Abstract

We investigate the linear propagation of 800 and 1530nm ultrashort optical pulses in water. For all pulse repetition rates studied, we observe pure exponential decay down to a transmission of 2.5×105. We further demonstrate that previous observations of nonmonoexponential decay and pulse splitup in broadband pulses are consistent with Beer’s law in the purely linear regime.

© 2007 Optical Society of America

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References

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  1. M. Stojanovic, "Recent advances in high-speed underwater acoustic communications," IEEE J. Ocean. Eng. 21, 125-136 (1996).
    [CrossRef]
  2. S. Choi and U. Österberg, "Observation of optical precursors in water," Phys. Rev. Lett. 92, 193903 (2004).
    [CrossRef] [PubMed]
  3. U. J. Gibson and U. L. Österberg, "Optical precursors and Beer's law violations; non-exponential propagation losses in water," Opt. Express 13, 2105-2110 (2005).
    [CrossRef] [PubMed]
  4. A. E. Fox and U. Österberg, "Observation of non-exponential absorption of ultra-fast pulses in water," Opt. Express 14, 3688-3693 (2006).
    [CrossRef] [PubMed]
  5. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).
  6. H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
    [CrossRef] [PubMed]
  7. K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).
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    [CrossRef]
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    [CrossRef]
  10. R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
    [CrossRef] [PubMed]
  11. J. Li, D. R. Alexander, H. Zhang, U. Parali, D. W. Doerr, J. C. Bruce III, and H. Wang, "Propagation of ultrashort laser pulses through water," Opt. Express 15, 1939-1945 (2007).
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  14. P. D. T. Huibers, "Models for the wavelength dependence of the index of refraction of water," Appl. Opt. 36, 3785-3787 (1997).
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  15. X. H. Quan and E. S. Fry, "Empirical-equation for the index of refraction of seawater," Appl. Opt. 34, 3477-3480 (1995).
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2007 (1)

2006 (2)

A. E. Fox and U. Österberg, "Observation of non-exponential absorption of ultra-fast pulses in water," Opt. Express 14, 3688-3693 (2006).
[CrossRef] [PubMed]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

2005 (2)

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

U. J. Gibson and U. L. Österberg, "Optical precursors and Beer's law violations; non-exponential propagation losses in water," Opt. Express 13, 2105-2110 (2005).
[CrossRef] [PubMed]

2004 (2)

T. M. Roberts, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 93, 269401 (2004).
[CrossRef]

S. Choi and U. Österberg, "Observation of optical precursors in water," Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

1996 (1)

M. Stojanovic, "Recent advances in high-speed underwater acoustic communications," IEEE J. Ocean. Eng. 21, 125-136 (1996).
[CrossRef]

1995 (1)

1993 (1)

Alexander, D. R.

Alfano, R. R.

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

Alrubaiee, M.

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

Birman, J. L.

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

Bruce, J. C.

Cheylek, P.

Choi, S.

S. Choi and U. Österberg, "Observation of optical precursors in water," Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef] [PubMed]

Cubeddu, R.

Das, B. B.

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

Dawes, A. M. C.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Doerr, D. W.

Fox, A. E.

Fry, E. S.

Gauthier, D. J.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Gibson, U. J.

Huibers, P. D. T.

Jeong, H.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Kou, L.

Labrie, D.

Li, J.

Ni, X.

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

Österberg, U.

Österberg, U. L.

Oughstun, K. E.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Parali, U.

Pifferi, A.

Quan, X. H.

Roberts, T. M.

T. M. Roberts, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 93, 269401 (2004).
[CrossRef]

Segelstein, D.

D. Segelstein, "The complex refractive index of water," M.S. thesis, (University of Missouri-Kansas City, 1981).

Sherman, G. C.

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

Stojanovic, M.

M. Stojanovic, "Recent advances in high-speed underwater acoustic communications," IEEE J. Ocean. Eng. 21, 125-136 (1996).
[CrossRef]

Taroni, P.

Torricelli, A.

Valentini, G.

Wang, H.

Zhang, H.

Appl. Opt. (4)

IEEE J. Ocean. Eng. (1)

M. Stojanovic, "Recent advances in high-speed underwater acoustic communications," IEEE J. Ocean. Eng. 21, 125-136 (1996).
[CrossRef]

Opt. Express (3)

Phys. Rev. Lett. (4)

S. Choi and U. Österberg, "Observation of optical precursors in water," Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef] [PubMed]

T. M. Roberts, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 93, 269401 (2004).
[CrossRef]

R. R. Alfano, J. L. Birman, X. Ni, M. Alrubaiee, and B. B. Das, "Comment on 'Observation of optical precursors in water'," Phys. Rev. Lett. 94, 239401 (2005).
[CrossRef] [PubMed]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, "Direct observation of optical precursors in a region of anomalous dispersion," Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef] [PubMed]

Other (3)

K. E. Oughstun and G. C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, 1994).

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960).

D. Segelstein, "The complex refractive index of water," M.S. thesis, (University of Missouri-Kansas City, 1981).

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Figures (4)

Fig. 1
Fig. 1

Theoretical analysis of linear propagation of broadband pulses in water. (a) Transmitted power as a function of propagation distance for Gaussian pulses with a spectral width of 50 and 20 nm (FWHM) for three different center wavelengths. Inset, absorption spectrum of water in the visible and NIR range [12, 13]. Solid line, fit to monoexponential decay for the 760 ± 20 nm pulse. (b) Temporal pulse splitup of linearly chirped 540 fs , 780 ± 60 nm pulses after traveling through 250 cm of water. Note that this pulse breakup is obtained solely from wavelength-dependent linear absorption (Beer’s law) and dispersion.

Fig. 2
Fig. 2

Experimental setup of water cell for transmission measurements at 800 nm . The path length was varied by moving the pick-off mirror to change the total number of bounces.

Fig. 3
Fig. 3

(a) Plot of transmitted power through distilled water as a function of path length for a 60 fs pulse train with an 80 MHz repetition rate centered at 795 nm . The solid line is a monoexponential fit to the data. (b) Plot of transmitted power through distilled water as a function of path length for an 84 fs pulse train with a 1 kHz repetition rate centered at 805 nm . The solid line is a monoexponential fit to the data.

Fig. 4
Fig. 4

Plot of transmitted power through distilled water as a function of path length for (a) a 100 fs pulse train with a 1 kHz repetition rate centered at 1530 nm and (b) a 270 fs pulse train with an 80 MHz repetition rate centered at 1532 nm . Solid lines are monoexponential fits to the data.

Equations (6)

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I 0 ( λ ) = exp [ ( λ λ 0 ) 2 2 σ 2 ] ,
I ( λ ) = I 0 ( λ ) e α ( λ ) z ,
n ( λ ) = 1.128 + 15.76 λ 1 4382 λ 2 + 1145500 λ 3 ,
I 0 ( t ) = exp [ ( t t 0 ) 2 2 τ 2 ] ,
λ ( t ) = t σ τ + λ 0 ,
t arrive ( λ ) = t 0 [ t ( λ ) n ( λ ) z c ] ,

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