Abstract

Limiting devices protect sensitive optical elements from laser-induced damage (LID). Passive devices use focusing optics to concentrate the light through a nonlinear optical (NLO) element (or elements) to reduce the limiting threshold. Unfortunately, these NLO elements may themselves undergo LID for high inputs, restricting the useful dynamic range (DR). Recently, efforts at optimizing this DR have focused on distributing the NLO material along the propagation path z of a focused beam, resulting in different portions of the device (in z) exhibiting NLO response at different inputs. For example, nonlinear absorbers closer to the lens, i.e., upstream, protect device elements downstream near the focal plane. This results in an undesirable increase in the threshold, although the lowest threshold is always obtained with the final element at focus. Thus there is a compromise between DR and threshold. This compromise is determined by the material. We concentrate on reverse saturable absorber (RSA) materials (molecules exhibiting larger excited-state than ground-state absorption). We look at both tandem devices and devices in which the concentration of the NLO material is allowed to spatially vary in z. These latter devices require solid-state hosts. The damage threshold of currently available solid-state hosts is too low to allow known RSA materials to reach their maximum absorption, which occurs when all molecules are in their excited state. This is demonstrated by approximate analytical methods as well as by a full numerical solution of the nonlinear wave propagation equation over extremely large distances in z (up to 103 Z 0, where Z 0 is the Rayleigh range of the focused beam). The numerical calculations, based on a one-dimensional fast Fourier transform, indicate that proper inclusion of diffraction reduces the effectiveness of reverse saturable absorption for limiting, sometimes by more than a factor of 10. Liquid-based devices have higher damage thresholds (damage occurs to the cuvette wall) and, thus, larger nonlinear absorption. However, RSA material in liquid hosts may suffer from larger thermal lensing.

© 1997 Optical Society of America

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  1. G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
    [CrossRef]
  2. L. W. Tutt, T. F. Boggess, “A review of optical limiting mechanisms and devices using organics fullerenes semiconductors and other materials, ,” Prog. Quantum Electron. 17, 299–338 (1993).
    [CrossRef]
  3. K. Mansour, E. W. Van Stryland, M. J. Soileau, “Nonlinear optical properties of carbon black suspensions,” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
    [CrossRef]
  4. A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
    [CrossRef] [PubMed]
  5. D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
    [CrossRef]
  6. E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
    [CrossRef]
  7. T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
    [CrossRef]
  8. D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
    [CrossRef]
  9. K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.
  10. D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.
  11. P. A. Miles, “Bottleneck optical limiters: the optimal use of excited-state absorbers,” Appl. Opt. 33, 6965–6979 (1994).
    [CrossRef] [PubMed]
  12. D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
    [CrossRef]
  13. J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
    [CrossRef]
  14. C. R. Guliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser radiation,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).
    [CrossRef]
  15. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
    [CrossRef]
  16. A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
    [CrossRef]
  17. S. W. McCahon, L. W. Tutt, “Optical Limiter Including Optical Convergence and Absorbing Body with Inhomogeneous Distribution of Reverse Saturable Material,” U.S. Patent5,080,469 (14January1992).
  18. M. D. Feit, J. A. Fleck, “Simple spectral method for solving propagation problems in cylindrical geometry,” Opt. Lett. 14, 662–664 (1989).
    [CrossRef] [PubMed]
  19. J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
    [CrossRef]
  20. S. C. Sheng, “Studies of Laser Resonators and Beam Propagation Using Fast Transform Methods,” (Stanford University, Stanford, Calif., 1980).
  21. T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1994).
  22. A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
    [CrossRef]

1995 (1)

1994 (2)

P. A. Miles, “Bottleneck optical limiters: the optimal use of excited-state absorbers,” Appl. Opt. 33, 6965–6979 (1994).
[CrossRef] [PubMed]

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

1993 (3)

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

L. W. Tutt, T. F. Boggess, “A review of optical limiting mechanisms and devices using organics fullerenes semiconductors and other materials, ,” Prog. Quantum Electron. 17, 299–338 (1993).
[CrossRef]

1992 (2)

K. Mansour, E. W. Van Stryland, M. J. Soileau, “Nonlinear optical properties of carbon black suspensions,” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

1990 (1)

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

1989 (1)

1988 (2)

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

1976 (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

1967 (1)

C. R. Guliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser radiation,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).
[CrossRef]

Bartoli, F. J.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

Boggess, T. F.

