Abstract

Recently observed nonlinear-propagation and optical-limiting effects of nanosecond and picosecond laser pulses through a fiber are analyzed with a model that accounts for various molecular photonic-absorption processes including linear, two-photon, intermediate, and excited-state absorptions. Explicit expressions for the laser-induced molecular-level density changes, the thermal–density effects following photoabsorption, and their effects on the laser propagation transmission are obtained for conditions corresponding to the experimental situations. These theoretical considerations are found to correlate very well with experimental results for the transmission of picosecond and nanosecond laser pulses through the nonlinear fiber. Our analyses show that in the picosecond regime, nonlinear photonic absorptions are efficient optical-limiting processes, whereas in the nanosecond regime, thermal–density effects are the dominant contributor. We also identify a particular nonlinear core liquid that gives very low optical-limiting thresholds and clamped transmission for picosecond as well as nanosecond laser pulses.

© 1998 Optical Society of America

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References

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  1. See, for example, all the materials featured in Materials for Optical Limiting, R. Crane, K. Lewis, E. V. Stryland, and M. Khoshnevisan, eds., Mater. Res. Soc. Symp. Proc. 374 (1995). See also L. Tutt and T. Boggess, Prog. Quantum Electron. 17, 299–338 (1993).
    [CrossRef]
  2. I. C. Khoo, M. V. Wood, and B. D. Guenther, Opt. Lett. 21, 1625–1627 (1996); I. C. Khoo, U.S. patent 5, 589, 101 (31 December 1996).
    [CrossRef] [PubMed]
  3. I. C. Khoo, H. Li, P. G. LoPresti, and Y. Liang, Opt. Lett. 19, 530 (1994); see also I. C. Khoo, in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley Interscience, New York, 1996), Chap. 10, pp. 271–293.
    [CrossRef] [PubMed]
  4. I. C. Khoo and H. Li, J. Appl. Phys. B 59, 573 (1994).
    [CrossRef]
  5. F. W. Deeg and M. D. Feyer, J. Chem. Phys. 91, 2269 (1989); see also C. David and B. Baeyens-Volant, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 59, 181 (1980).
    [CrossRef]
  6. H. J. Eichler, R. Macdonald, and B. Trosken, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 231, 1 (1993); R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater. 4, 245–260 (1995).
    [CrossRef]
  7. For fullerene systems, see, for example, K. M. Nashold and D. P. Walter, J. Opt. Soc. Am. B 12, 1228–1237 (1995); see also, D. G. Mclean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, and T. Pottenger, Opt. Lett. 18, 858 (1993) and references therein.
    [CrossRef]
  8. For phthalocyanine systems, see, for example, H. S. Nalwa and J. S. Shirk, in Phthalocyanines: Properties and Applications, C. C. Leznoff and A. B. P. Lever, eds. (VCH, Deerfield Beach, Fla., 1995), Vol. 4.
  9. I. C. Khoo Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994); see also, I. C. Khoo, R. R. Michael, R. G. Lindquist, and R. J. Mansfield, J. Appl. Phys. 69, 3853 (1991).
    [CrossRef]
  10. A. Yariv, Optical Electronics in Modern Communication (Oxford U. Press, Oxford, UK, 1997).
  11. I. C. Khoo, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 207, 317–329 (1991).
    [CrossRef]

1994

I. C. Khoo and H. Li, J. Appl. Phys. B 59, 573 (1994).
[CrossRef]

1991

I. C. Khoo, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 207, 317–329 (1991).
[CrossRef]

Khoo, I. C.

I. C. Khoo and H. Li, J. Appl. Phys. B 59, 573 (1994).
[CrossRef]

I. C. Khoo, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 207, 317–329 (1991).
[CrossRef]

Li, H.

I. C. Khoo and H. Li, J. Appl. Phys. B 59, 573 (1994).
[CrossRef]

J. Appl. Phys. B

I. C. Khoo and H. Li, J. Appl. Phys. B 59, 573 (1994).
[CrossRef]

Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A

I. C. Khoo, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 207, 317–329 (1991).
[CrossRef]

Other

See, for example, all the materials featured in Materials for Optical Limiting, R. Crane, K. Lewis, E. V. Stryland, and M. Khoshnevisan, eds., Mater. Res. Soc. Symp. Proc. 374 (1995). See also L. Tutt and T. Boggess, Prog. Quantum Electron. 17, 299–338 (1993).
[CrossRef]

I. C. Khoo, M. V. Wood, and B. D. Guenther, Opt. Lett. 21, 1625–1627 (1996); I. C. Khoo, U.S. patent 5, 589, 101 (31 December 1996).
[CrossRef] [PubMed]

I. C. Khoo, H. Li, P. G. LoPresti, and Y. Liang, Opt. Lett. 19, 530 (1994); see also I. C. Khoo, in Novel Optical Materials and Applications, I. C. Khoo, F. Simoni, and C. Umeton, eds. (Wiley Interscience, New York, 1996), Chap. 10, pp. 271–293.
[CrossRef] [PubMed]

