Abstract

We develop a model for exponential decay of broadband pulses, and examine its implications for experiments on optical precursors. One of the signature features of Brillouin precursors is attenuation with a less rapid decay than that predicted by Beer’s Law. Depending on the pulse parameters and the model that is adopted for the dielectric properties of the medium, the limiting z-dependence of the loss has been described as z -1/2, z -1/3, exponential, or, in more detailed descriptions, some combination of the above. Experimental results in the search for precursors are examined in light of the different models, and a stringent test for sub-exponential decay is applied to data on propagation of 500 femtosecond pulses through 1–5 meters of water.

© 2005 Optical Society of America

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References

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  1. Seung-Ho Choi and Ulf Österberg,“Observation of optical precursors in water,” Phys.Rev.Lett. 92, 193903–193905 (2004).
    [Crossref] [PubMed]
  2. L. Brillouin.Wave Propagation and Group Velocity(Academic Press, New York, 1960).
  3. K.E. Oughstun and G.C. Sherman, Electromagnetic Pulse Propagation in Causal Dielectrics (Springer-Verlag, Berlin, 1994).
  4. M.D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1, 1604–1611 (1970).
    [Crossref]
  5. S. L. McCall and E. L. Hahn, “Self induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
    [Crossref]
  6. T.W. Barrett, “Energy transfer & propagation and the dielectrics of materials: transient versus steady state effects,” in Ultra-Wide Band Radar Proceedings from the First Los Alamos Symposium, (CRC Press, Boca Raton, FL.1991).
  7. T.M. Roberts, “Radiated pulses decay exponentially materials in the far fields of antennas,” Elec. Lett. 38, 679–680 (2002).
    [Crossref]
  8. T.M. Roberts, “Pave Paws radiation decays exponentially in lossy materials”, talk to the National research Council, Sep. 9, 2002.
  9. E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
    [Crossref]
  10. J.A. StrattonElectromagnetic Theory(McGraw Hill, New York, 1941).
  11. E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface.” Phys. Rev. A 13, 763–776 (1976).
    [Crossref]
  12. D.J. Segelstein, The complex refractive index of water (M.Sc. Thesis, Department of Physics. University of Missouri-Kansas City, 1981).

2004 (1)

Seung-Ho Choi and Ulf Österberg,“Observation of optical precursors in water,” Phys.Rev.Lett. 92, 193903–193905 (2004).
[Crossref] [PubMed]

2002 (1)

T.M. Roberts, “Radiated pulses decay exponentially materials in the far fields of antennas,” Elec. Lett. 38, 679–680 (2002).
[Crossref]

1986 (1)

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
[Crossref]

1976 (1)

E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface.” Phys. Rev. A 13, 763–776 (1976).
[Crossref]

1970 (1)

M.D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1, 1604–1611 (1970).
[Crossref]

1967 (1)

S. L. McCall and E. L. Hahn, “Self induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[Crossref]

Avenel, O.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
[Crossref]

Barrett, T.W.

T.W. Barrett, “Energy transfer & propagation and the dielectrics of materials: transient versus steady state effects,” in Ultra-Wide Band Radar Proceedings from the First Los Alamos Symposium, (CRC Press, Boca Raton, FL.1991).

Brillouin, L.

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

Choi, Seung-Ho

Seung-Ho Choi and Ulf Österberg,“Observation of optical precursors in water,” Phys.Rev.Lett. 92, 193903–193905 (2004).
[Crossref] [PubMed]

Crisp, M.D.

M.D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1, 1604–1611 (1970).
[Crossref]

Gitterman, E.

E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface.” Phys. Rev. A 13, 763–776 (1976).
[Crossref]

Gitterman, M.

E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface.” Phys. Rev. A 13, 763–776 (1976).
[Crossref]

Hahn, E. L.

S. L. McCall and E. L. Hahn, “Self induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[Crossref]

McCall, S. L.

