Abstract

We theoretically and experimentally study absorption of picosecond laser pulses in materials described by a four-level system that exhibit reverse saturable absorption (RSA). Using an approximate solution to the rate equations, we derive, analyze, and verify, numerically and experimentally, a single dynamical equation for the spatial evolution of the pulse fluence that includes both the rate equations and the propagation equation. This analytical approach considerably simplifies the study of optical limiting with picosecond pulses and helps to predict the behavior of the nonlinear transmittance, the level of output signal clamping, and a possible turnover from RSA to saturable absorption that restricts the performance of optical limiters based on RSA. The results obtained can also be used to characterize RSA materials by the pump–probe technique.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. Perry, “Organic and metal-containing reverse saturable absorbers for optical limiters,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa and S. Miyata, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 813–840.
  2. K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
    [CrossRef]
  3. J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
    [CrossRef]
  4. O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
    [CrossRef]
  5. K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
    [CrossRef]
  6. T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
    [CrossRef]
  7. S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
    [CrossRef]
  8. L. W. Tutt and 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]
  9. E. W. Van Stryland, D. J. Hagan, T. Xia, and A. A. Said, “Application of nonlinear optics to passive optical limiting” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa and S. Miyata, eds., (CRC Press, Boca Raton, Fla., 1997), pp. 840–860.
  10. J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
    [CrossRef]
  11. J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
    [CrossRef]
  12. F. E. Hernández, S. Yang, E. W. Van Stryland, and D. J. Hagan, “High-dynamic-range cascaded-focus optical limiter,” Opt. Lett. 25, 1180–1182 (2000).
    [CrossRef]
  13. J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
    [CrossRef]
  14. D. J. Hagan, T. Xia, A. A. Said, T. H. Wei, and E. W. Van Stryland, “High dynamic range passive optical limiters,” Int. J. Nonlinear Opt. Phys. 2, 483–501 (1993).
    [CrossRef]
  15. M. Hercher, “An analysis of saturable absorbers,” Appl. Opt. 6, 947–954 (1967).
    [CrossRef] [PubMed]
  16. C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
    [CrossRef] [PubMed]
  17. C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
    [CrossRef] [PubMed]
  18. S. Hughes and B. Wherrett, “Multilevel rate equation analysis to explain the recent observations of limitations to optical limiting dyes,” Phys. Rev. A 54, 3546–3552 (1996).
    [CrossRef] [PubMed]
  19. T. Xia, D. J. Hagan, A. Dogariu, A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited state absorption,” Appl. Opt. 36, 4110–4122 (1997).
    [CrossRef] [PubMed]
  20. P. Miles, “Bottleneck optical pulse limiters revisited,” Appl. Opt. 38, 566–570 (1999).
    [CrossRef]
  21. P. Miles, “Bottleneck optical limiters: the optimal use of excited-state absorbers,” Appl. Opt. 33, 6965–6979 (1994).
    [CrossRef] [PubMed]
  22. X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
    [CrossRef]
  23. A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Analytical approach to dynamics of reverse saturable absorbers,” J. Opt. Soc. Am. B 17, 1884–1893 (2000).
    [CrossRef]
  24. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760–769 (1990).
    [CrossRef]
  25. S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
    [CrossRef]
  26. J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
    [CrossRef]

2000 (2)

1999 (7)

P. Miles, “Bottleneck optical pulse limiters revisited,” Appl. Opt. 38, 566–570 (1999).
[CrossRef]

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
[CrossRef]

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

1998 (1)

1997 (2)

T. Xia, D. J. Hagan, A. Dogariu, A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[CrossRef] [PubMed]

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

1996 (3)

S. Hughes and B. Wherrett, “Multilevel rate equation analysis to explain the recent observations of limitations to optical limiting dyes,” Phys. Rev. A 54, 3546–3552 (1996).
[CrossRef] [PubMed]

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

1995 (3)

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

1994 (2)

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

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

1993 (2)

L. W. Tutt and 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]

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

1990 (1)

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

1967 (1)

Bartoli, F. J.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Bedworth, P. V.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Boggess, T. F.

L. W. Tutt and 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]

Bondar, M. V.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

Boyle, M. E.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Bramerie, L.

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

Brinkmann, D.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Chen, C. T.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Deng, X.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

Dogariu, A.

Dou, K.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Flom, S. R.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Guo, Y.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Hagan, D. J.

