Abstract

We performed a series of experiments on suspensions of carbon particles in liquids (ink) and carbon particles deposited on glass to determine the mechanisms for the observed optical-limiting behavior. Both materials show reduced transmittance for increasing fluence (energy per unit area). We found that nonlinear scattering dominates the transmissive losses and that the limiting is fluence dependent, so that limiters based on black ink are effective for nanosecond pulses but not for picosecond pulses. Additionally, the nonlinear scattering and the limiting behavior cease after repeated irradiation. For the liquid, flowing eliminates this effect. All the data obtained are consistent with a model of direct heating of the microscopic-sized carbon particles by linear absorption with subsequent optical breakdown initiated by thermally ionized carriers. A simple calculation gives temperatures higher than the sublimation temperature at the onset of limiting. Emission spectra measurements show singly ionized carbon emission lines with a hot blackbody background emission consistent with temperatures of ≃4000 K. A rapid expansion of the microscopic plasmas generated by the breakdown will effectively scatter further input light. Indeed, in time-resolved experiments the trailing portion of the pulse is most heavily scattered. The time-resolved transmittance of a weak cw probe beam also follows the temporal dependence of the singly ionized carbon emission (≃102 ns). We directly monitored the expansion of the scattering centers by angularly resolving the scattered light for different input fluences and fitting to Mie scattering theory. Since the carbon is black and the microplasmas are initiated by linear absorption, the limiting is extremely broadband. Within the context of this model we discuss the limitations and optimization of ink-based optical limiters.

© 1992 Optical Society of America

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References

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  1. K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).
  2. K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).
  3. W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
    [CrossRef]
  4. K. Mansour, Ph.D. dissertation (University of North Texas, Denton, Tex., 1990).
  5. M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
    [CrossRef]
  6. K. C. Jungling, O. L. Gaddy, IEEE J. Quantum Electron. QE-7, 97 (1973).
  7. T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
    [CrossRef]
  8. M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  9. J. H. Marburger, Progress in Quantum Electronics (Pergamon, London, 1977), pp. 35–110.
  10. C. N. K. Patel, A. C. Tam, Rev. Modern Phys. 53, 517 (1981).
    [CrossRef]
  11. Y. P. Raizer, Sov. Phys. Usp. 8, 650 (1966);also see F. Docchio, C. Sacchi, Invest. Ophthalmol. Vis. Sci. 29, 437 (1986).
    [CrossRef]
  12. R. G. Meyerand, A. F. Haught, Phys. Rev. Lett. 13, 7 (1964);also see F. Docchio, P. Regondi, M. R. C. Capon, J. Mellerio, Appl. Opt. 27, 3669 (1988).
    [CrossRef] [PubMed]
  13. C. D. David, J. Appl. Lett. 11, 394 (1967).
    [CrossRef]
  14. J. F. Ready, Effects of High-Power Laser Radiation (Academic Press, New York, 1971).
  15. A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
    [CrossRef]
  16. K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).
  17. C. G. Morgan, Rep. Progr. Phys.38, 621 (1976).
    [CrossRef]
  18. T. P. Ackerman, O. B. Toon, Appl. Opt. 20, 3661 (1981).
    [CrossRef] [PubMed]
  19. J. B. Donnet, A. Voet, Carbon Black Physics, Chemistry and Elastomer Reinforcement (Dekker, New York, 1976).
  20. C. D. David, J. Appl. Phys. 40, 3674 (1969).
    [CrossRef]

1990

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1989

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).

A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
[CrossRef]

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

1985

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

1984

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

1983

M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
[CrossRef]

1981

C. N. K. Patel, A. C. Tam, Rev. Modern Phys. 53, 517 (1981).
[CrossRef]

T. P. Ackerman, O. B. Toon, Appl. Opt. 20, 3661 (1981).
[CrossRef] [PubMed]

1973

K. C. Jungling, O. L. Gaddy, IEEE J. Quantum Electron. QE-7, 97 (1973).

1969

C. D. David, J. Appl. Phys. 40, 3674 (1969).
[CrossRef]

1967

C. D. David, J. Appl. Lett. 11, 394 (1967).
[CrossRef]

1966

Y. P. Raizer, Sov. Phys. Usp. 8, 650 (1966);also see F. Docchio, C. Sacchi, Invest. Ophthalmol. Vis. Sci. 29, 437 (1986).
[CrossRef]

1964

R. G. Meyerand, A. F. Haught, Phys. Rev. Lett. 13, 7 (1964);also see F. Docchio, P. Regondi, M. R. C. Capon, J. Mellerio, Appl. Opt. 27, 3669 (1988).
[CrossRef] [PubMed]

Ackerman, T. P.

Boggess, T. B.

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Boyd, I. W.

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Brown, R. A.

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

David, C. D.

C. D. David, J. Appl. Phys. 40, 3674 (1969).
[CrossRef]

C. D. David, J. Appl. Lett. 11, 394 (1967).
[CrossRef]

Donnet, J. B.

J. B. Donnet, A. Voet, Carbon Black Physics, Chemistry and Elastomer Reinforcement (Dekker, New York, 1976).

Gaddy, O. L.

