Abstract

We describe a simple and passive nanosecond-long laser-pulse stretcher using multiple optical ring cavities. We present a model of the pulse-stretching process for an arbitrary number of optical ring cavities. This new model explicitly includes the effects of cavity delay time, beam-splitter reflectivity, total number of optical cavities, and describes the effects of spatial profile sensitivity. Using the model, we optimize the design of a pulse stretcher for use in a spontaneous Raman-scattering excitation system that avoids laser-induced plasma spark problems. From the optimized design, we then experimentally demonstrate and verify the model with a three-cavity pulse-stretcher system that converts a 1000-mJ, 8.4-ns-long input laser pulse into an approximately 75-ns-long (FWHM) output laser pulse with a peak power reduction of 0.10× and an 83% efficiency.

© 2002 Optical Society of America

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References

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  1. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon Breach, Amsterdam, 1996), pp. 209–273.
  2. R. S. Barlow, C. D. Carter, “Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames,” Combust. Flame 97, 261–280 (1994).
    [CrossRef]
  3. S. P. Nandula, T. M. Brown, R. W. Pitz, P. A. DeBarber, “Single-pulse, simultaneous multipoint multispecies Raman measurements in turbulent nonpremixed jet flames,” Opt. Lett. 19, 414–416 (1994).
    [PubMed]
  4. D. F. Marran, J. H. Frank, M. B. Long, S. H. Stårner, R. W. Bilger, “Intracavity technique for improved Raman/Rayleigh imaging in flames,” Opt. Lett. 20, 791–793 (1995).
    [CrossRef] [PubMed]
  5. P. C. Miles, “Raman line imaging for spatially and temporally resolved mole fraction measurements in internal combustion engines,” Appl. Opt. 38, 1714–1732 (1999).
    [CrossRef]
  6. Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
    [CrossRef]
  7. F. Rabenstein, A. Leipertz, “Two-dimensional temperature determination in the exhaust region of a laminar flat-flame burner with linear Raman scattering,” Appl. Opt. 36, 6989–6996 (1997).
    [CrossRef]
  8. L. J. Radziemski, D. A. Cremers, eds., Laser-Induced Plasma and Applications (Marcel Dekker, New York, 1989).
  9. Y.-L. Chen, J. W. L. Lewis, “Visualization of laser-induced breakdown and ignition,” Opt. Exp. 9, 360–372 (2001); http.//www.opticsexpress.org .
    [CrossRef]
  10. G. Harigel, C. Baltay, M. Bregman, M. Hibbs, A. Schaffer, H. Bjelkhagen, J. Hawkins, W. Williams, P. Nailor, R. Michaels, H. Akbari, “Pulse stretching in a Q-switched ruby laser for bubble chamber holography,” Appl. Opt. 25, 4102–4110 (1986).
    [CrossRef] [PubMed]
  11. S. Pflüger, M. Sellhorst, V. Sturm, R. Noll, “Fiber-optic transmission of stretched pulses from a Q-switched ruby laser,” Appl. Opt. 35, 5165–5169 (1996).
    [CrossRef] [PubMed]
  12. M. Matsumoto, “Theory of stretched-pulse transmission in dispersion-managed fibers,” Opt. Lett. 22, 1238–1240 (1997).
    [CrossRef] [PubMed]
  13. V. Cautaerts, D. J. Richardson, R. Paschotta, D. C. Hanna, “Stretched pulse Yb3+:silica fiber laser,” Opt. Lett. 22, 316–318 (1997).
    [CrossRef] [PubMed]
  14. R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).
  15. T. J. Anderson, R. D. Woodward, M. Winter, “Oxygen concentration measurements in a high pressure environment using Raman imaging,” paper AIAA-95-0140, presented at the Thirty-Third Aerospace Science Meeting and Exhibit, Reno, Nev., 5–8 Jan. 1995.
  16. B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
    [CrossRef]
  17. F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).
  18. R. S. Barlow, P. C. Miles, “A shutter-based line-imaging system for single-shot Raman scattering measurements of gradients in mixture fraction,” in the Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28, pp. 269–277.
    [CrossRef]
  19. P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
    [CrossRef]
  20. J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
    [CrossRef]
  21. Turbulent Combustion Laboratory, Sandia National Laboratories, http://www.ca.sandia.gov/CRF/03_facilities/03_FacTDFL.html (2001).
  22. X. T. Phuoc, “Laser spark ignition: experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175, 419–423 (2000).
    [CrossRef]

