Abstract

We made pulse-resolved observations of subharmonic oscillations in the pulse train of a Kerr-lens mode-locked Ti:sapphire laser. Pulse-resolved beam profiles demonstrate that these oscillations, which include period doubling as well as P3, P4, and quasi periodicity, are accompanied by spatial modulation of the beam. A pulse-resolved autocorrelation technique believed to be novel is used to show that temporal pulse reshaping does not accompany these dynamics. The power dependence of subharmonic oscillation frequencies exhibits the frequency locking characteristic of nonlinear dynamics in systems of coupled oscillators.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Asaki, C. P. Huang, D. Garvey, J. Zhou, H. Kapteyn, and M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti:sapphire Laser,” Opt. Lett. 18, 977–979 (1993).
    [CrossRef] [PubMed]
  2. C. Wang, W. Zang, and K. M. Yoo, “Pulse shortening and spectral broadening by periodic pulse-train amplitude modulation in a self-mode-locked Ti:sapphire laser,” J. Opt. Soc. Am. B 14, 1881–1884 (1997).
    [CrossRef]
  3. D. Cote and H. M. van Driel, “Period doubling of a femtosecond Ti:sapphire laser by total mode locking,” Opt. Lett. 23, 715–717 (1998).
    [CrossRef]
  4. S. Bolton, G. Sucha, R. Jenks, and C. Elkinton, “Spatio-temporal nonlinear dynamics in a mode-locked Ti:sapphire laser,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 158–159.
  5. D. H. Auston, “Transverse mode locking,” IEEE J. Quantum Electron. QE-4, 420–422 (1968).
    [CrossRef]
  6. P. L. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342–1357 (1970).
    [CrossRef]
  7. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 574.
  8. D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
    [CrossRef]
  9. M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
    [CrossRef]

1998

1997

1993

1992

D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

1984

M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
[CrossRef]

1970

P. L. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342–1357 (1970).
[CrossRef]

1968

D. H. Auston, “Transverse mode locking,” IEEE J. Quantum Electron. QE-4, 420–422 (1968).
[CrossRef]

Asaki, M.

Auston, D. H.

D. H. Auston, “Transverse mode locking,” IEEE J. Quantum Electron. QE-4, 420–422 (1968).
[CrossRef]

Bak, P.

M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
[CrossRef]

Bohr, T.

M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
[CrossRef]

Cote, D.

Garvey, D.

Georgiev, D.

D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Herrman, J.

D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Huang, C. P.

Jensen, M. H.

M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
[CrossRef]

Kapteyn, H.

Murnane, M.

Smith, P. L.

P. L. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342–1357 (1970).
[CrossRef]

Stam, U.

D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

van Driel, H. M.

Wang, C.

Yoo, K. M.

Zang, W.

Zhou, J.

IEEE J. Quantum Electron.

D. H. Auston, “Transverse mode locking,” IEEE J. Quantum Electron. QE-4, 420–422 (1968).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

D. Georgiev, J. Herrman, and U. Stam, “Cavity design for optimum nonlinear absorption in Kerr-lens mode-locked solid-state lasers,” Opt. Commun. 92, 368–375 (1992).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. H. Jensen, P. Bak, and T. Bohr, “Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps,” Phys. Rev. A 30, 1960 (1984).
[CrossRef]

Proc. IEEE

P. L. Smith, “Mode-locking of lasers,” Proc. IEEE 58, 1342–1357 (1970).
[CrossRef]

Other

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 574.

S. Bolton, G. Sucha, R. Jenks, and C. Elkinton, “Spatio-temporal nonlinear dynamics in a mode-locked Ti:sapphire laser,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 158–159.

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 (11)

Fig. 1
Fig. 1

Cavity schematic.

Fig. 2
Fig. 2

Time-averaged spatial profile of the pulsed beam, measured approximately 1 m from the output. Full horizontal scale is 1.0 cm; full vertical scale is 0.8 cm.

Fig. 3
Fig. 3

Pulse train measured on a 1-ns Si photodiode placed approximately 1 m from the laser output, for x=0.3 cm (solid curve) and x=-0.2 cm (dotted curve).

Fig. 4
Fig. 4

(a) Two-dimensional spatial map of pulse profiles in the period-three regime. Taken at 4-W pump power. (b) Variations in pulse intensity as a function of position across the beam. Each symbol (triangle, square, and diamond) represents a different member of the P3 sequence.

Fig. 5
Fig. 5

Simulated pulse profiles for TEM00 and TEM01 modes, with α=0.5. (a), (b), and (c) show pulse profiles for locking with constant phase at 0. (d), (e), and (f) show profiles for locking with constant phase at π/2. (a) Δϕ=0, Ωt=0; (b) Δϕ=0, Ωt=2π/3; (c) Δϕ=0, Ωt=4π/3; (d) Δϕ=π/2, Ωt=0; (e) Δϕ=π/2, Ωt=2π/3; (f) Δϕ=π/2, Ωt=4π/3.

Fig. 6
Fig. 6

Spatial profile measured at 4.69-W pump power for a period-three pulse train with Δϕ=π/2.

Fig. 7
Fig. 7

Diagram of pulse intensity as a function of pump power for the period-three regime.

Fig. 8
Fig. 8

Comparison of spatial amplitudes of TEM01/TEM00 [called alpha(spatial)] to rf amplitudes of P3/P1 [called alpha(RF)], both as functions of pump intensity.

Fig. 9
Fig. 9

Theoretical versus experimental beat frequencies as a function of pump power. The arrow shows the frequency, 29.87 MHz, at which the subharmonic pulse train is precisely P3.

Fig. 10
Fig. 10

Schematic for pulse-resolved autocorrelation.

Fig. 11
Fig. 11

Pulse-resolved autocorrelations taken in the P3 regime.

Equations (8)

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

Etotal(t)=mnqamnqHmn(x, y)exp(iωmnqt).
ωmnq=qω0+(m+n+1)Ω.
Etotal(t)=Epulse(t)[Hmn(x, y)+αHmn(x, y)exp(-iΩt)exp(iΔϕ)].
I(x, y, t)=Ipulse[Hmn(x, y)αHmn(x, y)cos(Ωt+Δϕ)+Hmn2(x, y)+α2Hmn2(x, y)].
Ω=(c/2πL)cos-1(AD).
ABCD=1-z4/fz2+z4-z2z4/f-1/f1-z2/f10-p1×1-z1/fz1+z3-z1z3/f-1/f1-z3/f.
p=-L/2L/2 8n2PLπw4dz+-L/2L/2 nϑχPpump/Lπwp2kthCpρdz.
w14=-λπ ABCD.

Metrics