Abstract

Analysis of dispersion produced by a λ/4 multilayer dielectric mirror as a function of its construction parameters is presented. The amount of dispersion can be estimated from a careful inspection of the measured reflectivity curve. In some cases, which seem to be of practical relevance, the value of dispersion is such as to prevent pulses shorter than ∼50 fsec from being produced in the mode-locked laser cavity.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
    [CrossRef]
  2. J. M. Halbout, C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
    [CrossRef]
  3. W. Dietel, J. J. Fontaine, J.-C. Diels, Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]
  4. W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
    [CrossRef]
  5. J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
    [CrossRef]
  6. D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
    [CrossRef]
  7. D. Kühlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
    [CrossRef]
  8. C. V. Shank, R. L. Fork, R. T. Yen, in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, A. Laubereau, eds. (Springer-Verlag, Heidelberg, 1982), p.2.
    [CrossRef]
  9. E. I. Ippen, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (personal communication).
  10. S. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked dye lasers,” IEEE J. Quantum Electron. (to be published).
  11. H. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), pp.51–70.
  12. G. A. Mourou, Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623,and J.-C. Diels, Center for Applied Quantum Electronics, North Texas State University, P.O. Box 5368, Denton, Texas 76203 (personal communications).
    [PubMed]
  13. E. Ritter, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), pp. 297–921.
  14. J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp.8.58–8.69.
  15. M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
    [CrossRef]

1984 (1)

D. Kühlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

1983 (4)

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

1982 (2)

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

J. M. Halbout, C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

1981 (1)

R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Born, H.

H. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), pp.51–70.

De Silvestri, S.

S. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked dye lasers,” IEEE J. Quantum Electron. (to be published).

Diels, J.-C.

J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

Dietel, W.

W. Dietel, J. J. Fontaine, J.-C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Dobrowolski, J. A.

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp.8.58–8.69.

Döpel, E.

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Fontaine, J. J.

J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J.-C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

Fork, R. L.

R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

C. V. Shank, R. L. Fork, R. T. Yen, in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, A. Laubereau, eds. (Springer-Verlag, Heidelberg, 1982), p.2.
[CrossRef]

Greene, B. I.

R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Halbout, J. M.

J. M. Halbout, C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

Ippen, E. I.

E. I. Ippen, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (personal communication).

Ippen, E. P.

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Kühlke, D.

D. Kühlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
[CrossRef]

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Laporta, P.

S. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked dye lasers,” IEEE J. Quantum Electron. (to be published).

Mourou, G. A.

G. A. Mourou, Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623,and J.-C. Diels, Center for Applied Quantum Electronics, North Texas State University, P.O. Box 5368, Denton, Texas 76203 (personal communications).
[PubMed]

Ritter, E.

E. Ritter, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), pp. 297–921.

Rudolph, W.

D. Kühlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
[CrossRef]

Shank, C. V.

C. V. Shank, R. L. Fork, R. T. Yen, in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, A. Laubereau, eds. (Springer-Verlag, Heidelberg, 1982), p.2.
[CrossRef]

Shank, V. C.

R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

Stix, M. S.

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Svelto, O.

S. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked dye lasers,” IEEE J. Quantum Electron. (to be published).

Tang, C. L.

J. M. Halbout, C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

Wilhelmi, B.

D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
[CrossRef]

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Wolf, E.

H. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), pp.51–70.

Yen, R. T.

C. V. Shank, R. L. Fork, R. T. Yen, in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, A. Laubereau, eds. (Springer-Verlag, Heidelberg, 1982), p.2.
[CrossRef]

Appl. Phys. Lett. (2)

R. L. Fork, B. I. Greene, V. C. Shank, Appl. Phys. Lett. 38, 671 (1981).
[CrossRef]

J. M. Halbout, C. L. Tang, Appl. Phys. Lett. 40, 765 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

J. J. Fontaine, W. Dietel, J.-C. Diels, IEEE J. Quantum Electron. QE-19, 1467 (1983).
[CrossRef]

D. Kühlke, W. Rudolph, B. Wilhelmi, IEEE J. Quantum Electron. QE-19, 526 (1983).
[CrossRef]

Opt. Commun. (1)

W. Dietel, E. Döpel, D. Kühlke, B. Wilhelmi, Opt. Commun. 43, 433 (1982).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

D. Kühlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

Other (7)

C. V. Shank, R. L. Fork, R. T. Yen, in Picosecond Phenomena III, K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser, A. Laubereau, eds. (Springer-Verlag, Heidelberg, 1982), p.2.
[CrossRef]

E. I. Ippen, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (personal communication).

S. De Silvestri, P. Laporta, O. Svelto, “The role of cavity dispersion in cw mode-locked dye lasers,” IEEE J. Quantum Electron. (to be published).

H. Born, E. Wolf, Principles of Optics (Pergamon, London, 1970), pp.51–70.

G. A. Mourou, Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623,and J.-C. Diels, Center for Applied Quantum Electronics, North Texas State University, P.O. Box 5368, Denton, Texas 76203 (personal communications).
[PubMed]

E. Ritter, in Laser Handbook, F. T. Arecchi, E. O. Schulz-Dubois, eds. (North-Holland, Amsterdam, 1972), pp. 297–921.

J. A. Dobrowolski, “Coatings and filters,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, eds. (McGraw-Hill, New York, 1978), pp.8.58–8.69.

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 (4)

Fig. 1
Fig. 1

Plot of reflectivity R and second derivative ϕ″ of the phase shift versus ω/ωm for a λ/4 dielectric mirror made of 19 layers of high- (nH = 2.28) and low- (nL = 1.45) refractive-index materials. In the case shown by solid lines all layers have an optical thickness of λ/4. In the case shown by dashed lines, the first three layers, starting from air, are assumed to have a thickness 8% smaller than λ/4.

Fig. 2
Fig. 2

Second derivative ϕ″ of the phase shift as a function of the number of layers for a perfect λ/4 stack at different mirror transmission values: ◊, 1% transmission; Δ, 2% transmission; □, 4% transmission.

Fig. 3
Fig. 3

Second derivative ϕ″ of the phase shift as a function of the ratio nH/nL for a 23-layer stack and for a few combinations of film refractive indices [ZrO2−SiO2(nH/nL) = 1.45; TiO2−SiO2(nH/nL) = 1.57; CeO2−MgF2(nH/nL) = 1.67; ZnS−MgF2(nH/nL) = 1.70] at different transmission values: ◊,1% transmission; Δ, 2% transmission; □, 4% transmission. The width of the high-reflectivity zone Δω (normalized to the central frequency ωm) is also plotted versus the ratio nH/nL (solid line).

Fig. 4
Fig. 4

Steady-state pulse duration T of a mode-locked laser cavity as a function of the filter bandwidth ωc. The dashed curve represents the dispersionless case; the solid curves show the results for different values of the dispersion parameter ϕ″ (expressed in units of 10−30 sec2).

Equations (3)

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

δ T / T = 2 ϕ 2 / T 4 .
2 / ω c 2 T 2 = S ,
2 / ω c 2 T 2 + 2 ϕ 2 / T 4 = S ,

Metrics