Abstract

We study propagation of short laser pulses through water and use a spectral hole filling technique to essentially perform a sensitive balanced comparison of absorption coefficients for pulses of different duration. This study is motivated by an alleged violation of the Bouguer–Lambert–Beer law at low light intensities, where the pulse propagation is expected to be linear, and by a possible observation of femtosecond optical precursors in water. We find that at low intensities, absorption of laser light is determined solely by its spectrum and does not directly depend on the pulse duration, in agreement with our earlier work and in contradiction to some work of others. However, as the laser fluence is increased, interaction of light with water becomes nonlinear, causing energy exchange among the pulse’s spectral components and resulting in peak-intensity dependent (and therefore pulse-duration dependent) transmission. For 30fs pulses at 800nm center wavelength, we determine the onset of nonlinear propagation effects to occur at a peak value of about 0.12mJ/cm2 of input laser energy fluence.

© 2010 Optical Society of America

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References

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2009 (1)

2008 (2)

2007 (2)

2006 (2)

A. E. Fox and U. Osterberg, “Observation of nonexponential 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 (1)

2004 (1)

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

2003 (1)

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

2000 (1)

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

1998 (1)

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406-4409(1998).
[CrossRef]

1997 (2)

1995 (1)

1993 (1)

1991 (1)

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353-R5356 (1991).
[CrossRef] [PubMed]

Aaviksoo, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353-R5356 (1991).
[CrossRef] [PubMed]

Agha, I. H.

Alexander, D. R.

Ariunbold, G. O.

Barille, R.

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Belthangady, C.

Brillouin, L.

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

Brodeur, A.

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406-4409(1998).
[CrossRef]

Bruce, J. C.

Chin, S. L.

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406-4409(1998).
[CrossRef]

Choi, S. H.

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

Chylek, P.

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.

Du, S.

Fischer, M. C.

Fox, A. E.

Fry, E. S.

Gaeta, A. L.

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]

Geraghty, D. F.

Gibson, U. J.

Harris, S. E.

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]

Katona, G.

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

Kattawar, G. W.

Kolchin, P.

Koselik, M.

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

Kou, L.

Kudriavtseva, A. D.

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Kuhl, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353-R5356 (1991).
[CrossRef] [PubMed]

Labrie, D.

Li, J. C.

Liu, H. C.

Moloney, J. V.

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

Naveira, L. M.

Okawachi, Y.

Osterberg, U.

Osterberg, U. L.

Österberg, U.

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

Parali, U. P.

Piletic, I. R.

Ploog, K.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353-R5356 (1991).
[CrossRef] [PubMed]

Pope, R. M.

Quan, X.

Rivoire, G.

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Slepkov, A. D.

Sokolov, A. V.

Sokolovskaia, A.

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Strycker, B. D.

Tcherniega, N.

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Wang, H.

Wang, J.

Warren, W. S.

Wright, E. M.

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

Yin, G. Y.

Zhang, H. F.

Appl. Opt. (5)

Appl. Phys. B (1)

M. Koselik, G. Katona, J. V. Moloney, and E. M. Wright, “Theory and simulation of supercontinuum generation in transparent bulk media,” Appl. Phys. B 77, 185-195 (2003).
[CrossRef]

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

Opt. Commun. (1)

N. Tcherniega, A. Sokolovskaia, A. D. Kudriavtseva, R. Barille, and G. Rivoire, “Backward stimulated Raman scattering in water,” Opt. Commun. 181, 197-205 (2000).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353-R5356 (1991).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

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]

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

A. Brodeur and S. L. Chin, “Band-gap dependence of the ultrafast white-light continuum,” Phys. Rev. Lett. 80, 4406-4409(1998).
[CrossRef]

Other (2)

“Optical glass data sheets,” Schott, Inc., http://www.us.schott.com/advanced_optics/english/download/datasheet_all_us.pdf

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

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Figures (7)

Fig. 1
Fig. 1

Spectral-hole-filling experiment: (a) Frequency domain and (b) time domain schematics. (c) Experimental setup (femtosecond laser oscillator not shown). Initial 7 fs laser pulses pass through the pulse shaper, which produces a spectral hole and reduces the total spectral bandwidth, and enter the water cell. The transmitted spectra are measured by the spectrometer.