L. W. Tutt, T. F. Boggess, “A review of optical limiting mechanisms and devices using organics fullerenes semiconductors and other materials, ,” Prog. Quantum Electron. 17, 299–338 (1993).
[CrossRef]

Chen, C. T.

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

Clark, W. W.

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

Coulter, D. R.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

DeSalvo, J. R.

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

Dillard, A. G.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

Dogariu, A.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

Feit, M. D.

M. D. Feit, J. A. Fleck, “Simple spectral method for solving propagation problems in cylindrical geometry,” Opt. Lett. 14, 662–664 (1989).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Fleck, J. A.

M. D. Feit, J. A. Fleck, “Simple spectral method for solving propagation problems in cylindrical geometry,” Opt. Lett. 14, 662–664 (1989).
[CrossRef] [PubMed]

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Guliano, C. R.

C. R. Guliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser radiation,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).
[CrossRef]

Hagan, D. J.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

Hess, L. D.

C. R. Guliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser radiation,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).
[CrossRef]

Mansour, K.

K. Mansour, E. W. Van Stryland, M. J. Soileau, “Nonlinear optical properties of carbon black suspensions,” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

Marder, S. R.

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

McCahon, S. W.

S. W. McCahon, L. W. Tutt, “Optical Limiter Including Optical Convergence and Absorbing Body with Inhomogeneous Distribution of Reverse Saturable Material,” U.S. Patent5,080,469 (14January1992).

Miles, P.

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

Miles, P. A.

Miller, M. J.

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

Miskowski, V. M.

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

Mohebi, M.

Morris, J. R.

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Perry, J. W.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

Pong, R. G. S.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

Reinherdt, B. A.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

Roderer, P.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

Said, A. A.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

Salamo, G. J.

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

Sence, M. J.

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

Sharp, E. J.

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

Sheng, S. C.

S. C. Sheng, “Studies of Laser Resonators and Beam Propagation Using Fast Transform Methods,” (Stanford University, Stanford, Calif., 1980).

Shirk, J. S.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

Snow, A. W.

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

Soileau, M. J.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

K. Mansour, E. W. Van Stryland, M. J. Soileau, “Nonlinear optical properties of carbon black suspensions,” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

Tutt, L. W.

L. W. Tutt, T. F. Boggess, “A review of optical limiting mechanisms and devices using organics fullerenes semiconductors and other materials, ,” Prog. Quantum Electron. 17, 299–338 (1993).
[CrossRef]

S. W. McCahon, L. W. Tutt, “Optical Limiter Including Optical Convergence and Absorbing Body with Inhomogeneous Distribution of Reverse Saturable Material,” U.S. Patent5,080,469 (14January1992).

Van Stryland, E. W.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

K. Mansour, E. W. Van Stryland, M. J. Soileau, “Nonlinear optical properties of carbon black suspensions,” J. Opt. Soc. Am. B 9, 1100–1109 (1992).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

Wamsley, C.

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

Wei, T. H.

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

Wood, G. L.

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

Wu, Y. Y.

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

Xia, T.

A. A. Said, T. Xia, A. Dogariu, D. J. Hagan, M. J. Soileau, E. W. Van Stryland, M. Mohebi, “Measurement of the optical damage threshold in fused quartz,” Appl. Opt. 34, 3374–3376 (1995).
[CrossRef] [PubMed]

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1994).

