Abstract

Abstract

A theoretical analysis of the solitary pulse parameters of the Ginzburg-Landau distributed model of a mode-locked laser is presented. For a stable operation, the mode-locked gain (g-l)<0 is optimized relative to the chirp and a stable operation point is found in the normal dispersion regime. When the energy in the pulse is optimized relative to the mode-locking parameter, a stable point is also found in the normal dispersion regime. The two opmimizations yield the same pulse parameters when the chirp is very large which are the characteristics of the similariton regime.

© 2007 Optical Society of America

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References

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  1. H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Top. Quantum Electron. 6,1173-1185 (2000).
    [CrossRef]
  2. O. Prochnow, A. Ruehl, M. Schultz, D. Wandt, and D. Kracht, "All-fiber similariton laser at 1 ?m without dispersion compensation," Opt. Express 15,6889-6893 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6889.
    [CrossRef] [PubMed]
  3. C. K. Nielsen, and S. R. Keiding, "All-fiber mode-locked laser," Opt. Lett. 32,1474-1476 (2007).
    [CrossRef] [PubMed]
  4. C. Antonelli, J. Chen, and F. X. Kärtner, "Intracavity pulse dynamics and stability for passive mode-locked lasers," Opt. Express 15,5919-5924 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5919
    [CrossRef] [PubMed]
  5. P. -A. Bélanger, "On the profile of pulses generated by fiber lasers:the highly-chirped positive dispersion regime (similariton)," Opt. Express 14,12174-12182 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-25-12174.
    [CrossRef] [PubMed]
  6. A. Ruehl, O. Prochnow, D. Wandt, D. Kracht, B. Burgoyne, N. Godbout, and S. Lacroix, "Dynamics of parabolic pulses in a ultrafast fiber laser," Opt. Lett. 31,2734-2736 (2006).
    [CrossRef] [PubMed]
  7. J. W. Lou, M. Currie, and F. K. Fatemi, "Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser," Opt. Express 15,4960-4965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-4960.
    [CrossRef] [PubMed]
  8. A. Chong, J. Buckley, W. Renninger, and F. Wise, "All-normal-dispersion femtosecond fiber laser," Opt. Express 14,10095-10100 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10095.
    [CrossRef]
  9. F. Ilday, F. Wise, and F. Kaertner, "Possibility of self-similar pulse evolution in a Ti:sapphire laser," Opt. Express 12,2731-2738 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-12-2731.
    [CrossRef] [PubMed]
  10. P. A. Bélanger, and C. Paré "Second-order moment analysis of dispersion-managed solitons," IEEE J. Lightwave Technol. 17,445-451 (1999).
    [CrossRef]
  11. B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ö. Ilday, "Generation of parabolic bound pulses from a Yb-fiber laser," Opt. Express 14,6075-6083 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6075.
    [CrossRef] [PubMed]
  12. L. M. Zhao, D. Y. Tang, and C. Lu, "Gain-guided solitons in a positive group-dispersion fiber laser," Opt. Lett. 31,1788-1790 (2006).
    [CrossRef] [PubMed]

2007 (5)

2006 (4)

2004 (1)

2000 (1)

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Top. Quantum Electron. 6,1173-1185 (2000).
[CrossRef]

1999 (1)

P. A. Bélanger, and C. Paré "Second-order moment analysis of dispersion-managed solitons," IEEE J. Lightwave Technol. 17,445-451 (1999).
[CrossRef]

Antonelli, C.

Bélanger, P. A.

P. A. Bélanger, and C. Paré "Second-order moment analysis of dispersion-managed solitons," IEEE J. Lightwave Technol. 17,445-451 (1999).
[CrossRef]

Bélanger, P. -A.

Brunel, M.

Buckley, J.

Burgoyne, B.

Chédot, C.

Chen, J.

Chong, A.

Currie, M.

Fatemi, F. K.

Godbout, N.

Haus, H. A.

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Top. Quantum Electron. 6,1173-1185 (2000).
[CrossRef]

Hideur, A.

Ilday, F.

Ilday, F. Ö.

Kaertner, F.

Kärtner, F. X.

Keiding, S. R.

Kracht, D.

Lacroix, S.

Limpert, J.

Lou, J. W.

Lu, C.

Nielsen, C. K.

Ortaç, B.

Paré, C.

P. A. Bélanger, and C. Paré "Second-order moment analysis of dispersion-managed solitons," IEEE J. Lightwave Technol. 17,445-451 (1999).
[CrossRef]

Prochnow, O.

Renninger, W.

Ruehl, A.

Schultz, M.

Tang, D. Y.

Tünnermann, A.

Wandt, D.

Wise, F.

Zhao, L. M.

