Abstract

A number of factors that influence spectral position of ultrashort pulses in mode-locked lasers have been identified: high-order dispersion, gain saturation, reabsorption from the ground state, and stimulated Raman scattering. Using the one-dimensional numerical model for the simulation of the laser cavity, we analyze the relative contributions of different factors to the spectral position of the mode-locked pulses using the example of the Cr:LiSGaF laser. In this case the Raman effect provides the largest self-frequency shift from the gain peak (up to 60 nm), followed by the gain saturation (∼25 nm), whereas the high-order dispersion contribution is insignificant (∼5 nm). The results of the simulation are in good agreement with experimental data, confirming that stimulated Raman scattering is the dominant mechanism that causes the pulse self-frequency shift.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
    [CrossRef]
  2. C. Chudoba, J. G. Fjimoto, E. P. Ippen, H. A. Haus, U. Morgner, F. X. Kärtner, V. Scheuer, G. Angelow, and T. Tschudi, “All-solid-state Cr:forsterite laser generating 14-fs pulses at 1.3 μm,” Opt. Lett. 26, 292–294 (2001).
    [CrossRef]
  3. S. Uemura and K. Torizuka, “Generation of 12-fs pulses from a diode-pumped Kerr-lens mode-locked Cr:LiSAF laser,” Opt. Lett. 24, 780–782 (1997).
    [CrossRef]
  4. I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
    [CrossRef]
  5. I. T. Sorokina, E. Sorokin, and E. Wintner, “Femtosecond Cr:LiSGaF and Cr:LiSAF lasers: phenomena and limitations in the 15-fs regime,” in ICONO’98: Ultrafast Phenomena and Interaction of Superstrong Laser Fields with Matter, Proc. SPIE 3735, 2–21 (1999).
    [CrossRef]
  6. Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
    [CrossRef]
  7. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Springer, New York, 1992), Chap. 1.
  8. J. Jasapara, V. L. Kalashnikov, D. O. Krimer, I. G. Poloyko, M. Lenzner, and W. Rudolph, “Automodulation in Kerr-lens mode-locked solid-state laser,” J. Opt. Soc. Am. B 17, 319–326 (2000).
    [CrossRef]
  9. H. A. Haus, I. Sorokina, and E. Sorokin, “Raman-induced redshift of ultrashort mode-locked laser pulses,” J. Opt. Soc. Am. B 15, 223–231 (1998).
    [CrossRef]
  10. I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” in Advanced Solid State Lasers, W. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1998), p. 359.
  11. K. M. Gäbel, R. Lebert, R. Poprawe, and A. Valster, “Signature of the Raman self-frequency shift on the autocorrelation of sub-20-fs pulses from colquiriite lasers,” in Conference on Lasers and Electro-Optics, Vol. 39 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), p. 484.
  12. V. L. Kalashnikov, V. P. Kalosha, V. P. Mikhailov, and I. G. Poloyko, “Self-mode locking of four-mirror cavity solid-state lasers by Kerr self-focusing,” J. Opt. Soc. Am. B 12, 462–467 (1995).
    [CrossRef]
  13. H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
    [CrossRef]
  14. J. Herrmann and B. Wilhelmi, Laser fur Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984).
  15. R. L. Sutherland; Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 305.
  16. Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
    [CrossRef]
  17. I. P. Christov, M. M. Murnane, H. C. Kapteyn, Z. Jianping, and P. H. Chung, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465–1467 (1994).
    [CrossRef] [PubMed]
  18. A. Sennaroglu, C. R. Pollock, and H. Nathel, “Continuous-wave self-mode-locked operation of a femtosecond Cr4+:YAG laser,” Opt. Lett. 19, 390–392 (1994).
    [PubMed]
  19. Y. Ishida and K. Naganuma, “Characteristics of femtosecond pulses near 1.5 μm in a self-mode-locked Cr4+:YAG,” Opt. Lett. 19, 2003–2005 (1994).
    [CrossRef] [PubMed]
  20. Zh. Zhigang, T. Nakagawa, K. Torizuka, T. Sugaya, and K. Kobayashi, “Self-starting mode-locked Cr4+:YAG laser with a low-loss broadband semiconductor saturable-absorber mirror,” Opt. Lett. 24, 1768–1770 (1999).
    [CrossRef]

2001

2000

1999

I. T. Sorokina, E. Sorokin, and E. Wintner, “Femtosecond Cr:LiSGaF and Cr:LiSAF lasers: phenomena and limitations in the 15-fs regime,” in ICONO’98: Ultrafast Phenomena and Interaction of Superstrong Laser Fields with Matter, Proc. SPIE 3735, 2–21 (1999).
[CrossRef]

Zh. Zhigang, T. Nakagawa, K. Torizuka, T. Sugaya, and K. Kobayashi, “Self-starting mode-locked Cr4+:YAG laser with a low-loss broadband semiconductor saturable-absorber mirror,” Opt. Lett. 24, 1768–1770 (1999).
[CrossRef]

1998

H. A. Haus, I. Sorokina, and E. Sorokin, “Raman-induced redshift of ultrashort mode-locked laser pulses,” J. Opt. Soc. Am. B 15, 223–231 (1998).
[CrossRef]

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[CrossRef]

1997

1995

1994

1992

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Angelow, G.