2001 (1)

Y.-L. Chen, J. W. L. Lewis, “Visualization of laser-induced breakdown and ignition,” Opt. Exp. 9, 360–372 (2001); http.//www.opticsexpress.org .
[CrossRef]

2000 (2)

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

X. T. Phuoc, “Laser spark ignition: experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175, 419–423 (2000).
[CrossRef]

1999 (1)

1998 (1)

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

1997 (3)

1996 (2)

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

S. Pflüger, M. Sellhorst, V. Sturm, R. Noll, “Fiber-optic transmission of stretched pulses from a Q-switched ruby laser,” Appl. Opt. 35, 5165–5169 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (2)

R. S. Barlow, C. D. Carter, “Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames,” Combust. Flame 97, 261–280 (1994).
[CrossRef]

S. P. Nandula, T. M. Brown, R. W. Pitz, P. A. DeBarber, “Single-pulse, simultaneous multipoint multispecies Raman measurements in turbulent nonpremixed jet flames,” Opt. Lett. 19, 414–416 (1994).
[PubMed]

1986 (1)

Akbari, H.

Anderson, T. J.

T. J. Anderson, R. D. Woodward, M. Winter, “Oxygen concentration measurements in a high pressure environment using Raman imaging,” paper AIAA-95-0140, presented at the Thirty-Third Aerospace Science Meeting and Exhibit, Reno, Nev., 5–8 Jan. 1995.

Baltay, C.

Barlow, R. S.

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

R. S. Barlow, C. D. Carter, “Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames,” Combust. Flame 97, 261–280 (1994).
[CrossRef]

R. S. Barlow, P. C. Miles, “A shutter-based line-imaging system for single-shot Raman scattering measurements of gradients in mixture fraction,” in the Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28, pp. 269–277.
[CrossRef]

Bilger, R. W.

Bjelkhagen, H.

Bregman, M.

Brinkmann, R.

R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).

Brown, T. M.

Carter, C. D.

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

R. S. Barlow, C. D. Carter, “Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames,” Combust. Flame 97, 261–280 (1994).
[CrossRef]

Cautaerts, V.

Chen, Y.-L.

Y.-L. Chen, J. W. L. Lewis, “Visualization of laser-induced breakdown and ignition,” Opt. Exp. 9, 360–372 (2001); http.//www.opticsexpress.org .
[CrossRef]

D’Alfonso, N.

F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Dally, B. B.

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

DeBarber, P. A.

Dibble, R. W.

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

Eckbreth, A. C.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon Breach, Amsterdam, 1996), pp. 209–273.

Egermann, J.

J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
[CrossRef]

F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Engelhardt, R.

R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).

Fiechtner, G. J.

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

Frank, J. H.

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

D. F. Marran, J. H. Frank, M. B. Long, S. H. Stårner, R. W. Bilger, “Intracavity technique for improved Raman/Rayleigh imaging in flames,” Opt. Lett. 20, 791–793 (1995).
[CrossRef] [PubMed]

Hanna, D. C.

Harigel, G.

Hawkins, J.

Heller, D. F.

R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).

Hibbs, M.

Ipp, W.

J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
[CrossRef]

Koebcke, W.

J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
[CrossRef]

Leipertz, A.

F. Rabenstein, A. Leipertz, “Two-dimensional temperature determination in the exhaust region of a laminar flat-flame burner with linear Raman scattering,” Appl. Opt. 36, 6989–6996 (1997).
[CrossRef]

J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
[CrossRef]

F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Lewis, J. W. L.