IEEE J. Lightwave Technol. (1)

P. A. Bélanger, and C. Paré "Second-order moment analysis of dispersion-managed solitons," IEEE J. Lightwave Technol. 17,445-451 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. A. Haus, "Mode-locking of lasers," IEEE J. Sel. Top. Quantum Electron. 6,1173-1185 (2000).
[CrossRef]

Opt. Express (7)

O. Prochnow, A. Ruehl, M. Schultz, D. Wandt, and D. Kracht, "All-fiber similariton laser at 1 ?m without dispersion compensation," Opt. Express 15,6889-6893 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-11-6889.
[CrossRef] [PubMed]

F. Ilday, F. Wise, and F. Kaertner, "Possibility of self-similar pulse evolution in a Ti:sapphire laser," Opt. Express 12,2731-2738 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-12-2731.
[CrossRef] [PubMed]

B. Ortaç, A. Hideur, M. Brunel, C. Chédot, J. Limpert, A. Tünnermann, and F. Ö. Ilday, "Generation of parabolic bound pulses from a Yb-fiber laser," Opt. Express 14,6075-6083 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-13-6075.
[CrossRef] [PubMed]

A. Chong, J. Buckley, W. Renninger, and F. Wise, "All-normal-dispersion femtosecond fiber laser," Opt. Express 14,10095-10100 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-10095.
[CrossRef]

P. -A. Bélanger, "On the profile of pulses generated by fiber lasers:the highly-chirped positive dispersion regime (similariton)," Opt. Express 14,12174-12182 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-25-12174.
[CrossRef] [PubMed]

J. W. Lou, M. Currie, and F. K. Fatemi, "Experimental measurements of solitary pulse characteristics from an all-normal-dispersion Yb-doped fiber laser," Opt. Express 15,4960-4965 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-8-4960.
[CrossRef] [PubMed]

C. Antonelli, J. Chen, and F. X. Kärtner, "Intracavity pulse dynamics and stability for passive mode-locked lasers," Opt. Express 15,5919-5924 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-10-5919
[CrossRef] [PubMed]

Opt. Lett. (3)

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Equations (44)

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i V x + ( β ̅ i ε ) 2 V τ τ i ( g l ) V γ 0 ( 1 + i ε 0 ) V 2 V = 0
V ( τ , x ) = V 0 sech ( α τ ) exp { i [ β ln ( sech ( α τ ) ) + Γ x ] }
Γ = β α 2 [ ε + β ̅ 2 β ( β 2 1 ) ]
2 γ 0 V 0 2 = α 2 [ ( β 2 2 ) β ̅ + 3 β ε ]
γ 0 P 0 = 2 γ 0 V 0 2 α
( g 1 ) = β α 2 [ β ̅ ε 2 β ( β 2 1 ) ]
ε 0 = [ 3 β β ̅ ( β 2 2 ) ε ] [ ( β 2 2 ) β ̅ + 3 β ε ]
β = β ̅ ε
g l = α 2 ε 2 ( β 2 + 1 )
ε 0 = 2 β
Γ = α 2 β ̅ 2 ( β 2 + 1 )
γ 0 V 0 2 = Γ
γ 0 P 0 = α β ̅ ( β 2 + 1 )
ε = 2 ω g 2 = 1 2 π 2 v g 2 0.05 v g 2
β = 20 β ̅ v g 2
τ 0 v f = 0.3572 sinh 1 [ cosh ( π 2 β ) ]
( g l ) = 0.25 ( v f v g ) 2
τ 0 = 0.5611 β v f
Γ = π 2 2 β ̅ v f 2
γ 0 P 0 = 2 Γ α = 1.1346 Γ τ 0
e 2 l = T = 1 R
R e 2 g = 1
( v f v g ) 2 = 2 ln ( R ( 1 R ) )
( τ 0 ) max = 2 τ 0 ( 1 + R )
( τ 0 ) min = R ( τ 0 ) max
V ̂ NPE = V ̂ i exp ( ε 0 γ 0 V 0 2 ω 2 α 2 β 2 ) for β > > 1
V ̂ NPE = V ̂ i exp ( ε 0 β ̅ ω 2 2 )
V ̂ NPE + FILTER = V ̂ i exp [ ω 2 ( ε 0 β ̅ 2 + 1.3863 ω 0 F 2 ) ]
ε 0 ε 0 + 0.07 β v 0 F 2
β ̅ β = 0.05 v g 2 + 0.0351 v 0 F 2
P out = ( 1 R ) R P 0
V ( τ , x ) = V 0 { sech [ α ( τ + b x ) ] } 1 i β exp [ i ( a τ Γ x ) ]
β ̅ = ε β + 5 3 β 3 a
β 3 a = 3 ε β a 2 α 2
β ̅ = ε β [ 1 20 ( Δ v v F ) 2 ]
( g l ) op = ε 2 π 2 v F 2 [ 1 20 ( Δ v v F ) 2 ]
( γ 0 P 0 ) 2 = 2 ( g l ) ε ( β 2 + 1 ) ( β 2 + 4 ) 2 [ ε 0 ( β 2 2 ) 3 β ] [ ε 0 ( β 2 + 2 ) β ]
ε 0 = 2 β ( β 2 + 1 ) ( β 4 4 )
β ̅ = ε ( β 4 + 2 ) β ( β 2 2 )
ε 0 = 2 β
C = β 2 σ 2
C = 3.3665 v F τ 0
D = C σ 2 σ 2 ̂
D = 0.271 τ 0 v f

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