Abstract

An analysis of passive mode locking with the intracavity self-focusing effect is presented, and the self-starting issue is addressed. The analysis shows that the initial pulse-shortening force of this mechanism is too weak to start the mode locking from mode beating or noise and how it can be greatly enhanced with a dilute dye saturable absorber in the cavity. This analysis also shows how the pulse-width evolution is related to the pulse-shortening force in cw mode-locking lasers.

© 1991 Optical Society of America

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References

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1991 (4)

1990 (4)

1989 (1)

1975 (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

1971 (1)

C. R. Giuliano, J. H. Marburger, Phys. Rev. Lett. 27, 905 (1971).
[CrossRef]

1961 (1)

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

Brabec, T.

Brun, A.

Chung, Y.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Couillaud, B.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Dagli, N.

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

Fan, T. Y.

Fox, A. G.

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

Fujimoto, J. G.

Gabetta, G.

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

Georges, P.

Giuliano, C. R.

C. R. Giuliano, J. H. Marburger, Phys. Rev. Lett. 27, 905 (1971).
[CrossRef]

Goldblatt, N.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Goodberlet, J.

Haus, H. A.

E. P. Ippen, L. Y. Liu, H. A. Haus, Opt. Lett. 15, 183 (1990).
[CrossRef] [PubMed]

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

Huang, D.

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

Ippen, E. P.

E. P. Ippen, L. Y. Liu, H. A. Haus, Opt. Lett. 15, 183 (1990).
[CrossRef] [PubMed]

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

Ishida, Y.

N. Sarukura, Y. Ishida, H. Nakano, Opt. Lett. 16, 153 (1991).
[PubMed]

Y. Ishida, N. Sarukura, H. Nakano, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper JMB2.

Jacobson, J.

Kean, P. N.

Krausz, F.

Le Saux, G.

Li, T.

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

Liu, L. Y.

Marburger, J. H.

C. R. Giuliano, J. H. Marburger, Phys. Rev. Lett. 27, 905 (1971).
[CrossRef]

Nakano, H.

N. Sarukura, Y. Ishida, H. Nakano, Opt. Lett. 16, 153 (1991).
[PubMed]

Y. Ishida, N. Sarukura, H. Nakano, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper JMB2.

Negus, D. K.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Ramaswamy, M.

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

Roger, G.

Salin, F.

Sarukura, N.

N. Sarukura, Y. Ishida, H. Nakano, Opt. Lett. 16, 153 (1991).
[PubMed]

Y. Ishida, N. Sarukura, H. Nakano, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper JMB2.

Schulz, P. A.

Sibbett, W.

Spence, D. E.

Spielmann, Ch.

Spinelli, L.

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

Wang, J.

J. Wang, Opt. Lett. 16, 1104 (1991).
[CrossRef] [PubMed]

J. Goodberlet, J. Wang, J. G. Fujimoto, P. A. Schulz, Opt. Lett. 14, 1125 (1989).
[CrossRef] [PubMed]

J. Wang, “Analysis of passive additive-pulse mode-locking with eigenmode theory,” IEEE J. Quantum Electron. (to be published).

Bell Syst. Tech. J. (1)

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

IEEE J. Quantum Electron. (1)

Y. Chung, N. Dagli, IEEE J. Quantum Electron. 26, 1335 (1990).
[CrossRef]

J. Appl. Phys. (1)

H. A. Haus, J. Appl. Phys. 46, 3049 (1975).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. Lett. (1)

C. R. Giuliano, J. H. Marburger, Phys. Rev. Lett. 27, 905 (1971).
[CrossRef]

Other (4)

L. Spinelli, B. Couillaud, N. Goldblatt, D. K. Negus, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP7.

G. Gabetta, D. Huang, J. Jacobson, M. Ramaswamy, H. A. Haus, E. P. Ippen, J. G. Fujimoto, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper CPDP8.

J. Wang, “Analysis of passive additive-pulse mode-locking with eigenmode theory,” IEEE J. Quantum Electron. (to be published).

Y. Ishida, N. Sarukura, H. Nakano, in Conference on Lasers and Electro-Optics, Vol. 10 of 1991 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1991), paper JMB2.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of a laser utilizing the intracavity self-focusing effect for cw mode locking. Self-focusing occurs at the gain medium. The arm lengths l1 and l2 are 75 and 50 cm, respectively.

Fig. 2
Fig. 2

(a) Solid line, beam radius around the iris shown in Fig. 1 for the cw low-power case; short dashed line, beam radius around the iris for a power of 1.0 × 105 W and d1 = 4.96 cm and d2 = 5.16 cm; long dashed line, beam radius around the iris for a power of 1.0 × 105 W and d1 = 5.16 cm and d2 = 4.96 cm. (b) Diffraction loss as a function of the instantaneous power. The diameter of the iris is chosen to be 1.7 mm.

Equations (13)

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q = A q + B C q + D ,
q = q [ I ( t ) ] .
g ( t ) = g 0 + c I ( t ) ,
Δ l ( t ) = - σ l ω A a - t I ( t ) exp ( - t - t T 1 ) d t ,
Δ l ( t ) = - σ l T 1 ω A a I ( t ) .
I n + 1 ( t ) = I n ( t ) [ g n + σ l ω A a - t I ( t ) × exp ( - t - t T 1 ) d t + c I n ( t ) ] ,
I n ( t ) = E 2 τ n sech 2 ( t τ n ) ,
τ n 2 = 12 π 2 E t 2 I n ( t ) d t .
E = I n + 1 ( t ) d t = E [ g n + c E 3 τ n + f ( τ n ) E σ l ω A a ] ,
f ( τ n ) = τ n T 1 + 4 8 ( τ n T 1 + 2 ) 2 .
τ n + 1 2 = g n τ n 2 + c 1 c E τ n + h ( τ n ) E σ l ω A a τ n 2 ,
c 1 = 3 π 2 - x 2 sech 4 ( x ) d x 0.131 , h ( τ n ) = ( τ n T 1 ) 3 + 8 ( τ n T 1 ) 2 + 28 ( τ n T 1 ) + 64 32 ( τ n T 1 + 2 ) 4 .
2 τ ( n ) d τ ( n ) d n = - ( 1 3 - c 1 ) c E τ n - [ f ( τ n ) - h ( τ n ) ] E σ l ω A a τ n 2 .

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