S. L. McCall and E. L. Hahn, “Self induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[Crossref]

Österberg, Ulf

Seung-Ho Choi and Ulf Österberg,“Observation of optical precursors in water,” Phys.Rev.Lett. 92, 193903–193905 (2004).
[Crossref] [PubMed]

Oughstun, K.E.

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

Roberts, T.M.

T.M. Roberts, “Radiated pulses decay exponentially materials in the far fields of antennas,” Elec. Lett. 38, 679–680 (2002).
[Crossref]

T.M. Roberts, “Pave Paws radiation decays exponentially in lossy materials”, talk to the National research Council, Sep. 9, 2002.

Segelstein, D.J.

D.J. Segelstein, The complex refractive index of water (M.Sc. Thesis, Department of Physics. University of Missouri-Kansas City, 1981).

Sherman, G.C.

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

Stratton, J.A.

J.A. StrattonElectromagnetic Theory(McGraw Hill, New York, 1941).

Varoquaux, E.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
[Crossref]

Williams, G. A.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
[Crossref]

Elec. Lett. (1)

T.M. Roberts, “Radiated pulses decay exponentially materials in the far fields of antennas,” Elec. Lett. 38, 679–680 (2002).
[Crossref]

Phys. Rev. A (2)

M.D. Crisp, “Propagation of small-area pulses of coherent light through a resonant medium,” Phys. Rev. A 1, 1604–1611 (1970).
[Crossref]

E. Gitterman and M. Gitterman, “Transient processes for incidence of a light signal on a vacuum-medium interface.” Phys. Rev. A 13, 763–776 (1976).
[Crossref]

Phys. Rev. Lett. (1)

S. L. McCall and E. L. Hahn, “Self induced transparency by pulsed coherent light,” Phys. Rev. Lett. 18, 908–911 (1967).
[Crossref]

Phys.Rev. B (1)

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: Application to sound waves in superfluid He3-B.” Phys.Rev. B 34, 7617–7640 (1986).
[Crossref]

Phys.Rev.Lett. (1)

Seung-Ho Choi and Ulf Österberg,“Observation of optical precursors in water,” Phys.Rev.Lett. 92, 193903–193905 (2004).
[Crossref] [PubMed]

Other (6)

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

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

T.W. Barrett, “Energy transfer & propagation and the dielectrics of materials: transient versus steady state effects,” in Ultra-Wide Band Radar Proceedings from the First Los Alamos Symposium, (CRC Press, Boca Raton, FL.1991).

J.A. StrattonElectromagnetic Theory(McGraw Hill, New York, 1941).

T.M. Roberts, “Pave Paws radiation decays exponentially in lossy materials”, talk to the National research Council, Sep. 9, 2002.

D.J. Segelstein, The complex refractive index of water (M.Sc. Thesis, Department of Physics. University of Missouri-Kansas City, 1981).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental set-up. Where, OI-optical isolator, OF-optical fiber, BE-beam expander, W-water tube, and PMT-photomultiplier tube.

Fig. 2.
Fig. 2.

Pulse spectrum (dashed line) and the absorption coefficient for water from [12] over the wavelength range of interest.

Fig. 3.
Fig. 3.

Computed spectral evolution of the pulse for a series of propagation distances.

Fig. 4.
Fig. 4.

Transmitted energy as a function of distance for experimental measurements and two models.

Equations (6)

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2 f ( r , t ) + 1 v 2 2 f ( r , t ) t 2 = 0
f ( z , t ) = 1 2 π + i a + i a F ˜ ( 0 , ω ) e i ( ω t k ( ω ) z ) d ω
f B ( z , t ) 1 [ φ " ( ω s ) z ] 1 2 e i z φ ( ω s )
f ( z , t ) e k i min z ω min ω max F ˜ ( 0 , ω ) d ω
E ( z , λ ) F λ ( 0 , λ ) 2 e α ( λ ) z
E int ( z ) = F λ ( 0 , λ ) 2 e α ( λ ) z d λ

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