F. E. Hernández, S. Yang, E. W. Van Stryland, and D. J. Hagan, “High-dynamic-range cascaded-focus optical limiter,” Opt. Lett. 25, 1180–1182 (2000).
[CrossRef]

A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Analytical approach to dynamics of reverse saturable absorbers,” J. Opt. Soc. Am. B 17, 1884–1893 (2000).
[CrossRef]

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

T. Xia, D. J. Hagan, A. Dogariu, A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[CrossRef] [PubMed]

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

Hercher, M.

Hernández, F. E.

Hollins, R. C.

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Honerlage, B.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Huang, T. H.

T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
[CrossRef]

Hughes, S.

S. Hughes and B. Wherrett, “Multilevel rate equation analysis to explain the recent observations of limitations to optical limiting dyes,” Phys. Rev. A 54, 3546–3552 (1996).
[CrossRef] [PubMed]

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Jonusauskas, G.

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

Joucla, M.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Khodja, S.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

Knobbe, E. T.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Kobyakov, A.

Lee, Y. S.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Levy, R.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Li, C.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

Lim, J. H.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

Liu, S.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

Mansour, K.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Marder, S. R.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Miles, P.

P. Miles, “Bottleneck optical pulse limiters revisited,” Appl. Opt. 38, 566–570 (1999).
[CrossRef]

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

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

Ng, D.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Oberle, J.

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

Ohlmann, D.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Parkhill, R.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Perry, J. W.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Pong, R. G. S.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Przhonska, O. V.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

Rehspringer, J. L.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Ross, T. S.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

Rulliere, C.

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

Said, A.

Said, A. A.

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

Sambles, J. R.

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

Sasabe, H.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Schell, J.

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

Sheik-Bahae, M.

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

Shirk, J. S.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Si, J.

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

Slominsky, Y. L.

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

Snow, A. W.

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Song, Y.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

Spruce, G.

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Sun, X.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Swatton, S. N. R.

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Tian, M.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Till, S. J.

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

Tutt, L. W.

L. W. Tutt and 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]

Van Stryland, E. W.

A. Kobyakov, D. J. Hagan, and E. W. Van Stryland, “Analytical approach to dynamics of reverse saturable absorbers,” J. Opt. Soc. Am. B 17, 1884–1893 (2000).
[CrossRef]

F. E. Hernández, S. Yang, E. W. Van Stryland, and D. J. Hagan, “High-dynamic-range cascaded-focus optical limiter,” Opt. Lett. 25, 1180–1182 (2000).
[CrossRef]

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

O. V. Przhonska, J. H. Lim, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Nonlinear light absorption of polymethine dyes in liquid and solid media,” J. Opt. Soc. Am. B 15, 802–809 (1998).
[CrossRef]

T. Xia, D. J. Hagan, A. Dogariu, A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[CrossRef] [PubMed]

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

Wada, T.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Wang, H.

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

Wang, R.

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

Wang, X.

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

Wang, Y.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

Wei, T. H.

T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
[CrossRef]

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

Welford, K. R.

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Wen, T. C.

T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
[CrossRef]

Wherrett, B.

S. Hughes and B. Wherrett, “Multilevel rate equation analysis to explain the recent observations of limitations to optical limiting dyes,” Phys. Rev. A 54, 3546–3552 (1996).
[CrossRef] [PubMed]

Wherrett, B. S.

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Wu, X. L.

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Xia, T.

T. Xia, D. J. Hagan, A. Dogariu, A. Said, and E. W. Van Stryland, “Optimization of optical limiting devices based on excited state absorption,” Appl. Opt. 36, 4110–4122 (1997).
[CrossRef] [PubMed]

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

Yang, M.

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

Yang, S.

F. E. Hernández, S. Yang, E. W. Van Stryland, and D. J. Hagan, “High-dynamic-range cascaded-focus optical limiter,” Opt. Lett. 25, 1180–1182 (2000).
[CrossRef]

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

Zhang, L.

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

Zhang, X.

