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 �?sterberg, "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. Stratton Electromagnetic 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).

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. 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. (2)

S. L. McCall and E. L. Hahn, �??Self induced transparency by pulsed coherent light,�?? Phys. Rev. Lett. 18, 908-911 (1967).
[CrossRef]

Seung-Ho Choi, and Ulf �?sterberg, "Observation of optical precursors in water,�?? Phys. Rev. Lett. 92, 193903-193905 (2004).
[CrossRef] [PubMed]

Ultra-Wide Band Radar Proceedings (1)

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).

Other (5)

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).

J.A. Stratton Electromagnetic 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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