K. C. Jungling, O. L. Gaddy, IEEE J. Quantum Electron. QE-7, 97 (1973).

Hagen, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Haught, A. F.

R. G. Meyerand, A. F. Haught, Phys. Rev. Lett. 13, 7 (1964);also see F. Docchio, P. Regondi, M. R. C. Capon, J. Mellerio, Appl. Opt. 27, 3669 (1988).
[CrossRef] [PubMed]

Honey, R. C.

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

Jungling, K. C.

K. C. Jungling, O. L. Gaddy, IEEE J. Quantum Electron. QE-7, 97 (1973).

Lauterborn, W.

A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
[CrossRef]

Mansour, K.

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).

K. Mansour, Ph.D. dissertation (University of North Texas, Denton, Tex., 1990).

Marburger, J. H.

J. H. Marburger, Progress in Quantum Electronics (Pergamon, London, 1977), pp. 35–110.

Meyerand, R. G.

R. G. Meyerand, A. F. Haught, Phys. Rev. Lett. 13, 7 (1964);also see F. Docchio, P. Regondi, M. R. C. Capon, J. Mellerio, Appl. Opt. 27, 3669 (1988).
[CrossRef] [PubMed]

Morgan, C. G.

C. G. Morgan, Rep. Progr. Phys.38, 621 (1976).
[CrossRef]

Moss, S. C.

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Nashold, K. M.

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

Patel, C. N. K.

C. N. K. Patel, A. C. Tam, Rev. Modern Phys. 53, 517 (1981).
[CrossRef]

Raizer, Y. P.

Y. P. Raizer, Sov. Phys. Usp. 8, 650 (1966);also see F. Docchio, C. Sacchi, Invest. Ophthalmol. Vis. Sci. 29, 437 (1986).
[CrossRef]

Ready, J. F.

J. F. Ready, Effects of High-Power Laser Radiation (Academic Press, New York, 1971).

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Smirl, A. L.

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

Soileau, M. J.

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
[CrossRef]

Tam, A. C.

C. N. K. Patel, A. C. Tam, Rev. Modern Phys. 53, 517 (1981).
[CrossRef]

Timm, R.

A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
[CrossRef]

Toon, O. B.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
[CrossRef]

Voet, A.

J. B. Donnet, A. Voet, Carbon Black Physics, Chemistry and Elastomer Reinforcement (Dekker, New York, 1976).

Vogel, A.

A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
[CrossRef]

Walter, D. P.

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

Wie, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Williams, W. E.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

M. J. Soileau, W. E. Williams, E. W. Van Stryland, IEEE J. Quantum Electron. QE-19, 731 (1983).
[CrossRef]

K. C. Jungling, O. L. Gaddy, IEEE J. Quantum Electron. QE-7, 97 (1973).

T. B. Boggess, A. L. Smirl, S. C. Moss, I. W. Boyd, E. W. Van Stryland, IEEE J. Quantum Electron. QE-21, 488 (1985).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wie, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Appl. Lett.

C. D. David, J. Appl. Lett. 11, 394 (1967).
[CrossRef]

J. Appl. Phys.

C. D. David, J. Appl. Phys. 40, 3674 (1969).
[CrossRef]

J. Fluid Mech.

A. Vogel, W. Lauterborn, R. Timm, J. Fluid Mech. 206, 299 (1989).
[CrossRef]

Opt. Commun.

W. E. Williams, M. J. Soileau, E. W. Van Stryland, Opt. Commun. 50, 256 (1984).
[CrossRef]

Phys. Rev. Lett.

R. G. Meyerand, A. F. Haught, Phys. Rev. Lett. 13, 7 (1964);also see F. Docchio, P. Regondi, M. R. C. Capon, J. Mellerio, Appl. Opt. 27, 3669 (1988).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng.

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 91 (1989).

K. Mansour, E. W. Van Stryland, M. J. Soileau, Proc. Soc. Photo-Opt. Instrum. Eng. 1307, 350 (1990).

K. M. Nashold, R. A. Brown, D. P. Walter, R. C. Honey, Proc. Soc. Photo-Opt. Instrum. Eng. 1105, 78 (1989).

Rev. Modern Phys.

C. N. K. Patel, A. C. Tam, Rev. Modern Phys. 53, 517 (1981).
[CrossRef]

Sov. Phys. Usp.

Y. P. Raizer, Sov. Phys. Usp. 8, 650 (1966);also see F. Docchio, C. Sacchi, Invest. Ophthalmol. Vis. Sci. 29, 437 (1986).
[CrossRef]

Other

J. F. Ready, Effects of High-Power Laser Radiation (Academic Press, New York, 1971).

C. G. Morgan, Rep. Progr. Phys.38, 621 (1976).
[CrossRef]

J. B. Donnet, A. Voet, Carbon Black Physics, Chemistry and Elastomer Reinforcement (Dekker, New York, 1976).

K. Mansour, Ph.D. dissertation (University of North Texas, Denton, Tex., 1990).

J. H. Marburger, Progress in Quantum Electronics (Pergamon, London, 1977), pp. 35–110.

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Figures (18)

Fig. 1
Fig. 1

Power or energy output of an ideal passive optical limiter as a function of the input peak power or energy.

