Abstract

The stability of the steady-state solutions of a synchronously mode-locked cw laser and the mode-locking threshold condition is investigated. The condition for the existence of a stable solution is presented for the first time to the authors’ knowledge for the synchronously pumped dye-laser system.

© 1987 Optical Society of America

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References

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  1. D. J. Kuizenga, IEEE J. Quantum Electron. QE-17, 1694 (1985).
  2. G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
    [CrossRef]
  3. E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
    [CrossRef]
  4. H. A. Haus, IEEE J. Quantum Electron. QE-11, 736 (1975).
    [CrossRef]
  5. C. P. Ausschnitt, IEEE J. Quantum Electron. QE-13, 321 (1977).
    [CrossRef]
  6. X. Y. Bao, X. Guan, Chin. J. Lasers 13, 193 (1975).

1985

D. J. Kuizenga, IEEE J. Quantum Electron. QE-17, 1694 (1985).

G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
[CrossRef]

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

1977

C. P. Ausschnitt, IEEE J. Quantum Electron. QE-13, 321 (1977).
[CrossRef]

1975

X. Y. Bao, X. Guan, Chin. J. Lasers 13, 193 (1975).

H. A. Haus, IEEE J. Quantum Electron. QE-11, 736 (1975).
[CrossRef]

Albrecht, G. F.

G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
[CrossRef]

Ausschnitt, C. P.

C. P. Ausschnitt, IEEE J. Quantum Electron. QE-13, 321 (1977).
[CrossRef]

Balmer, J. E.

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

Bao, X. Y.

X. Y. Bao, X. Guan, Chin. J. Lasers 13, 193 (1975).

Gruneisen, M. T.

G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
[CrossRef]

Guan, X.

X. Y. Bao, X. Guan, Chin. J. Lasers 13, 193 (1975).

Haus, H. A.

H. A. Haus, IEEE J. Quantum Electron. QE-11, 736 (1975).
[CrossRef]

Kuizenga, D. J.

D. J. Kuizenga, IEEE J. Quantum Electron. QE-17, 1694 (1985).

Roschger, E. W.

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

Schwarzenbach, A. P.

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

Smith, D.

G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
[CrossRef]

Weber, H. P.

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

Chin. J. Lasers

X. Y. Bao, X. Guan, Chin. J. Lasers 13, 193 (1975).

IEEE J. Quantum Electron.

D. J. Kuizenga, IEEE J. Quantum Electron. QE-17, 1694 (1985).

G. F. Albrecht, M. T. Gruneisen, D. Smith, IEEE J. Quantum Electron. QE-21, 1189 (1985).
[CrossRef]

E. W. Roschger, A. P. Schwarzenbach, J. E. Balmer, H. P. Weber, IEEE J. Quantum Electron. QE-21, 465 (1985).
[CrossRef]

H. A. Haus, IEEE J. Quantum Electron. QE-11, 736 (1975).
[CrossRef]

C. P. Ausschnitt, IEEE J. Quantum Electron. QE-13, 321 (1977).
[CrossRef]

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Equations (28)

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[ G ( t ) - L + δ T d d t + 1 ω c 2 d 2 d t 2 ] V ( t ) = 0 ,
d G ( t ) d t = d G s ( t ) d t - I ( t ) G ( t ) ,
V ( t ) = 0 ,             G ( t ) = G s ( t ) = 0             for t 0
V ( t ) = 0             for t 0.
I s ( t ) = I 0 s ( 1 + t 3 6 ω c 2 δ T τ 4 ) 2 exp ( - t 2 / τ 2 ) ,
I 0 s = 2 π G m E p 0 / τ p 2 [ ω c 2 δ T 2 + G m E p 0 ( 1 + t 0 τ p ) ] ,
τ 2 = δ T τ p G m E p 0 π + τ p 5 ω c 2 δ T ( 1 + t 0 τ p ) ,
V ( t ) = U ( t ) exp ( - ω c 2 δ T 2 t ) ,
1 ω c 2 d 2 U d t 2 = - [ G ( t ) - L - ω c 2 δ T 2 4 ] U ( t ) .
G = L + ω c 2 δ T 2 4 .
V ( t ) = ( C 1 + C 2 t ) exp ( - ω c 2 δ T 2 t ) ,
d G d t = d G s d t - I ( t ) G ( t ) ,
G s ( t ) = I ( t ) G ( t ) d t = [ - C 1 2 ω c 2 δ T - 2 C 1 C 2 ω c 2 δ T ( t + 1 ω c 2 δ T ) - C 2 2 ω c 2 δ T × ( t 2 + 2 t ω c 2 δ T + 2 ω c 4 δ T 2 ) ] × ( L + ω c 2 δ T 2 4 ) exp ( - ω c 2 δ T t ) .
G s ( t ) = G m I p ( t ) d t ,
I p ( t ) = E p 0 π τ p exp [ - ( t + t 0 τ p ) 2 ] .
G s ( t ) = G m E p 0 2 [ 1 + erf ( t + t 0 τ p ) ] ,
erf ( t + t 0 τ p ) = 2 π 0 t + t 0 / τ p exp ( - t 2 ) d t = t + t 0 τ p - 1 3 ( t + t 0 ) 3 τ p 3 .
G s ( t ) = G m E p 0 2 ( 1 + t + t 0 τ p - t 3 + 3 t 2 t 0 + 3 t t 0 2 + t 0 3 3 τ p 3 ) .
G s ( t ) = [ ( - C 1 2 ω c 2 δ T - 2 C 1 C 2 ω c 4 δ T 2 - 2 C 2 2 ω c 6 δ T 3 ) + C 1 t + t 2 ( - C 1 2 ω c 2 δ T - C 2 2 ω c 2 δ T ) - C 1 C 2 ω c 2 δ T t 3 ] ( L + ω c 2 δ T 2 4 ) .
G m E p 0 2 ( 1 + t 0 τ p - t 0 3 3 τ p 3 ) = ( L + ω c 2 δ T 2 4 ) ( - C 1 2 ω c 2 δ T - 2 C 1 C 2 ω c 4 δ T 2 - 2 C 2 2 ω c 6 δ T 3 ) ,
C 1 = G m E p 0 2 τ p ( 1 - t 0 2 τ p 2 ) .
I th ( 0 ) = C 1 2 = G m 2 E p 0 2 4 τ p 2 ( 1 - t 0 2 τ p 2 ) 2 .
V ( t ) = V s ( t ) + δ V ( t ) = V s ( t ) + m 0 δ V m exp ( j m 2 π t T R ) ,
m 0 { [ I G ( t ) - L ] + δ T j m 2 π T R - 1 ω c 2 4 π 2 m 2 T cav 2 } × δ V m exp ( j m 2 π t T cav ) = 0.
G ( t ) = L + 1 ω c 2 4 π m 2 T cav 2 ,
G = L + 1 ω c 2 τ 2 .
4 π 2 m 2 T cav 2 = I 0 s / τ p 2 2 ω c 2 δ T 2 + 2 τ p δ T I th 1 - t 0 / τ p 1 τ p 2 ,
I 0 s = 8 τ p δ T I th π 2 1 - t 0 / τ p τ p 2 T cav 2 ω c 2 δ T 2 + 8 π 2 T cav 2 ω c 2 δ T 2 .

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