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. Lett. (2)

S. N. R. Swatton, K. R. Welford, R. C. Hollins, and J. R. Sambles, “A time resolved double pump-probe experimental technique to characterize excited-state parameters of organic dyes,” Appl. Phys. Lett. 71, 10–12 (1997).
[CrossRef]

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868–1870 (1995).
[CrossRef]

Chem. Phys. (1)

J. H. Lim, O. V. Przhonska, S. Khodja, S. Yang, T. S. Ross, D. J. Hagan, E. W. Van Stryland, M. V. Bondar, and Y. L. Slominsky, “Polymethine and squarylium molecules with large excited-state absorption,” Chem. Phys. 245, 79–97 (1999).
[CrossRef]

Chem. Phys. Lett. (1)

T. H. Wei, T. H. Huang, and T. C. Wen, “Mechanism of reverse saturable absorption in chloro-aluminium phthalocyanine solution studied with Z-scan,” Chem. Phys. Lett. 314, 403–410 (1999).
[CrossRef]

IEEE J. Quantum Electron. (2)

K. Dou, X. Sun, X. Wang, R. Parkhill, Y. Guo, and E. T. Knobbe, “Optical limiting and nonlinear absorption of excited states in metalloporphyrin-doped sol gels,” IEEE J. Quantum Electron. 35, 1004–1014 (1999).
[CrossRef]

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

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

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

J. Chem. Phys. (1)

J. Schell, D. Ohlmann, D. Brinkmann, R. Levy, M. Joucla, J. L. Rehspringer, and B. Honerlage, “Reverse saturable absorption in C60-doped porous glasses studied by single- and double-pulse pump-probe experiments,” J. Chem. Phys. 111, 5929–5937 (1999).
[CrossRef]

J. Opt. Soc. Am. B (2)

Mater. Res. Soc. Symp. Proc. (1)

K. R. Welford, S. N. R. Swatton, S. Hughes, S. J. Till, G. Spruce, R. C. Hollins, and B. S. Wherrett, “Nonlinear absorption in organic dyes,” Mater. Res. Soc. Symp. Proc. 374, 239–256 (1995).
[CrossRef]

Opt. Commun. (2)

X. Deng, X. Zhang, Y. Wang, Y. Song, S. Liu, and C. Li, “Intensity threshold in the conversion from reverse saturable absorption to saturable absorption and its application in optical limiting,” Opt. Commun. 168, 207–212 (1999).
[CrossRef]

J. Oberle, L. Bramerie, G. Jonusauskas, and C. Rulliere, “Optical-limiting properties of a push-pull diphenyl-butadiene,” Opt. Commun. 169, 325–332 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (3)

C. Li, L. Zhang, M. Yang, H. Wang, and Y. Wang, “Dynamic and steady- state behaviors of reverse saturable absorption in metallophthalocyanine,” Phys. Rev. A 49, 1149–1157 (1994).
[CrossRef] [PubMed]

C. Li, J. Si, M. Yang, R. Wang, and L. Zhang, “Excited-state nonlinear absorption in multi-energy-level molecular systems,” Phys. Rev. A 51, 569–575 (1995).
[CrossRef] [PubMed]

S. Hughes and B. Wherrett, “Multilevel rate equation analysis to explain the recent observations of limitations to optical limiting dyes,” Phys. Rev. A 54, 3546–3552 (1996).
[CrossRef] [PubMed]

Prog. Quantum Electron. (1)

L. W. Tutt and 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]

Pure Appl. Opt. (1)

J. S. Shirk, R. G. S. Pong, S. R. Flom, F. J. Bartoli, M. E. Boyle, and A. W. Snow, “Lead phthalocyanine reverse saturable absorption optical limiters,” Pure Appl. Opt. 5, 701–707 (1996).
[CrossRef]

Science (1)

J. W. Perry, K. Mansour, Y. S. Lee, X. L. Wu, P. V. Bedworth, C. T. Chen, D. Ng, S. R. Marder, P. Miles, T. Wada, M. Tian, and H. Sasabe, “Organic optical limiter with a strong nonlinear response,” Science 273, 1533–1536 (1996).
[CrossRef]

Other (2)

J. W. Perry, “Organic and metal-containing reverse saturable absorbers for optical limiters,” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa and S. Miyata, eds. (CRC Press, Boca Raton, Fla., 1997), pp. 813–840.

E. W. Van Stryland, D. J. Hagan, T. Xia, and A. A. Said, “Application of nonlinear optics to passive optical limiting” in Nonlinear Optics of Organic Molecules and Polymers, H. S. Nalwa and S. Miyata, eds., (CRC Press, Boca Raton, Fla., 1997), pp. 840–860.

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 (8)

Fig. 1
Fig. 1

Schematic diagram of the four-level model of RSA with picosecond pulse illumination; 0 is the ground state and 1–3 are excited singlet states.

Fig. 2
Fig. 2

Chemical structure of dye PD3.

