Abstract

We analyze the mode properties of a laser with a Gaussian gain profile by using the beam propagation method. The resonance properties of the Petermann K factor and the M2 beam quality are shown to be related in the vicinity of degenerate cavity geometries. K is unity for a confocal cavity, even under conditions with strong gain guiding, while M2 is a maximum.

© 2004 Optical Society of America

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  1. W. J. Firth, Opt. Commun. 22, 226 (1977).
    [CrossRef]
  2. W. J. Firth, Opt. Commun. 27, 267 (1978).
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  3. B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
    [CrossRef]
  4. Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).
  5. J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
    [CrossRef]
  6. N. J. van Druten, M. P. van Exter, and J. P. Woerdman, Opt. Lett. 26, 1176 (2001).
    [CrossRef]
  7. K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
    [CrossRef]
  8. A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
    [CrossRef] [PubMed]
  9. A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
    [CrossRef] [PubMed]
  10. M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).
  11. A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
    [CrossRef]
  12. A. E. Siegman, Proc. SPIE 1224, 2 (1990).
    [CrossRef]
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    [CrossRef] [PubMed]
  14. C. F. Maes, “Transverse mode properties of lasers with Gaussian gain,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 2003).
  15. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  16. The standard result for phase,15D-A/2B, results in a flat phase for A=D (i.e., all symmetric resonators) as opposed to Eq. (6) that is consistent with our numerical result for variation of Petermann’s K factor.
  17. A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
    [CrossRef]
  18. J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
    [CrossRef]

2001

J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, Opt. Lett. 26, 1176 (2001).
[CrossRef]

1999

Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).

1997

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

1991

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

1990

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

1989

J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
[CrossRef]

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

1983

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
[CrossRef]

1979

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

1978

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

1977

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

1970

1961

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Degnan, J. J.

Dingjan, J.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Doumont, J. L.

J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
[CrossRef]

Firth, W. J.

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

Fox, A. G.

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Li, T.

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Lindberg, Å. M.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

Maes, C. F.

C. F. Maes, “Transverse mode properties of lasers with Gaussian gain,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 2003).

Mussche, P. L.

J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
[CrossRef]

Newstein, M.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
[CrossRef]

Ozygus, B.

Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).

Perry, B. N.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
[CrossRef]

Petermann, K.

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

Rabinowitz, P.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
[CrossRef]

Ramsay, I. A.

Siegman, A. E.

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
[CrossRef]

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

Thijssen, M. S.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

van Druten, N. J.

van Eijkelenborg, M. A.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

van Exter, M. P.

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, Opt. Lett. 26, 1176 (2001).
[CrossRef]

J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

Weber, H.

Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).

Woerdman, J. P.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, Opt. Lett. 26, 1176 (2001).
[CrossRef]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

Zhang, Q.

Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).

Appl. Opt.

Bell Syst. Tech. J.

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Eur. Phys. J. Appl. Phys.

Q. Zhang, B. Ozygus, and H. Weber, Eur. Phys. J. Appl. Phys. 6, 293 (1999).

IEEE J. Quantum Electron.

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

A. E. Siegman, IEEE J. Quantum Electron. 27, 1146 (1991).
[CrossRef]

J. L. Doumont, P. L. Mussche, and A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
[CrossRef]

Opt. Commun.

J. Dingjan, M. P. van Exter, and J. P. Woerdman, Opt. Commun. 188, 345 (2001).
[CrossRef]

W. J. Firth, Opt. Commun. 22, 226 (1977).
[CrossRef]

W. J. Firth, Opt. Commun. 27, 267 (1978).
[CrossRef]

Opt. Lett.

Phys. Rev. A

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. A 27, 1989 (1983).
[CrossRef]

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 55, 4556 (1997).

Proc. SPIE

A. E. Siegman, Proc. SPIE 1224, 2 (1990).
[CrossRef]

Other

C. F. Maes, “Transverse mode properties of lasers with Gaussian gain,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 2003).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).

The standard result for phase,15D-A/2B, results in a flat phase for A=D (i.e., all symmetric resonators) as opposed to Eq. (6) that is consistent with our numerical result for variation of Petermann’s K factor.

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Figures (2)

Fig. 1
Fig. 1

K (solid curve) and M2 (dashed curve) for various cavity geometries plotted versus degeneracy number N. Results are for pump width wp=0.5w0.

Fig. 2
Fig. 2

Close up of Fig. 1 around N=4.

Equations (8)

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

Ex,y,zz=i2k0n0T2+Gx,y2Ex,y,z,
Gx,y=G0 exp-x2+y2/wp2
K=--E0x,y2dxdy2--E02x,ydxdy2.
Mx2=4πσx0σsx.
L=-l-fn0+cos2πk/Nfn0-ln0/n0.
ϕx=x2D-1/A/2B,
1Rz=-λ2πw2z-xϕx,zx2Ex,z2dx,
K00=1+πw2Rλ2.

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