Appl. Opt. (2)

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, M. D. Feit, “Time-dependent propagation of high energy laser beams through the atmosphere,” Appl. Phys. 10, 129–160 (1976).
[CrossRef]

Appl. Phys. B (1)

T. H. Wei, D. J. Hagan, M. J. Sence, E. W. Van Stryland, J. W. Perry, D. R. Coulter, “Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines,” Appl. Phys. B 54, 46–51 (1992).
[CrossRef]

Appl. Phys. Lett. (1)

J. S. Shirk, R. G. S. Pong, F. J. Bartoli, A. W. Snow, “Optical limiter using a lead phthalocyanine,” Appl. Phys. Lett. 63, 1880–1882 (1993).
[CrossRef]

Chem. Phys. Lett. (1)

A. A. Said, C. Wamsley, D. J. Hagan, E. W. Van Stryland, B. A. Reinherdt, P. Roderer, A. G. Dillard, “Third and fifth order optical nonlinearities in organic materials,” Chem. Phys. Lett. 228, 646–650 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

C. R. Guliano, L. D. Hess, “Nonlinear absorption of light: optical saturation of electronic transitions in organic molecules with high intensity laser radiation,” IEEE J. Quantum Electron. QE-3, 358–367 (1967).
[CrossRef]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. QE-26, 760–769 (1990).
[CrossRef]

Int. J. Nonlinear Opt. Phys. (1)

D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

E. W. Van Stryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. 5, 1980–1989 (1988).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Opt. Lett. B (1)

D. J. Hagan, E. W. Van Stryland, M. J. Soileau, Y. Y. Wu, “Self-protecting semiconductor optical limiters,” Opt. Lett. B 13, 315–317 (1988).
[CrossRef]

Prog. Quantum Electron. (1)

L. W. Tutt, T. F. Boggess, “A review of optical limiting mechanisms and devices using organics fullerenes semiconductors and other materials, ,” Prog. Quantum Electron. 17, 299–338 (1993).
[CrossRef]

Other (8)

G. L. Wood, W. W. Clark, M. J. Miller, G. J. Salamo, E. J. Sharp, “Evaluation of passive optical switches and limiters,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 154–180 (1989).
[CrossRef]

K. Mansour, C. T. Chen, S. R. Marder, J. W. Perry, P. Miles, ‘Demonstration of strongly saturated multiple plate optical limiter based on excited state absorbers,” in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D. C., 1994), p. 418.

D. J. Hagan, T. Xia, A. A. Said, A. Dogariu, E. W. Van Stryland, “Optimization of reverse saturable absorber limiters: material requirements and design considerations,” in Materials for Optical Limiting, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds., MRS Symp. Proc.374, (Materials Research Society, Boston, 1995), pp. 161–172.

D. R. Coulter, V. M. Miskowski, J. W. Perry, T. H. Wei, E. W. Van Stryland, D. J. Hagan, “Optical limiting in solutions of metallo-phthalocyanines,” in Materials for Optical Switches, Isolators, and Limiters, M. J. Soileau, ed., Proc. SPIE1105, 42–51 (1989).
[CrossRef]

A. A. Said, T. H. Wei, J. R. DeSalvo, M. Sheik-Bahae, D. J. Hagan, E. W. Van Stryland, “Self-protecting optcal limiters using cascaded geometries,” in Nonlinear and Electro Optic Materials for Optical Switching, M. Soileau, ed., Proc. SPIE1692, 37–44 (1992).
[CrossRef]

S. W. McCahon, L. W. Tutt, “Optical Limiter Including Optical Convergence and Absorbing Body with Inhomogeneous Distribution of Reverse Saturable Material,” U.S. Patent5,080,469 (14January1992).

S. C. Sheng, “Studies of Laser Resonators and Beam Propagation Using Fast Transform Methods,” (Stanford University, Stanford, Calif., 1980).

T. Xia, “Modeling and experimental studies of nonlinear optical self-action,” Ph.D. dissertation (University of Central Florida, Orlando, Florida, 1994).

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Figures (13)

Fig. 1
Fig. 1

On-axis fluence as a function of propagation distance for (a) a single-element limiter, (b) a two-element tandem limiter, and (c) a four-element limiter at maximum input energy. Each limiter uses the same nonlinear material, with concentrations adjusted so that the overall limiter transmittance is the same in each case.

