Abstract

The azimuthally symmetric diffractive transverse eigenmodes in an unstable optical resonator with a super-Gaussian reflectivity output mirror are computed in the low-Fresnel-number region to quantify the limits of validity of the geometrical-optics solution. It is found that for low cavity magnifications (M ≤ 2) and with mirrors of super-Gaussian orders n ≤ 8, the diffractive eigenvalues deviate significantly from the geometrical-optics value for equivalent Fresnel numbers Neq < 1 and are nearly equal to it for Neq > 2. These new results indicate that for the geometrical-optics approximation to be valid, resonators with M ≤ 2 and n ≤ 8 should be designed with Neq ≥ 2. This will ensure that the cavity exhibits good azimuthally symmetric transverse-mode discrimination and a super-Gaussian fundamental mode.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Parent, P. Lavigne, Appl. Opt. 28, 901 (1989).
    [CrossRef] [PubMed]
  2. K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
    [CrossRef]
  3. S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, Opt. Lett. 13, 201 (1988).
    [CrossRef] [PubMed]
  4. A. Parent, P. Lavigne, Opt. Lett. 14, 399 (1989).
    [CrossRef] [PubMed]
  5. S. De Silvestri, V. Magni, O. Svelto, G. Valentini, IEEE J. Quantum Electron. 26, 1500 (1990).
    [CrossRef]
  6. S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, Opt. Lett. 16, 642 (1991).
    [CrossRef] [PubMed]
  7. R. Beach, J. Davin, S. Mitchell, W. Benett, B. Freitas, R. Solarz, P. Avizonis, Opt. Lett. 17, 124 (1992).
    [CrossRef] [PubMed]
  8. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 22 and 23.
  9. A. Parent, M. Morin, P. Lavigne, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CThR4.
  10. M. S. Bowers, Appl. Opt. 31, 1185 (1992).
    [CrossRef] [PubMed]
  11. J.-L. Doumont, P. L. Mussche, A. E. Siegman, IEEE J. Quantum Electron. 25, 1960 (1989).
    [CrossRef]

1992

1991

1990

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, IEEE J. Quantum Electron. 26, 1500 (1990).
[CrossRef]

1989

1988

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, Opt. Lett. 13, 201 (1988).
[CrossRef] [PubMed]

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

Avizonis, P.

Beach, R.

Benett, W.

Bowers, M. S.

Davin, J.

De Silvestri, S.

Doumont, J.-L.

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

Freitas, B.

Laporta, P.

Lavigne, P.

A. Parent, P. Lavigne, Appl. Opt. 28, 901 (1989).
[CrossRef] [PubMed]

A. Parent, P. Lavigne, Opt. Lett. 14, 399 (1989).
[CrossRef] [PubMed]

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

A. Parent, M. Morin, P. Lavigne, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CThR4.

Magni, V.

Majocchi, B.

McCarthy, N.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

Mitchell, S.

Morin, M.

A. Parent, M. Morin, P. Lavigne, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CThR4.

Mussche, P. L.

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

Parent, A.

A. Parent, P. Lavigne, Opt. Lett. 14, 399 (1989).
[CrossRef] [PubMed]

A. Parent, P. Lavigne, Appl. Opt. 28, 901 (1989).
[CrossRef] [PubMed]

A. Parent, M. Morin, P. Lavigne, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CThR4.

Piché, M.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

Siegman, A. E.

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

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 22 and 23.

Snell, K. J.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

Solarz, R.

Svelto, O.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, IEEE J. Quantum Electron. 26, 1500 (1990).
[CrossRef]

S. De Silvestri, P. Laporta, V. Magni, O. Svelto, B. Majocchi, Opt. Lett. 13, 201 (1988).
[CrossRef] [PubMed]

Taccheo, S.

Valentini, G.

S. De Silvestri, V. Magni, S. Taccheo, G. Valentini, Opt. Lett. 16, 642 (1991).
[CrossRef] [PubMed]

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, IEEE J. Quantum Electron. 26, 1500 (1990).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

S. De Silvestri, V. Magni, O. Svelto, G. Valentini, IEEE J. Quantum Electron. 26, 1500 (1990).
[CrossRef]

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

Opt. Commun.

K. J. Snell, N. McCarthy, M. Piché, P. Lavigne, Opt. Commun. 65, 377 (1988).
[CrossRef]

Opt. Lett.

Other

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 22 and 23.

A. Parent, M. Morin, P. Lavigne, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CThR4.

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 (3)

Fig. 1
Fig. 1

Feedback ratio of the lowest-loss fundamental transverse mode as a function of equivalent Fresnel number for a cavity magnification M = 2 and super-Gaussian orders n = 2, 4, 6, and 8 and the hard-edged limit (n = ∞).

Fig. 2
Fig. 2

Eigenvalue magnitude versus equivalent Fresnel number for the l = 0 azimuthally varying eigenmodes with M = 2, super-Gaussian order n = 6, and R0 = 1. A transverse-mode-crossing point occurs at Neq = 1.13.

Fig. 3
Fig. 3

Intracavity intensity distribution incident upon the super-Gaussian output coupler of the first two lowest-loss eigenmodes near the transverse-mode-crossing point at Neq = 1.13, n = 6, and M = 2.

Equations (4)

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

R ( r ) = R 0 exp [ 2 ( r / ω m ) n ] ,
γ l p ν l p ( ξ ) = 2 π i l + 1 N ga R 0 × 0 ξ 0 d ξ 0 exp ( ξ 0 n ) ν l p ( ξ 0 ) J l ( 2 π N ga ξ ξ 0 ) × exp [ i π N ga ( M ξ 0 2 + ξ 2 / M ) ]
N ga = ω m 2 B λ .
N eq = M 2 1 2 M N ga

Metrics