Brabec, T.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
[CrossRef]

Cassanho, A.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

Christov, I. P.

Chudoba, C.

Chung, P. H.

Curley, P. F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
[CrossRef]

Fjimoto, J. G.

Fujimoto, J. G.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Haus, H. A.

Ippen, E. P.

Ishida, Y.

Jasapara, J.

Jenssen, H. P.

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

Jianping, Z.

Kalashnikov, V. L.

Kalosha, V. P.

Kapteyn, H. C.

Kärtner, F. X.

Kobayashi, K.

Krausz, F.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
[CrossRef]

Krimer, D. O.

Lenzner, M.

Lin, Q.

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[CrossRef]

Mikhailov, V. P.

Morgner, U.

Murnane, M. M.

Naganuma, K.

Nakagawa, T.

Nathel, H.

Pollock, C. R.

Poloyko, I. G.

Rudolph, W.

Scheuer, V.

Sennaroglu, A.

Sorokin, E.

Sorokina, E.

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

Sorokina, I.

H. A. Haus, I. Sorokina, and E. Sorokin, “Raman-induced redshift of ultrashort mode-locked laser pulses,” J. Opt. Soc. Am. B 15, 223–231 (1998).
[CrossRef]

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[CrossRef]

Sorokina, I. T.

I. T. Sorokina, E. Sorokin, and E. Wintner, “Femtosecond Cr:LiSGaF and Cr:LiSAF lasers: phenomena and limitations in the 15-fs regime,” in ICONO’98: Ultrafast Phenomena and Interaction of Superstrong Laser Fields with Matter, Proc. SPIE 3735, 2–21 (1999).
[CrossRef]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

Spielmann, Ch.

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
[CrossRef]

Sugaya, T.

Szipöcs, R.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

Torizuka, K.

Tschudi, T.

Uemura, S.

Wintner, E.

I. T. Sorokina, E. Sorokin, and E. Wintner, “Femtosecond Cr:LiSGaF and Cr:LiSAF lasers: phenomena and limitations in the 15-fs regime,” in ICONO’98: Ultrafast Phenomena and Interaction of Superstrong Laser Fields with Matter, Proc. SPIE 3735, 2–21 (1999).
[CrossRef]

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “14-fs pulse generation in Kerr-lens mode-locked prismless Cr:LiSGaF and Cr:LiSAF lasers: observation of pulse self-frequency shift,” Opt. Lett. 22, 1716–1718 (1997).
[CrossRef]

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

Zhigang, Zh.

Appl. Phys. B

I. T. Sorokina, E. Sorokina, E. Wintner, A. Cassanho, H. P. Jenssen, and R. Szipöcs, “Sub-20 fs pulse generation from the mirror dispersion controlled Cr:LiSGaF and Cr:LiSAF lasers,” Appl. Phys. B 65, 245–253 (1997).
[CrossRef]

IEEE J. Quantum Electron.

H. A. Haus, J. G. Fujimoto, and E. P. Ippen, “Analytic theory of additive pulse and Kerr lens mode locking,” IEEE J. Quantum Electron. 28, 2086–2096 (1992).
[CrossRef]

Ch. Spielmann, P. F. Curley, T. Brabec, and F. Krausz, “Ultrabroadband femtosecond lasers,” IEEE J. Quantum Electron. 30, 1100–1114 (1994). Please note that due to typographical error the word mode locked has been substituted by ed throughout this paper!
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

Q. Lin and I. Sorokina, “High-order dispersion effects in solitary mode-locked lasers: side-band generation,” Opt. Commun. 153, 285–288 (1998).
[CrossRef]

Opt. Lett.

Proc. SPIE

I. T. Sorokina, E. Sorokin, and E. Wintner, “Femtosecond Cr:LiSGaF and Cr:LiSAF lasers: phenomena and limitations in the 15-fs regime,” in ICONO’98: Ultrafast Phenomena and Interaction of Superstrong Laser Fields with Matter, Proc. SPIE 3735, 2–21 (1999).
[CrossRef]

Other

J. Herrmann and B. Wilhelmi, Laser fur Ultrakurze Lichtimpulse (Akademie-Verlag, Berlin, 1984).

R. L. Sutherland; Handbook of Nonlinear Optics (Marcel Dekker, New York, 1996), p. 305.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (Springer, New York, 1992), Chap. 1.

I. T. Sorokina, E. Sorokin, E. Wintner, A. Cassanho, and H. P. Jenssen, “Raman induced pulse self-frequency shift in the sub-20 fs Kerr-lens mode-locked Cr:LiSGaF and Cr:LiSAF lasers,” in Advanced Solid State Lasers, W. Bosenberg and M. M. Fejer, eds., Vol. 19 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington D.C., 1998), p. 359.

