is the miscellaneous loss factor; and G is the single-pass amplification.

Fig. 5
Fig. 5

Experimentally determined radial distribution of the gain coefficient for the rods used in the experiments.

Fig. 6
Fig. 6

Model of the resonator with a quadratic phase duct inside: h 1, h 2, the distances from the main optical planes; H 1, H 2, distances from the duct ends; f, the focal length of the equivalent thin lens in the resonator.

Fig. 7
Fig. 7

Near-field and far-field intensity patterns observed in single-pulse operation at the conditions of the (a) first, (b) second, and (c) third experiments. M b 2 are the experimentally determined beam propagation factors.

Fig. 8
Fig. 8

Beam propagation constant M b 2 (curve 1), output energy (curve 2), and the output brightness (curve 3) dependence on the pump repetition rate in the conditions of the first experimental case (pulse duration τ p = 1.5 ms).

Fig. 9
Fig. 9

(a), (c), (e) Experimentally observed mode patterns when the resonator magnification is slightly reduced by a positive thermal lens in the conditions of experiment 1. (b), (d), (f) The gray scale visualized calculations of the complex argument mode’s TEM01, TEM02, and TEM03 intensity patterns. For the calculations we used the model in Fig. 6 assuming a spherical thermal lens of focal length f T = 12 m and a cylindrical lens with f = 24 m. Related quantities are M = 1.29, M = 1.08, G(0) = 2.7, ω b = 1.24 mm, ω b = 0.68 mm, R = 5.5 m, R = 6.3 m (the last two quantities represent the wave-front radii).

Fig. 10
Fig. 10

Experimental plane-plane resonator.

Fig. 11
Fig. 11

Saturation-guiding mode intensity patterns: (a) γ = 0.86 and (b) γ = 0.56. A definition of the two modes sizes is included in (b). The mode size dependence on gain saturation is given in (c).

Tables (1)

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Table 1 Gain-Saturation-Guiding Experimental Conditions and Results

Equations (10)

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gSr, z=g0zexp-2r2/ωg2z1+Szexp-2r2/ωb2z,
gSr, z=g0z1+Sz1-2r21ωg2z-S1+S1ωb2z,
ωb2=S1+S+ln Mln G0 ωg2,
ωb2>S1+S ωg2,
γ0=1M21+W; γ1=1M41+W/21+W2,
G20Rγm=1,
NrA/ωb2,
ωm,nN ωbrA.
gr=0.12 exp-2|r|ωg3+0.05 cm-1, ωg=2.8 mm.
dI0dI1=ωb2+ωg2ωg21.2,

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