Fig. 2
Fig. 2

Energy output for CS2 and CBS as a function of input peak power for 14-ns (FWHM), 532-nm pulses focused to w0 ≃ 3.5 μm for input powers of 1 to 12 kW.

Fig. 3
Fig. 3

Energy output for CS2 and CBS as a function of input peak power for 14-ns (FWHM), 532-nm pulses focused to w0 ≃ 3.5 μm for input powers of 1 to 1000 W.

Fig. 4
Fig. 4

Limiting threshold fluence as a function of beam radius for 20-ns (FWHM), 1064-nm laser pulses. Circles represent the measured value for a 100-μm-thick flowing jet of CBS with 70% linear transmittance, and ×’s are for a 1-cm-thick sample of CBS with a 70% linear transmittance at 1064 nm (the thin-sample criterion is satisfied).

Fig. 5
Fig. 5

Energy output for CBG and glass substrate as a function of input peak power for 20-ns (FWHM), 1064-nm pulses focused to w0 ≃ 8 μm. The solid lines are guides for the eye.

Fig. 6
Fig. 6

Transmittance of flowing (open diamonds) and nonflowing (filled circles) CBS as a function of the number of pulses at a repetition rate of 10 Hz with a beam radius of 330 μm and input energy of 2.8 mJ for 20-ns (FWHM), 1064-nm laser pulses. The maximum transmittance of ≃70% is from the finite aperture of the detector in this experiment.

Fig. 7
Fig. 7

Schematic diagram for simultaneous measurements of transmittance, absorptance, and the fraction of side-scattered light. BS, beam splitter.

Fig. 8
Fig. 8

Transmittance, absorptance, and scattering fraction as a function of incident fluence for 1064-nm, 20-ns (FWHM) pulses focused to w0 ≃ 156 μm for incident fluences of 0.08 to 1 J/cm2.

Fig. 9
Fig. 9

Transmittance, absorptance, and scattering fraction as a function of incident fluence for 1064-nm, 20-ns (FWHM) pulses focused to w0 ≃ 156 μm for incident fluences of 1 to 12 J/cm2.

Fig. 10
Fig. 10

Photographs of side-scattered 532-nm light from a 1-cm cuvette of CBS for (a) low and (b) high incident intensities (fluences).

Fig. 11
Fig. 11

Temporal profiles of the incident and transmitted 532-nm, 14-ns (FWHM) laser pulses. (a) Incident and transmitted pulses for fluences of ≃100 mJ/cm2 (below threshold). (b) Incident (attenuated by a factor of 10) and transmitted pulses for a fluence of ≃1.1 J/cm2 (above threshold). The spot size was w0 ≃ 250 μm.

Fig. 12
Fig. 12

Spectral emission from carbon particles irradiated by 40-ns, 1.064-μm laser pulses. The triangles show tabulated wavelengths for singly ionized emission lines. The thick solid curve shows the calculated emission for a blackbody source at 4250 K.

Fig. 13
Fig. 13

Semilogarithmic plot of the emission signal at 800 nm as a function of time.

Fig. 14
Fig. 14

Semilogarithmic plot of the He–Ne probe-beam transmittance as a function of time for different input powers for 20-ns (FWHM), 1.064-μm excitation pulses for a sample of a CBS with 70% linear transmittance. The dots highlight the digitized curves at specific time intervals.

Fig. 15
Fig. 15

Semilogarithmic plot of the He–Ne probe-beam transmittance as a function of time for a 4.2-kW, 20-ns (FWHM), 1.064-μm laser pulse for a sample of CBG with 28% linear transmission at 632.8 nm. The dots, triangles, and squares highlight the digitized curves at specific time intervals.

Fig. 16
Fig. 16

Polar plot of the fraction of scattered light (arbitrarily scaled) for a CBS for an incident fluence of ≃550 mJ/cm2 for 20-ns (FWHM), 1064-nm linearly polarized light parallel to the plane of observation. The spot size was w0 ≃ 96 μm. The theoretical fit is based on Mie scattering theory.

Fig. 17
Fig. 17

Polar plot of the fraction of scattered light (arbitrarily scaled) for a CBS for an incident fluence of ≃1.5 J/cm2 for 20-ns (FWHM), w0 ≃ 96 μm, 1064-nm linearly polarized light parallel to the plane of observation. The theoretical fit is based on Mie scattering theory.

Fig. 18
Fig. 18

Plot of transmittance of a 1-cm-thick sample of CBS with ≃60% linear transmittance at 532 nm as a function of input energy for a thick limiter for 5-ns (FWHM) laser pulses for input lenses with focal lengths of 51, 25.5, and 10 mm.

Tables (1)

Tables Icon

Table 1 Limiting Thresholds for CBS and CS2 in a Tight-Focusing Geometry

Equations (5)

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

z 0 = π w 0 2 λ ,
A = π w 0 2 2 .
Δ T F z 0 = Energy A z 0 = Energy 2 π w 0 2 π w 0 2 λ = Energy 2 λ .
d I I = β I d z ,
Δ T = Δ I I = β I L eff ,

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