Abstract

A functional relationship between M 2 of a multimode laser and its extraction efficiency from a uniformly pumped cylindrical laser medium is derived from numerical calculations by use of helicoid modes.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. E. Siegman, S. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
    [Crossref]
  2. E. C. Honea, R. J. Beach, S. C. Mitchell, J. A. Skidmore, M. A. Emanuel, S. B. Sutton, S. A. Payne, “High-power dual-rod Yb:YAG laser,” Opt. Lett. 25, 805–807 (2000).
    [Crossref]
  3. A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
    [Crossref]
  4. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
    [Crossref]
  5. J. M. Vaughan, D. V. Willetts, “Temporal and interference fringe analysis of TEM01* laser modes,” J. Opt. Soc. Am. 73, 1018–1021 (1983).
    [Crossref]
  6. R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999).
    [Crossref]

2000 (1)

1999 (1)

R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999).
[Crossref]

1993 (1)

A. E. Siegman, S. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[Crossref]

1992 (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

1991 (1)

A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[Crossref]

1983 (1)

Beach, R. J.

Borghi, R.

R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999).
[Crossref]

Emanuel, M. A.

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Honea, E. C.

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Mitchell, S. C.

Payne, S. A.

Rubinsztein-Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Santarsiero, M.

R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999).
[Crossref]

Siegman, A. E.

A. E. Siegman, S. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[Crossref]

A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[Crossref]

Skidmore, J. A.

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Sutton, S. B.

Townsend, S.

A. E. Siegman, S. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[Crossref]

Vaughan, J. M.

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Willetts, D. V.

IEEE J. Quantum Electron. (3)

A. E. Siegman, S. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[Crossref]

A. E. Siegman, “Defining the effective radius of curvature for a nonideal optical beam,” IEEE J. Quantum Electron. 27, 1146–1148 (1991).
[Crossref]

R. Borghi, M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams,” IEEE J. Quantum Electron. 35, 745–750 (1999).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Top graph: Mode power partition for sample laser. Modes up to m = 37 are capable of operating in isolation, but such high-order modes cannot compete with the cluster of low-loss modes at approximately m = 25. Bottom graph: Total beam profile for a set of helicoid modes.

Fig. 2
Fig. 2

Top graph: Mode power partition for sample laser with g = 0.5. Modes up to m = 121 are capable of operating in isolation. However, only high-order modes around 97, 75, and 59 operate. Bottom graph: Total beam profile for a set of helicoid modes.

Fig. 3
Fig. 3

Calculation results for low-mode content.

Fig. 4
Fig. 4

Calculated results for near-TEM00 mode.

Fig. 5
Fig. 5

Helicoid mode profiles for a sequence of modes that have uniform overlaps. The sequence obeys the rule m = n(3n + 1)/2. These modes tend to appear as the dominant ones in the calculations in Figs. 14.

Fig. 6
Fig. 6

Beam quality versus M 2 for the gain, loss, aperture, resonator length, and output coupling for the laser system in Table 1 obtained when the rod focal power is varied to effect the changes in beam quality. The curve is the best-fit function: y = 317.57{[1 + 0.0514/(2x - 1)]/[1 + 0.351/(sqrt(2x - 1)]}2, R 2 = 0.9917986.

Tables (1)

Tables Icon

Table 1 Input Data and Results of Calculations Shown in Figs. 14

Equations (12)

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

M2=4πσσs
INr= 2πω2exp-2 r2ω2m=0N1m!2 r2ω2m,
Imr= 2πω2m!2 r2ω2m exp-2 r2ω2,
Ir= PmImr.
gnPn=02π 2π 0b Inr×g01+1Ismn PmImr+PnInr rdr =αn,
PM2= P1+s2M2-11+t2M2-11/ 22,
σm2= 12πσ2m!  x2+y22σ2m expx2+y22σ2dyx2dx.
σm2= 1πm!  n=0mmnx22σ2ny22σ2m-n×expx2+y22σ2dy x22σ2dx.
σm2= 2σ2m!n=0mmnΠj=1m-n2j-12m-nΠk=1n+12k-12n+1.
σm2= σ22mn=0mΠj=1m-n2j-1m-n!Πk=1n+12k-1n!,
Ir= PmImr
σ2=x2PmImrdxdyPmImrdxdy=Pm x2ImrdxdyPm=σ2Pmm+1Pm,

Metrics