Y.-L. Chen, J. W. L. Lewis, “Visualization of laser-induced breakdown and ignition,” Opt. Exp. 9, 360–372 (2001); http.//www.opticsexpress.org .
[CrossRef]

Long, M. B.

Marran, D. F.

Masri, A. R.

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

Matsumoto, M.

Michaels, R.

Miles, P. C.

P. C. Miles, “Raman line imaging for spatially and temporally resolved mole fraction measurements in internal combustion engines,” Appl. Opt. 38, 1714–1732 (1999).
[CrossRef]

R. S. Barlow, P. C. Miles, “A shutter-based line-imaging system for single-shot Raman scattering measurements of gradients in mixture fraction,” in the Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28, pp. 269–277.
[CrossRef]

Nailor, P.

Nandula, S. P.

Nguyen, Q. V.

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

Noll, R.

Nooren, P. A.

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

Paschotta, R.

Pflüger, S.

Phuoc, X. T.

X. T. Phuoc, “Laser spark ignition: experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175, 419–423 (2000).
[CrossRef]

Pitz, R. W.

Rabensein, F.

F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).

Rabenstein, F.

Richardson, D. J.

Schaffer, A.

Sellhorst, M.

Stårner, S. H.

Sturm, V.

van der Meer, T. H.

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

Versluis, M.

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

Walling, J. C.

R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).

Williams, W.

Winter, M.

T. J. Anderson, R. D. Woodward, M. Winter, “Oxygen concentration measurements in a high pressure environment using Raman imaging,” paper AIAA-95-0140, presented at the Thirty-Third Aerospace Science Meeting and Exhibit, Reno, Nev., 5–8 Jan. 1995.

Woodward, R. D.

T. J. Anderson, R. D. Woodward, M. Winter, “Oxygen concentration measurements in a high pressure environment using Raman imaging,” paper AIAA-95-0140, presented at the Thirty-Third Aerospace Science Meeting and Exhibit, Reno, Nev., 5–8 Jan. 1995.

Appl. Opt. (4)

Appl. Phys. B (1)

P. A. Nooren, M. Versluis, T. H. van der Meer, R. S. Barlow, J. H. Frank, “Raman-Rayleigh-LIF measurements of temperature and species concentrations in the Delft piloted turbulent jet diffusion flame,” Appl. Phys. B 71, 95–111 (2000).
[CrossRef]

Combust. Flame (3)

B. B. Dally, A. R. Masri, R. S. Barlow, G. J. Fiechtner, “Instantaneous and mean compositional structure of bluff-body stabilized nonpremixed flames,” Combust. Flame 114, 119–148 (1998).
[CrossRef]

R. S. Barlow, C. D. Carter, “Raman/Rayleigh/LIF measurements of nitric oxide formation in turbulent hydrogen jet flames,” Combust. Flame 97, 261–280 (1994).
[CrossRef]

Q. V. Nguyen, R. W. Dibble, C. D. Carter, G. J. Fiechtner, R. S. Barlow, “Raman-LIF measurements of temperature, major species, OH, and NO in a methane-air bunsen flame,” Combust. Flame 105, 499–510 (1996).
[CrossRef]

Opt. Commun. (1)

X. T. Phuoc, “Laser spark ignition: experimental determination of laser-induced breakdown thresholds of combustion gases,” Opt. Commun. 175, 419–423 (2000).
[CrossRef]

Opt. Exp. (1)

Y.-L. Chen, J. W. L. Lewis, “Visualization of laser-induced breakdown and ignition,” Opt. Exp. 9, 360–372 (2001); http.//www.opticsexpress.org .
[CrossRef]

Opt. Lett. (4)

Other (8)

R. Engelhardt, R. Brinkmann, J. C. Walling, D. F. Heller, “Pulse stretched solid-state laser lithotripter,” U.S. patent5,496,306 (5March1996).