Fig. 2
Fig. 2

Results from the spectral hole filling experiment with low-power (laser oscillator) shaped pulses. Parts (a)–(c) show input spectra with the spectral hole centered at (a)  767 nm , (b)  800 nm , and (c)  827 nm wavelengths. Parts (d)–(f) show the corresponding output spectra after propagation through 1.15 m of distilled water; insets show zoomed-in spectral hole regions.

Fig. 3
Fig. 3

Experimental setup for measuring propagation of amplified laser pulses through water. An obstruction is placed in the compressor to produce a hole in the laser spectrum. Then the pulses propagate through the water cell, and the transmitted spectra are measured by the spectrometer.

Fig. 4
Fig. 4

Transformation of transmitted spectra with increasing input laser power: (a) Measured spectra. To aid in visualization, each spectrum has been vertically displaced, with larger upward vertical displacements corresponding to larger input powers. The input powers for the shown spectra are, from bottom to top: 5 mW , 15 mW , 25 mW , 40 mW , 60 mW , 80 mW , 100 mW , 120 mW , 140 mW , 180 mW , 250 mW , and 340 mW . (b) Changes in the spectrum, relative to spectra expected for linear transmission and calculated by scaling the output spectrum obtained for 20 mW input power. These curves are obtained by subtracting the expected linear-transmission spectra from the actual measured spectra, dividing by the input power, and scaling relative to the peak value obtained in the 200 mW curve. The input powers shown, with increasing spectral transformation, are 40 mW , 80 mW , 120 mW , 160 mW , and 200 mW . In both (a) and (b), dotted vertical lines correspond to wavelengths of 794 nm (spectral hole center at low power), and two wavelengths at the wings of the spectrum, 758 and 836 nm .

Fig. 5
Fig. 5

Transmitted intensity for three wavelengths as a function of input laser power. The three wavelengths correspond to the low-power spectral hole center ( 794 nm ) and two wavelengths at the spectral wings (758 and 836 nm ) having, at low input powers, the same spectral intensity as the hole center.

Fig. 6
Fig. 6

Plot on a log-log scale of transmitted spectral intensity at 794 nm (initial spectral hole center) as a function of the input power. The blue circles show the measured data. The red reference line has a slope of 1 and fits well to the data points in the low-power region, indicating a linear dependence. The green reference line has a slope of 2 and fits the data points in the region of intermediate power up to about 250 mW , indicating a quadratic dependence. The change from the linear dependence to quadratic dependence can be clearly seen at around 40 mW (where a dotted vertical line is drawn).

Fig. 7
Fig. 7

Calculated pulse duration versus propagation distance (a) in K7 glass and (b) in water for two transform- limited input pulses of 7 fs (blue lines and circles) and 30 fs (black lines and stars) initial duration (both at an 800 nm center wavelength). In both figures, the data points show the results calculated with the actual wavelength-dependent refractive indices, while the lines are obtained with the group velocity dispersion (GVD) approximation.

Equations (11)

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E ( ω ) = A ( exp [ ( ω ω c ) 2 8 ln ( 2 ) τ 1 2 ] exp [ ( ω ω c ) 2 8 ln ( 2 ) τ 2 2 ] ) ,
E ( t ) = B ( exp [ 2 ln ( 2 ) ( t τ 1 ) 2 ] τ 1 τ 2 exp [ 2 ln ( 2 ) ( t τ 2 ) 2 ] ) cos ( ω c t ) ,
E ( z , t ) = 1 2 π E ( ω ) exp [ i ( k ( ω ) z ω t ) ] d ω ,
n ( λ ) = 1 + B 1 λ 2 λ 2 C 1 + B 2 λ 2 λ 2 C 2 + B 3 λ 2 λ 2 C 3 ,
n ( λ ) = 1.31279 + 15.762 λ 1 4328 λ 2 + 1.1455 × 10 6 λ 3 ,
I ( z , t ) = E ( z , t ) E ( z , t ) * .
E ( 0 , t ) = 1 2 π exp [ 2 ln ( 2 ) t τ 0 2 2 ] cos ( ω c t ) .
E ( ω ) = exp [ ( ω ω c ) 2 τ 0 2 8 ln ( 2 ) ] = exp [ γ ( ω ω c ) 2 ] .
( i z b 1 i t ) ( ω ω c ) + ( i z b 2 2 ) ( ω ω c ) 2 + ,
I ( z , t ) exp [ 2 γ ( t z b 1 ) 2 4 γ 2 + z 2 b 2 2 ] .
τ ( z ) = τ 0 2 + ( 4 ln ( 2 ) GVD τ 0 ) 2 z 2 .

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