Abstract

Analytic expressions are presented for the fluence dependence of the populations of pulse-excited singlet and triplet states of metallo-organic molecules appropriate for the design of passive optical limiters in which the molecular density profile along the axis of a convergent beam is graded to avoid damage at high design fluences. The original model was relevant strictly for laser-pulse lengths greater than 10-7 s. This research extends the model to the range from 10-11 to 10-6 s and beyond. The factors that determine the appropriate concentration profiles, and the high-fluence performance of the device, are also reviewed.

© 1999 Optical Society of America

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  1. P. A. Miles, “Bottleneck optical limiters: the optimal use of excited-state absorbers,” Appl. Opt. 33, 6965–6979 (1994).
    [CrossRef] [PubMed]
  2. P. A. Miles, “Design principles for excited state absorptive limiters,” in LEOS Annual Meeting, Vol. 2 of 1994 LEOS Conference Proceedings (IEEE Lasers and Electro-Optics Society, Boston, Mass., 1994), pp. 83–84.
  3. P. A. Miles, “Material figures of merit for saturated excited state absorptive limiters,” in Organic, Metallo-Organic and Polymeric Materials for Nonlinear Optical Applications, S. R. Marder, J. W. Perry, eds., Proc. SPIE2143, 251–262 (1994).
    [CrossRef]
  4. P. A. Miles, “Optical bandwidth determinants for excited state absorptive limiters,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 51–59.
  5. 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.
  6. J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.
  7. T. Xia, D. J. Hagan, A. Dogariu, A. A. Said, E. W. Van Stryland, “Optimization of optical limiting devices based on excited-state absorption,” Appl. Opt. 36, 4110–4122 (1997).
    [CrossRef] [PubMed]

1997 (1)

1994 (1)

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.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

Dogariu, A.

Hagan, D. J.

Kenney, M. E.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

Kwag, G.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

Mansour, K.

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.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

Marder, S. R.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

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.

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.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

Miles, P. A.

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

P. A. Miles, “Material figures of merit for saturated excited state absorptive limiters,” in Organic, Metallo-Organic and Polymeric Materials for Nonlinear Optical Applications, S. R. Marder, J. W. Perry, eds., Proc. SPIE2143, 251–262 (1994).
[CrossRef]

P. A. Miles, “Optical bandwidth determinants for excited state absorptive limiters,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 51–59.

P. A. Miles, “Design principles for excited state absorptive limiters,” in LEOS Annual Meeting, Vol. 2 of 1994 LEOS Conference Proceedings (IEEE Lasers and Electro-Optics Society, Boston, Mass., 1994), pp. 83–84.

Perry, J. W.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

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.

Said, A. A.

Van Stryland, E. W.

Xia, T.

Appl. Opt. (2)

Other (5)

P. A. Miles, “Design principles for excited state absorptive limiters,” in LEOS Annual Meeting, Vol. 2 of 1994 LEOS Conference Proceedings (IEEE Lasers and Electro-Optics Society, Boston, Mass., 1994), pp. 83–84.

P. A. Miles, “Material figures of merit for saturated excited state absorptive limiters,” in Organic, Metallo-Organic and Polymeric Materials for Nonlinear Optical Applications, S. R. Marder, J. W. Perry, eds., Proc. SPIE2143, 251–262 (1994).
[CrossRef]

P. A. Miles, “Optical bandwidth determinants for excited state absorptive limiters,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 51–59.

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.

J. W. Perry, K. Mansour, S. R. Marder, C.-T. Chen, P. Miles, M. E. Kenney, G. Kwag, “Approaches for optimizing and tuning the optical limiting response of phthalocyanine complexes,” in Materials for Optical Limiting, Vol. 374 of MRS Symposium Proceedings, R. Crane, K. Lewis, E. Van Stryland, M. Khoshnevisan, eds. (Materials Research Society, Boston, Mass., 1995), pp. 257–265.

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Figures (3)

Fig. 1
Fig. 1

Simplified seven-level model relevant to the response of metallo-organic dye molecules to optical radiation.

Fig. 2
Fig. 2

Dependence of fractional ground-state population on pulse fluence for various pulse lengths.

Fig. 3
Fig. 3

Dependence of excited-state absorption cross section at high pulse fluences on pulse length.

Tables (1)

Tables Icon

Table 1 Impact of Corrections in Dopant Profile on Low-Level Signal Transmittances for Limiters with σeg in the Range 10–30

Equations (28)

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ddt ng=-Iσghν ng+nsτs,  ddt ns=Iσghν ng-nsτs-nsτst,  ddt nt=nsτst,  ng+ns+nt=1,
ddt˜ ng=-fng+1-Φns,  ddt˜ ns=fng-ns,  ddt˜ nt=Φns,
f=IτFc, Fc=hνσg.
ng=λ+-λ--11+λ+expλ+t˜-1+λ-expλ-t˜,  ns=λ+-λ--1fexpλ+t˜-expλ-t˜,  nt=1-λ+-λ--11+λ++fexpλ+t˜-1+λ-+fexpλ-t˜,
λ2+1+fλ+fΦ=0.
ng=exp-F/Fs,  ns=1-exp-F/Fs  nt=0,
ng=exp-F/Fs,  ns=0,  nt=1-exp-F/Fs,
ng=1-Φf exp-Φt˜p,  =τpτsFcF exp-τp/τst.
ng=0.368 τstτsFcF.
σm,e=nsσs+ntσt.
σe=σs exp-τp/τst+σt1-exp-τp/τst,  =σt-σt-σsexp-τp/τst,
Δ=-τp αtItdt=0F αFdF=N0σF
σ=1F0F σmFdF.
αF=N0σmF with σm=ngσg+nsσs+ntσt.
Δ=N0σF=-dFzdz,
N0σ=-1EzdEzdz,
ng=exp-F/Fs,
ns=1-exp-F/Fs, Fs=Fc,
nt=1-exp-F/Fs, Fs=Fc/Φ.
σ=σe-σe-σgFsF1-exp-F/Fs,
-dFdz=N0σF=N0σeF-N0σe-σgFs,
Fz=F0 exp-N0σez+Fsσe-σgσe.
Fz=F0 exp-N0σez,
FI=Fsσe-σgσe
N0z=Nmyy2+a2, y=|z|λ0, a=nf/#2,
Nm=2σλ0,
T=exp-0L N0zσgdz.
σσg=σeσg-0.367σeσg-1.

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