T. J. Anderson, R. D. Woodward, M. Winter, “Oxygen concentration measurements in a high pressure environment using Raman imaging,” paper AIAA-95-0140, presented at the Thirty-Third Aerospace Science Meeting and Exhibit, Reno, Nev., 5–8 Jan. 1995.

L. J. Radziemski, D. A. Cremers, eds., Laser-Induced Plasma and Applications (Marcel Dekker, New York, 1989).

F. Rabensein, J. Egermann, A. Leipertz, N. D’Alfonso, “Vapor-phase structures of Diesel-type fuel sprays: an experimental analysis,” SAE paper 982543 (Society of Automotive Engineers, Warrendale, Pa., 1998).

R. S. Barlow, P. C. Miles, “A shutter-based line-imaging system for single-shot Raman scattering measurements of gradients in mixture fraction,” in the Proceedings of the Combustion Institute (Combustion Institute, Pittsburgh, Pa., 2000), Vol. 28, pp. 269–277.
[CrossRef]

J. Egermann, W. Koebcke, W. Ipp, A. Leipertz, “Investigation of the mixture formation inside a GDI engine by means of linear Raman spectroscopy,” in the Proceedings of the Combustion Institute (Pittsburgh, Pa., 2000), Vol. 28, pp. 1145–1151.
[CrossRef]

Turbulent Combustion Laboratory, Sandia National Laboratories, http://www.ca.sandia.gov/CRF/03_facilities/03_FacTDFL.html (2001).

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, 2nd ed. (Gordon Breach, Amsterdam, 1996), pp. 209–273.

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Figures (12)

Fig. 1
Fig. 1

Schematic of the basic right-triangle ring cavity used as a pulse stretcher. The input laser pulse is divided into multiple smaller output pulses that are extracted through a partially transmitting beam splitter.

Fig. 2
Fig. 2

Schematic of a pulse stretcher with multiple partially transmitting optical ring cavities (three-cavity arrangement). BS, beam splitter; M, mirror; τ i , a round-trip propagation time (delay time) for each ring cavity; τ i,j , propagation time between two cavities. τ1 ≥ τ2 ≥ τ3.

Fig. 3
Fig. 3

Schematic of the basic pulse-stretcher model with spatial pulse profile effects, including beam deviation δ and beam divergence θ (for cavity 1). Note that when δ < 1, the optical path length L = L′ = L″. BS, beam splitter; M, mirror.

Fig. 4
Fig. 4

Calculated output laser-pulse shapes for different delay-time ratios, τ123. Here a beam-splitter reflectivity of R BS = 38% was used, and τ1 + τ2 + τ3 = 7 was used as the constraint. The ordinate of the graph Λ/χ shows the nondimensional laser power.

Fig. 5
Fig. 5

Calculated variations in the output pulse power and width as a function of cavity 1 delay times, τ1. Effect on (a) peak power and (b) output pulse width. The following parameters were used: τ123 = 4:2:1 and R BS = 38%.

Fig. 6
Fig. 6

Calculated variations in output laser-pulse power and width as a function of beam-splitter reflectivity R BS. Effect on (a) peak power and (b) pulse width. τ123 = 4:2:1 and τ1 = 4.2.

Fig. 7
Fig. 7

Calculated output profiles with optimized parameters in a two-, three-, and four-cavity arrangement. τ1,2 = 0.1, τ2,3 = 0.1, and R BS = 40%. The integral of Q(χ) or D i (χ) is equal to Λ, that is, ∫ Q(χ)dχ = ∫ D i (χ)dχ = Λ. Each additional cavity provides an approximately 0.5× reduction in the peak laser power.

Fig. 8
Fig. 8

Calculated one-dimensional spatial profiles of the stretched output pulse that include the effects of laser beam angular deviation and divergence compared with a system that has perfect alignment. The graph ordinate Λ/χ shows the nondimensional laser power. The original laser beam is assumed to be spatially Gaussian with a FWHM diameter of one unit of ρ. δ = 25 µrad and θ = 250 µrad. Note that with perfect alignment both δ and θ are equal to 0. The integral of each profile equals Λ.

