Abstract

Our theoretical model of forced dipole oscillation demonstrates that when the amplitude of the forcing field is changing fast, the oscillations of the bound electron in the atom or molecule initially proceed at two frequencies: the frequency of the natural electron oscillations and the frequency of the forcing field. Particularly, applied to the science of scattering, this model of transient forced atomic and molecular oscillations suggests that accurate interpretation of the laser scattering experiments using short laser pulses must include both the conventionally known scattering at the laser frequency (Rayleigh) and the predicted by our theoretical spectral emission that corresponds to the natural frequency of the electronic oscillations. This article presents the results of numerical simulations using our model performed for the hydrogen atom. The characteristics of the components of scattered radiation, their polarization, and Doppler thermal broadening are discussed.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
    [Crossref]
  2. I. I. Sobel’man, “On the theory of light scattering in gases,” Phys.-Usp. 45(1), 75–80 (2002).
    [Crossref]
  3. V. V. Semak and M. N. Shneider, Invicem Lorentz Oscillator Model, arXiv: 1709.02466 [physics.optics] (2017)
  4. V. V. Semak and M. N. Shneider, “Predicted response of an atom to a short burst of electromagnetic radiation,” OSA Continuum 3(2), 186–193 (2020).
    [Crossref]
  5. V. V. Semak and M. N. Shneider, “Analysis of harmonic generation by a hydrogen-like atom using quasi-classical non-linear oscillator model with realistic electron potential,” OSA Continuum 2(8), 2343–2352 (2019).
    [Crossref]
  6. E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd Ed. (Oxford, 1948)
  7. A. B. Pippard, The Physics of Vibration. Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, Cambridge-London-New York-Melbourne, 1978)
  8. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” JETP 20, 1307 (1965).

2020 (1)

2019 (1)

2002 (1)

I. I. Sobel’man, “On the theory of light scattering in gases,” Phys.-Usp. 45(1), 75–80 (2002).
[Crossref]

2001 (1)

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
[Crossref]

1965 (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” JETP 20, 1307 (1965).

Forkey, J. N.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
[Crossref]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” JETP 20, 1307 (1965).

Lempert, W. R.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
[Crossref]

Miles, R. B.

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
[Crossref]

Pippard, A. B.

A. B. Pippard, The Physics of Vibration. Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, Cambridge-London-New York-Melbourne, 1978)

Semak, V. V.

Shneider, M. N.

Sobel’man, I. I.

I. I. Sobel’man, “On the theory of light scattering in gases,” Phys.-Usp. 45(1), 75–80 (2002).
[Crossref]

Titchmarsh, E. C.

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd Ed. (Oxford, 1948)

JETP (1)

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” JETP 20, 1307 (1965).

Meas. Sci. Technol. (1)

R. B. Miles, W. R. Lempert, and J. N. Forkey, “Laser Rayleigh scattering,” Meas. Sci. Technol. 12(5), R33–R51 (2001).
[Crossref]

OSA Continuum (2)

Phys.-Usp. (1)

I. I. Sobel’man, “On the theory of light scattering in gases,” Phys.-Usp. 45(1), 75–80 (2002).
[Crossref]

Other (3)

V. V. Semak and M. N. Shneider, Invicem Lorentz Oscillator Model, arXiv: 1709.02466 [physics.optics] (2017)

E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd Ed. (Oxford, 1948)

A. B. Pippard, The Physics of Vibration. Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, Cambridge-London-New York-Melbourne, 1978)

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Figures (3)

Fig. 1.
Fig. 1. (a) - Time dependent relative displacement of the forced electron oscillations divided by the amplitude of the laser electric field and the laser pulse shape; (b) - Same as in (a) shown during the later time; (c) normalized spectral power density of the response of hydrogen atom.
Fig. 2.
Fig. 2. (a) - Time dependent relative displacement of the forced electron oscillations divided by the amplitude of the laser electric field and the laser pulse shape for FWHM 31.4 fs and (b) normalized spectral power density of the response of hydrogen atom.
Fig. 3.
Fig. 3. (a) - Time dependent relative displacement of the forced electron oscillations divided by the amplitude of the laser electric field and the laser pulse shape for FWHM 78.54 fs and (b) normalized spectral power density of the response of hydrogen atom.

Equations (17)

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r ¨ + 2 U 0 r 0 2 m ( 1 r 0 r 2 1 r 3 ) ξ m r = e m E (t),
r ( 0 ) = r 0 , r ˙ ( 0 ) = 0 .
d ( t ) = e δ r ( t ) = e ( r ( t ) r 0 )
E d ( t ) d ¨ ( t ) ,
S ( ω ) a 2 ( ω ) + b 2 ( ω ) ,
a ( ω ) = 1 π E d ( t ) cos ( ω t ) d t ,
b ( ω ) = 1 π E d ( t ) sin ( ω t ) d t
I ( t ) I 0 = { cos 2 ( | t | / t p ) , | t | / t p π / 2 0 , | t | / t p > π / 2 ,
E a ( t ) / E 0 = ( I ( t ) / I 0 ) 1 / 2 .
d ( t ) = e δ r ( t ) e ( δ r ω L ( t ) + δ r ω ( t ) ) = d ω L ( t ) + d ω ( t ) .
ω 0 = ( 2 U 0 / m r 0 2 ) 1 / 2 ,
γ = ξ m ω 0 2 = e 2 ω 0 2 6 π ε 0 m c 3 , 1 / s .
ω = ( ω 0 2 1 4 γ 2 ) 1 / 2 ,
P t o t = P ω L + P ω = I L ( σ ω L + σ ω ) d ¨ 2 = d ¨ ω L 2 + d ¨ ω 2 ,
σ ω L / σ ω ω L 4 / ω 4 .
Δ ν T = ω L π c ( 8 k B T ln 2 M ) 1 / 2 sin ( θ 2 ) ,
Δ ν T = ω π c ( k B T ln 2 2 M ) 1 / 2 .