Fig. 3
Fig. 3

Population dynamics of two RSA materials excited by a temporal flat-topped pulse with a pulse width of τp=25 ps (FWHM). The results were obtained by use of the exact analytical solution to the rate equations, [Eq. (7); solid curves] and the approximate analytical solution [formulas (12)–(14); dashed curves]. The parameters are (a) for HITCI: A=2, α=32, β=0.1, τ10=1.7 ns, and τ21=10 ps and (b) for PD3: A=0.7, α=200, β=2, τ10=1 ns, τ21=1.9 ps. Each material has a linear transmittance of 0.905 (Z=0.1).

Fig. 4
Fig. 4

Transmittance (Fout/Fin) as a function of normalized propagation distance Z=σ01Nz for the dyes in Fig. 3: (a) HITCI, (b) PD3. Dotted and dashed curves, the numerical solutions to Eqs. (3) and (4) for a Gaussian (FWHM, τp=23.5 ps) and a flat-topped pulse shape, respectively. Solid curves, numerical solution to ODE (15).

Fig. 5
Fig. 5

Transmittance (Fout/Fin) as a function of normalized input fluence for the dyes in Fig. 3: (a) HITCI, (b) PD3. Solid curves, limiting curves calculated by use of the numerical solution to ODE (15). Open and solid circles, limiting curves calculated from the full system of PDEs (3) and (4) for flat-topped and Gaussian pulses, respectively.

Fig. 6
Fig. 6

Limiting curves calculated for HITCI from the numerical solution to Eq. (15) derived from the dynamical solution to the rate equations (filled circles) and the numerical solution to Eq. (17) derived from the steady-state solution to the rate equations (open circles). Pulse width, (FWHM) 25 ps.

Fig. 7
Fig. 7

Experimentally measured limiting curve (triangles) for (a) HITCI and (b) PD3 with the best-fit material parameters used in the numerical solution to Eq. (15) (solid curves) and the full system of PDEs (3) and (4) for a Gaussian pulse (dashed curves).

Fig. 8
Fig. 8

Experimentally measured limiting curve (triangles) for CAP with best-fit material parameters used in the numerical solution to Eq. (15) (solid curves) and the full system of PDEs (3) and (4) for a Gaussian pulse (dashed curve).

Tables (1)

Tables Icon

Table 1 Turnover Fluence (mJ/cm2) Determined from Experimental and Numerical Results

Equations (25)

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

N0t=-σ01IωN0+N1τ10,
N1t=σ01IωN0-N1τ10-σ12IωN1+N2τ21,
N2t=σ12IωN1-N2τ21,
Iz=-I(σ01N0+σ12N1+σ23N2).
n0T=-Φn0+T10n1,
n1T=Φn0-(αΦ+T10)n1+T21n2,
n2T=αΦn1-T21n2,
ΦZ=-Φ(n0+αn1+βn2).
λ±=(1/2)[-(α++q+1)±D]<0,
D=α2+2α(q-1+)+(q-1-)2,
n0n1n2=Cq-(λ-+q)λ+D(λ-+1)(λ++q)λ-D(λ++1)q-(λ-+q)λ+D(λ++q)λ-Dα-αλ+Dαλ-D×1exp(λ-AT)exp(λ+AT),
C=(λ++1)(λ-+1)λ+λ-(q-1).
n0n1n2=α++1(α++1)(α+)αα+1α++1-1α++10αα++1α(α++1)(α+)-αα+×1exp[-(α++1)AT]exp(-AT).
λ+-1+ 1-qα+q-1,
λ--α-q- αα+q-1,
Dα+q-1+ α-q+1α+q-1,
Cα+q,
n0(T)exp(-AT),
n1(T)qα+q+1-qα+q-1 exp(-AT),
n2(T)αα+q-αα+q-1 exp(-AT).
dFdZ=α (β-α)F(α-1)F+T21+α-1(1-e-F)-α1+(β-α)FαF+T21F=-σeff(F)F,
α(β-α)T21F2(αF-F+T21)2+T21F(αF+T21)2(1-e-F)(α2-αβ)+[(F+1)e-F-1](αF-F+T21)(αF+T21)2×[(2α-αβ-1)F-(α-1)T21]=0,
dA˜dZ=-A˜(V+αA˜+βαA˜2)V+A˜+αA˜2,
u(Fout)u(Fin)exp[-α(β+T21)Z],
u(F)=(F-1)T21+αF+T21βT21(α-β)/β.

Metrics