Fig. 9
Fig. 9

Schematic of the experimental layout of the three-cavity pulse stretcher used (each cavity is delimited by the beam splitter). The whole system (for approximately 11-m optical length in the first stage) can be assembled onto a standard 1.52 m (5 ft) × 0.91 m (3 ft) optical breadboard by use of folding mirrors as shown.

Fig. 10
Fig. 10

Schematic of the experimental arrangement used for the pulse-stretching measurements. In measurement of q(t), all cavities are blocked; in measurement of D 1(t), cavities 2 and 3 are blocked; in measurement of D 2(t), only cavity 3 is blocked; in the stretched-pulse measurement, no cavities are blocked. M i , mirrors; BS i , beam splitter; C i , ring cavity; PD, photodiode; BD, beam dump; OSC, oscilloscope; SP, scattering plate (beam dump).

Fig. 11
Fig. 11

Measured temporal profile of the stretched-pulse output by use of the three-cavity pulse stretcher shown in Fig. 9. The envelope shows shot-to-shot variations for 256 shots (from minimum to maximum). The graph ordinate shows photodiode (PD) currents (volts into 50 Ω) representing laser intensity as a function of time.

Fig. 12
Fig. 12

Temporal profiles of measured and calculated laser pulses. (a) q(t), original pulse; (b) D 1(t), output pulse from cavity 1 only; (c) D 2(t), output pulse from cavity 2 (after passing through cavity 1 and 2); (d) D 3(t), final output or stretched pulse. The solid curves represent the calculation and the dotted curves the experimental data. In both experiment and calculation, d t = 8.4 ns, τ1 = 35.2 ns (τ1/d t = 4.2), τ123 = 3.9:1.9:1, τ1,2 = 1.53 ns, τ2,3 = 1.10 ns, R BS ≈ 40%. In the calculation, N = 6 and E = 1000 mJ. The experimental data are averaged over 256 shots. The output energy of both the measured and the calculated stretched pulses are obtained by direct integration of the profiles in time. Note that the residual signal in the tail portion (30–45 ns) of q(t) as measured in (a) is most likely the result of a minor electrical impedance mismatch that shows up as a minor ringing.

Equations (19)

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

qtE 2ln2πdtexp-2ln2tdt2,
χtdt,
ΛEE0,
P0E0dt,
τiΔtidt,
τj,kΔtj,kdt,
QχΛ2ln2πexp-2ln2χ2,
D1χ=RBSQχInitial Reflection+1-RBS2Qχ-τ11st Pass+1-RBS2RBSQχ-2τ1 nth pass2nd Pass++1-RBS2RBSn-1Qχ-nτ1nth pass =RBSQχ+1-RBS2n=1N RBSn-1Qχ-nτ1,
D2χ=RBSD1χ-τ1,2+1-RBS2×m=1N RBSm-1D1χ-τ1,2+mτ2,
DiχRBSDi-1χ-τi-1,i+1-RBS2×k=1N RBSk-1Di-1χ-τi-1,i+kτi,
qr, LE 2ln2π2L tan θ+dr×exp-2ln2r2L tan θ+dr2,
ρrdr,
L˜iΔLidr,
L˜j,kΔLj,kdr,
Qρ, L˜iΛ 2ln2π2L˜i tan θ+1×exp-2ln2ρ2L˜i tan θ+12.
Diρ, ΨiRBSDi-1ρ, Ψin=0+1-RBS2n=1N RBSn-1Di-1ρ--1nΨi tan δ, Ψi,
D1t=1-LAR2RBSqt+1-LAR×1-RBS2n=1NRM45RM07nRBSn-1qt-nτ1,
D2t=1-LAR2RM45RBSD1t-τ12+1-LAR×1-RBS2m=1NRM45RM03mRBSm-1D1t-τ1,2+mτ2,
D3t1-LAR2RM45RBSD2t-τ23+1-LAR×1-RBS2k=1NRM45RM0kRBSk-1D2t-τ2,3+kτ3,

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