Abstract

In the cavity of a self-mode-locked (Kerr-lens mode-locked) laser, a noncircular beam experiences a nonlinear coupling between beam parameters in the x and y planes. This coupling produces a significant change in beam radii throughout the cavity and may result in more than one TEM00 cavity mode. The dramatic nature of this effect is demonstrated with the Ti:sapphire laser as an example.

© 1993 Optical Society of America

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Corrections

Robert E. Bridges, Robert W. Boyd, and Govind P. Agrawal, "Effect of beam ellipticity on self-mode locking in lasers: erratum," Opt. Lett. 19, 150-150 (1994)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-19-2-150

References

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  1. D. E. Spence, P. N. Kean, W. Sibbett, Opt. Lett. 16, 42 (1991).
    [CrossRef] [PubMed]
  2. W. H. Knox, Opt. Photon. News 3(5), 10 (1992).
    [CrossRef]
  3. L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.
  4. F. Salin, J. Squier, M. Piché, Opt. Lett. 16, 1674 (1991).
    [CrossRef] [PubMed]
  5. D. Huang, M. Ulman, L. H. Acioli, H. A. Haus, J. G. Fujimoto, Opt. Lett. 17, 511 (1992).
    [CrossRef] [PubMed]
  6. V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
    [CrossRef]
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 2.
  8. M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
    [CrossRef]
  9. J. H. Marburger, in Progress in Quantum Electronics, J. H. Saunders, S. Stenholm, eds. (Pergamon, Oxford, 1975), Vol. 4, pp. 35–110.
    [CrossRef]
  10. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 15 and 20.
  11. L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).
    [CrossRef]

1993 (1)

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

1992 (2)

1991 (3)

1974 (1)

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).
[CrossRef]

Acioli, L. H.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 2.

Casperson, L. W.

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).
[CrossRef]

Cerullo, G.

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Couillaud, B.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

De Silvestri, S.

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Fujimoto, J. G.

Goldblatt, N.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Haus, H. A.

Huang, D.

Kean, P. N.

Knox, W. H.

W. H. Knox, Opt. Photon. News 3(5), 10 (1992).
[CrossRef]

Magni, V.

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Marburger, J. H.

J. H. Marburger, in Progress in Quantum Electronics, J. H. Saunders, S. Stenholm, eds. (Pergamon, Oxford, 1975), Vol. 4, pp. 35–110.
[CrossRef]

Negus, D. K.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Piché, M.

Said, A. A.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Salin, F.

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Sibbett, W.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 15 and 20.

Soileau, M. J.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Spence, D. E.

Spinelli, L.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Squier, J.

Ulman, M.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. W. Casperson, IEEE J. Quantum Electron. QE-10, 629 (1974).
[CrossRef]

Opt. Commun. (1)

V. Magni, G. Cerullo, S. De Silvestri, Opt. Commun. 96, 348 (1993).
[CrossRef]

Opt. Eng. (1)

M. Sheik-Bahae, A. A. Said, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, Opt. Eng. 30, 1228 (1991).
[CrossRef]

Opt. Lett. (3)

Opt. Photon. News (1)

W. H. Knox, Opt. Photon. News 3(5), 10 (1992).
[CrossRef]

Other (4)

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989), Chap. 2.

J. H. Marburger, in Progress in Quantum Electronics, J. H. Saunders, S. Stenholm, eds. (Pergamon, Oxford, 1975), Vol. 4, pp. 35–110.
[CrossRef]

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chaps. 15 and 20.

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Figures (3)

Fig. 1
Fig. 1

(a) Asymmetric Z cavity. All distances are in centimeters. OC, output coupler. (b) Beam radii in the sagittal (y) plane as a function of position in the laser cavity by use of the following parameters typical of a Ti:sapphire laser: λ0 = 800 nm, n0 = 1.76, a = 4, n2 = 3 × 10−16 cm2/W. The position z = 0 is at the center of the crystal; positions z < 0 are on the side containing the output coupler (the left side). Three beams are calculated; a low-intensity beam without nonlinearity (CW), a mode-locked beam with nonlinear xy coupling (ML Uncoupled). Because of nonlinear xy coupling, a horizontal slit placed at the right edge of the cavity would encourage mode locking by causing more loss for the cw beam than for the mode-locked beam.

Fig. 2
Fig. 2

(a) Symmetric Z cavity. (b) Beam radii in the tangential (x) plane as a function of position in the laser cavity by use of the same parameters as in Fig. 1. Because of nonlinear xy coupling, a vertical slit or the edge of a prism placed anywhere in the cavity would encourage mode locking.

Fig. 3
Fig. 3

Beam radii versus cavity position for two asymmetric TEM00 modes. Tangential and sagittal radii for modes 1 and 2 are indicated by Tang. 1, Sag. 1, Tang. 2, and Sag. 2. Calculations are based on the cavity shown in Fig. 2.

Equations (4)

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Δ n = n 2 I = n 2 2 P π w x w y exp ( 2 x 2 w x 2 2 y 2 w x 2 ) n 2 2 P π w x w y ( b 2 x 2 a x w x 2 2 y 2 a y w y 2 ) ,
P crit = a P 1 = a λ 0 2 8 π n 0 n 2 .
M i = 1 γ i [ 1 d / n 0 n 0 γ i d ( 1 γ i ) 1 ] , i = x , y ,
γ x = [ r ( z ) P / P crit ] [ 1 + ( n 0 π w 1 x 2 / d λ 0 ) 2 ( 1 + d / R 1 x ) 2 ] 1 , γ y = [ P / r ( z ) P crit ] [ 1 + ( n 0 π w 1 y 2 / d λ 0 ) 2 ( 1 + d / R 1 y ) 2 ] 1 , r ( z ) = w x ( z ) w y ( z ) .

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