K. M. Gäbel, R. Lebert, R. Poprawe, and A. Valster, “Signature of the Raman self-frequency shift on the autocorrelation of sub-20-fs pulses from colquiriite lasers,” in Conference on Lasers and Electro-Optics, Vol. 39 of Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), p. 484.

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 (9)

Fig. 1
Fig. 1

General scheme of the KLM Cr:LiSGaF laser used in this paper. This scheme directly corresponds to the experiments in Refs. 1 and 4: HR, high reflector; CM, chirped mirror; OC, output coupler.

Fig. 2
Fig. 2

Measured group-delay dispersion of the active media (8 mm in double pass), output coupler, and chirped mirrors in dependence on the wavelength λ.

Fig. 3
Fig. 3

(a) Double-pass ground-state absorption of Cr:LiSGaF, (b), round-trip resonator losses due to the output coupler, and (c) gain cross section of Cr:LiSGaF.

Fig. 4
Fig. 4

Experimental demonstration of the pulse frequency shift. The output spectra of a mode-locked Cr:LiSGaF laser, with changing intracavity pulse energies and durations (for parameters, see Table 1). Spectrum 1 was observed with an additional chirped mirror in the resonator (corresponding to more negative dispersion); other spectra were observed in the same configuration as used in the simulations.

Fig. 5
Fig. 5

Raman gain of undoped LiSGaF. The exciting laser line at 514.5 nm and scattered light are both polarized along the crystallographic z axis, corresponding to the polarization of the laser radiation in a Cr:LiSGaF laser.

Fig. 6
Fig. 6

Spectral profiles of the output laser pulses, obtained with the discrete model. The corresponding pulse energies are used as subscripts to each curve.

Fig. 7
Fig. 7

Dependence of (a) dispersion and (b) generation spectra on wavelength. P=3.2×10-4, σ=1, γ=0.05, and pulse energy E is 20 nJ. Pulse durations tp: 27 (solid curve), 38 (dash), and 36 fs (dot).

Fig. 8
Fig. 8

Dependence of generation spectra on wavelength in the presence of high-order dispersion in the distributed (solid and dash curves) and the discrete-element (dot) models. σ=1 and γ=0.05. For the corresponding pulse parameters, see Table 3.

Fig. 9
Fig. 9

Pulse central wavelength as a function of the saturated gain coefficient. Solid curve: Net-gain maximum; ABCD, spectrum peak in the case of gain saturation without reabsorption and Raman scattering in the active medium; EFGH, contribution of the reabsorption; IJK, contribution of Raman scattering. Points correspond to Table 4.

Tables (4)

Tables Icon

Table 1 Pulse Durations and Pulse Energies for Fig. 4

Tables Icon

Table 2 Raman Gain of Undoped LiSGaF

Tables Icon

Table 3 Normalized Pump Power, Pulse Duration, and Energy for Fig. 8

Tables Icon

Table 4 Ultrashort-Pulse Energies and Durations for Fig. 9

Equations (20)

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

a(z, t)=-a(z, t)G(t-t)dt,
G(t-t)=12π - exp-ij=28 1j!Dj(ω-ω0)j-(t-t)ωdω,
αt=Ipσ14hν(αmax-α)-|a|2σ32hνα-αTr,
αz=P(αmax-α)-EEsα-TcavTrα,
asς=ij=13Qj*ap,
apς=ij=13Qjas,
2Qjt2+2Tj Qjt+Ωj2Qj=μjapas*,
Qj=μjapas*Ωj2-2i(ωp-ωs)Tj-(ωp-ωs)2μjapas*2Ωj(Ωj-[ωp-ωs])-2iΩjTj.
asς=iasj=13μjk |ap,k|22Ωj[Ωj-(ωp,k-ωs)]+2iΩjTj,
apς=iapj=13μjk |as,k|22Ωj[Ωj-(ωp-ωs,k)]-2iΩjTj,
asς=π4 j=13asgjs|ap|2,
apς=-π4 j=13apgjs|as|2.
χj=ωpωs2ns2gjsπc21-exp-ΩjkBT,
a(z, t)=--a(z, t)C(t-t)L(t-t)×A(t-t)G(t-t)dtdtdtdt,
a(z+1, t)=a(z, t)exp-γ1+σ|a(z, t)|2-i|a(z, t)|2,
α(z+1)=α(z)exp-τ-|a(z, t)|2dt-Tcav/Tr-P+Pαmax[1-exp(-Tcav/Tr-P)]P+Tcav/Tr,
A(t-t)=12π -[1+α(z)]Φα(ω)exp[iω(t-t)]dω,
L(t-t)=12π -Φr(ω)exp[iω(t-t)]dω,
C(t-t)=12π -Φout(ω)exp[iω(t-t)]dω,
Δλj gjsTjG(Ωjτ)(Eτ)L,

Metrics