Fig. 2
Fig. 2

Five-level model of excited-state absorption and equivalent quasi three-level model.

Fig. 3
Fig. 3

Dependence of σeff I g and σeff F g on normalized incident fluence F/F s for SnPc.

Fig. 4
Fig. 4

Normalized effective fluence cross section σeff F g for SnPc as numerically calculated for a five-level system for several pulse widths, as a function of normalized input fluence.

Fig. 5
Fig. 5

Graded limiter length L in units of Z 0 versus linear transmittance T L for several values of Σ.

Fig. 6
Fig. 6

Transmittance at maximum input versus linear transmittance T L for several values of Σ.

Fig. 7
Fig. 7

Dynamic range, or figure of merit, versus T L for a graded limiter and several tandem limiters with cell linear transmittance T l , based on the material parameters of SnPc.

Fig. 8
Fig. 8

Effective cell cross section σeff c versus fluence for several values of cell linear transmittance T l .

Fig. 9
Fig. 9

(a) Calculated on-axis fluence as a function of z for the analytically determined molecular distribution of Eq. 10 (solid curve) and the numerically optimized graded density limiter (dashed curve). The fluence at the input to both distributions (at z/Z 0 = -135) is 3 J/cm2. (b) Analytically (solid curve) and numerically (dashed curve) calculated molecular distributions for the graded density limiter.

Fig. 10
Fig. 10

(a) Radial distribution of fluence at the output of the graded density limiter, as calculated by the numerical propagation code as compared with a Gaussian. (b) Radial distribution of fluence at the output of the four-element tandem limiter, as calculated by the numerical propagation code as compared with a Gaussian.

Fig. 11
Fig. 11

(a) Numerically calculated irradiance at the output of the optimized graded density limiter, as a function of radial position and time for a spatially and temporally Gaussian input. Note that the output is greatly advanced in time as expected for a fluence limiter. (b) Output irradiance distribution for the four-element limiter, as calculated by the numerical propagation code.

Fig. 12
Fig. 12

(a) Numerically calculated on-axis fluence for the four-element limiter as a function of z/Z 0, as calculated with the numerical beam-propagation code. The material and geometric parameters are the same as used for Fig. 1, which was calculated assuming a constant beam shape. (b) Detail of Fig. 12(a) near the focal plane. Note that in the final nonlinear element, the fluence reaches a minimum and starts to increase with z, as predicted in Refs. 11 and 17.

Fig. 13
Fig. 13

Comparison between analytically and numerically determined figures of merit for (a) graded density and (b) four-element tandem limiters, as a function of T L .

Equations (29)

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

N1t=-σgIω N1+N2τ21,
N2t=σgIωN1-N2τ2,
N4t=N2τ24,
N0=N1+N2+N4,
Iz=-σgN1+σsN2+σtN4I,
DRMAX=TL1-σex/σg.
I/z=-N0Iσg exp-Ft/FS+σex1-exp-Ft/FS,
F/z=-σexN0F+σg-σexexp-F/FS-1N0FS,
F/z=-σeffFN0F.
Fz=--σgN1t+σsN2t+σtN4tItdt,
σeffc=lnFin/Fout/N0L.
FzF=Fd=0.
Fz=FzD+FzA=0,
N0x=-x1+x22σgZ01 for x < 0,
TL=exp-z1z2N0zσgdz=1+x221+x121/.
Em=1+x121+x22Eout=EoutTL-.
DR=TL1-,
x12=Fp/Fd-1,  x22=TLFp/Fd-1,
Eout=πFd2 w021+x22.
Eout=2π Fdλ2f/#2,
L=Z0TL--1.
DR=j=1,nTljTmj,
DR=TlTmn.
x1=Fp/Fd-1.
xj=1+xj-12Tmj-1-1,
Eout=2π Fdλ2f/#2Tmin1+xn2,
zΨr, z, t=12ikT2+k02χNLΨr, z, t,
Ψr, z+Δz, t=expzz+ΔzSzdzΨr, z, t,
Sz=12ikT2+k02χNLz.

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