F. W. Deeg and M. D. Feyer, J. Chem. Phys. 91, 2269 (1989); see also C. David and B. Baeyens-Volant, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 59, 181 (1980).
[CrossRef]

H. J. Eichler, R. Macdonald, and B. Trosken, Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 231, 1 (1993); R. J. McEwan and R. C. Hollins, J. Nonlinear Opt. Phys. Mater. 4, 245–260 (1995).
[CrossRef]

For fullerene systems, see, for example, K. M. Nashold and D. P. Walter, J. Opt. Soc. Am. B 12, 1228–1237 (1995); see also, D. G. Mclean, R. L. Sutherland, M. C. Brant, D. M. Brandelik, P. A. Fleitz, and T. Pottenger, Opt. Lett. 18, 858 (1993) and references therein.
[CrossRef]

For phthalocyanine systems, see, for example, H. S. Nalwa and J. S. Shirk, in Phthalocyanines: Properties and Applications, C. C. Leznoff and A. B. P. Lever, eds. (VCH, Deerfield Beach, Fla., 1995), Vol. 4.

I. C. Khoo Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley Interscience, New York, 1994); see also, I. C. Khoo, R. R. Michael, R. G. Lindquist, and R. J. Mansfield, J. Appl. Phys. 69, 3853 (1991).
[CrossRef]

A. Yariv, Optical Electronics in Modern Communication (Oxford U. Press, Oxford, UK, 1997).

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Figures (8)

Fig. 1
Fig. 1

Nonlinear optical processes occurring at the entrance region and the fiber core that limit the transmission of a laser pulse through the fiber.

Fig. 2
Fig. 2

(a) Molecular structures of the four components of an ILC mixture. (b) Molecular structure of L34. (c) Linear-absorption spectrum of L34.

Fig. 3
Fig. 3

Schematic depiction of two-photon, sequential, and excited-state absorption processes, intersystem crossing, and other processes occurring in the core molecule.

Fig. 4
Fig. 4

(a) Absorption spectrum of C60. (b) Absorption spectrum of LC-X-doped ILC; the spike around 300 nm is due to the ILC.

Fig. 5
Fig. 5

(a) Transmission and output energy versus the input picosecond laser pulse energy through a 3-mm-long ILC-cored fiber with f/6 optics. (b) Picosecond laser pulse limiting results through ILC-cored fibers for various fiber lengths with f/6 collection optics. Solid curves are analytical solutions.

Fig. 6
Fig. 6

(a) Transmission versus the input picosecond laser pulse energy through fibers with different core liquids. (b) Transmitted energies versus the input picosecond laser pulse energy. Fiber length is 5 mm, Core diameter is 30 μm, and f/6 optics are used.

Fig. 7
Fig. 7

(a) Output versus input energies of the ILC-cored fiber for nanosecond laser pulses (λ=0.532 mm; pulse width is 20 ns) for two fiber lengths. Core diameter is 30 μm. (b) Output versus input energies for nanosecond laser pulses (λ=0.532 mm; pulse width is 20 ns) with various core liquids. Fiber length is 5 mm; core diameter is 30 μm.

Fig. 8
Fig. 8

(a) Single nanosecond pulse transmitted versus input laser energy through a nonlinear fiber. The fiber length is 5 mm, the fiber-core diameter is 30 mm, and the core material is L34. Solid dots represent f/6 optics; open diamonds represent open-aperture collection optics. (b) Results with a 5-mm-thick bulk sample with the input laser focal plane located at the entrance surface.  

Equations (15)

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dN2/dt=(σ(2)I2/2h2ν2)N1-N2/τ21-N2/τ2i-N2σexcI/hν+NiσiI/hν=(βI2/N02hν)N1-N2/τ21-N2/τ2i-(αexc/N0hν)N2I+(αi/N0hν)NiI,
dNi/dt=N1σgI/hν+N2/τ2i-Ni/τi-NiσiI/hν,
dN1/dt=N2/τ21+Ni/τi-(βI2/N02hν)N1-σgN1I/hν,
αg=N0σg,αexc=N0σexc,
αi=N0σi,β=(N0/hν)σ(2).
dI/dz=-αg(N1/N0)I-αi(Ni/N0)I-β(N1/N0)I2-αexc(N2/N0)I.
N1N0 exp[-(B+C)t]N0[1-(B+C)t],
N2[B/(B+C)]N0{1-exp[-(B+C)t]}BN0t,
Ni[C/(B+C)]N0{1-exp[-(B+C)t]}CN0t,
B=βI2/N02hν,C=σgI/hν=αgI/N0hν.
dI/dz=-αgI-(αi-αg)ICt-βI2-(αexc-αg)IBt.
dI/dz=-αgI-[β+(αi-αg)σgt/hν]I2-(αexc-αg)tβI3/N02hν=-αgI-βeffI2-γexcI3.
dI/dz=-(αg+αs)I-βI2.
I(L)=αI(0)/{α exp(αL)-βI(0)[1-exp(αL)]},
Iclamped=1/βL,

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