Abstract

In this work, we present a hypothesis that spectral response of atoms or molecules to a pulse of electro-magnetic radiation with fast rising or falling fronts would contain a unique emission line that is located approximately near the frequency of the natural oscillations of optical electrons. The emission of this “pinging” spectral line would exist during the time that is determined by the time of radiative energy loss by the optical electron. The amplitude of the “pinging” spectral line would be higher for the pulses with faster rising or falling fronts. The simulations using our previously developed model confirmed existence of the “pinging” spectral response. If experimentally confirmed, this work could lead to a new high sensitivity, high signal to noise ratio stand-off detection techniques, and to other yet unknown applications.

© 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. H. A. Lorentz, The theory of electrons and its applications to the phenomena of light and radiant heat, 2nd edition (B. G. TEUBNER: LEIPZIG, 1916)
  2. S. A. Akhmanov and A. Yu. Nikitin, Physical Optics (Clarendon Press, 1997) chapter 8
  3. N. Bloembergen, Nonlinear optics. A lecture note, (Harvard University, W. A. Benjamin, Inc., 1965)
  4. R. W. Boyd, Nonlinear Optics (Academic Press, 2003)
  5. V. V. Semak and M. N. Shneider, Invicem Lorentz Oscillator Model (ILOM), arXiv:1709.02466.
  6. V. V. Semak and M. N. Shneider, “Analysis of harmonic generation by a hydrogen-like atom using a quasi-classical non-linear oscillator model with realistic electron potential,” OSA Continuum 2(8), 2343 (2019).
    [Crossref]
  7. A. B. Pippard, “The Physics of Vibration,” Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, 1978)
  8. L. Mandelstam, “On the dispersion theory,” Phys. Z. 8, 608 (1907).
  9. L. D. Landau and E. M. Lifshits, The classical theory of fields, Course of theoretical physics, Vol. 2, 3rd Edition, (Pergamon Press, 1971)
  10. A. M. Popov, O. V. Tikhonova, and Atomic Physics, (Nobel Press, 2019) p. 224–225 http://affp.phys.msu.ru/index.php/education/books .

2019 (1)

1907 (1)

L. Mandelstam, “On the dispersion theory,” Phys. Z. 8, 608 (1907).

Akhmanov, S. A.

S. A. Akhmanov and A. Yu. Nikitin, Physical Optics (Clarendon Press, 1997) chapter 8

Bloembergen, N.

N. Bloembergen, Nonlinear optics. A lecture note, (Harvard University, W. A. Benjamin, Inc., 1965)

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2003)

Landau, L. D.

L. D. Landau and E. M. Lifshits, The classical theory of fields, Course of theoretical physics, Vol. 2, 3rd Edition, (Pergamon Press, 1971)

Lifshits, E. M.

L. D. Landau and E. M. Lifshits, The classical theory of fields, Course of theoretical physics, Vol. 2, 3rd Edition, (Pergamon Press, 1971)

Lorentz, H. A.

H. A. Lorentz, The theory of electrons and its applications to the phenomena of light and radiant heat, 2nd edition (B. G. TEUBNER: LEIPZIG, 1916)

Mandelstam, L.

L. Mandelstam, “On the dispersion theory,” Phys. Z. 8, 608 (1907).

Nikitin, A. Yu.

S. A. Akhmanov and A. Yu. Nikitin, Physical Optics (Clarendon Press, 1997) chapter 8

Physics, Atomic

A. M. Popov, O. V. Tikhonova, and Atomic Physics, (Nobel Press, 2019) p. 224–225 http://affp.phys.msu.ru/index.php/education/books .

Pippard, A. B.

A. B. Pippard, “The Physics of Vibration,” Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, 1978)

Popov, A. M.

A. M. Popov, O. V. Tikhonova, and Atomic Physics, (Nobel Press, 2019) p. 224–225 http://affp.phys.msu.ru/index.php/education/books .

Semak, V. V.

Shneider, M. N.

Tikhonova, O. V.

A. M. Popov, O. V. Tikhonova, and Atomic Physics, (Nobel Press, 2019) p. 224–225 http://affp.phys.msu.ru/index.php/education/books .

OSA Continuum (1)

Phys. Z. (1)

L. Mandelstam, “On the dispersion theory,” Phys. Z. 8, 608 (1907).

Other (8)

L. D. Landau and E. M. Lifshits, The classical theory of fields, Course of theoretical physics, Vol. 2, 3rd Edition, (Pergamon Press, 1971)

A. M. Popov, O. V. Tikhonova, and Atomic Physics, (Nobel Press, 2019) p. 224–225 http://affp.phys.msu.ru/index.php/education/books .

H. A. Lorentz, The theory of electrons and its applications to the phenomena of light and radiant heat, 2nd edition (B. G. TEUBNER: LEIPZIG, 1916)

S. A. Akhmanov and A. Yu. Nikitin, Physical Optics (Clarendon Press, 1997) chapter 8

N. Bloembergen, Nonlinear optics. A lecture note, (Harvard University, W. A. Benjamin, Inc., 1965)

R. W. Boyd, Nonlinear Optics (Academic Press, 2003)

V. V. Semak and M. N. Shneider, Invicem Lorentz Oscillator Model (ILOM), arXiv:1709.02466.

A. B. Pippard, “The Physics of Vibration,” Vol. 1. Part 1: The Simple Classical Vibrator. (Cambridge University Press, 1978)

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Figures (6)

Fig. 1.
Fig. 1. a) Spectral response of hydrogen to irradiation with 10 mJ, 10 ns laser pulse at 532 nm wavelength, focused in the spot with uniform intensity distribution with 20 µm radius. The x-axis represents the frequency and has dimension of 1015 Hz. b) – the vertical scale is magnified to show the 2nd harmonic and “pinging” lines.
Fig. 2.
Fig. 2. a) Spectral response of hydrogen to irradiation with 0.01 mJ, 10 ns laser pulse at 532 nm wavelength, focused in the spot with uniform intensity distribution with 20 µm radius. The x-axis represents the frequency and has dimension 1015 Hz. b) same as previous.
Fig. 3.
Fig. 3. a) Spectral response of hydrogen to irradiation with 0.01 mJ, 10 ns laser pulse at 266 nm wavelength, focused in the spot with uniform intensity distribution with 20 µm radius. The x-axis represents the frequency and has dimension 1015 Hz. b) same as previous.
Fig. 4.
Fig. 4. a) Spectral response of hydrogen to irradiation with 10 mJ, 10 ns laser pulse at 1064 nm wavelength, focused in the spot with uniform intensity distribution with 20 µm radius. The x-axis represents the frequency and has dimension 1015 Hz. b) same as previous.
Fig. 5.
Fig. 5. a) Spectral response of hydrogen to irradiation with 10 mJ, 10 ns laser pulse at 532 nm wavelength, focused in the spot with uniform intensity distribution with 20 µm radius for various characteristic rise times: 50, 100 and 200 periods of laser oscillations. The x-axis represents the frequency and has dimension 1015 Hz. b) same as previous.
Fig. 6.
Fig. 6. Re-emission spectra computed for nonlinear and linear oscillators showing similar generation of “pinging” spectral line; a – the vertical scale is normalized to the scattered re-radiation line, b – the vertical scale is magnified to show the “pinging” line (note the second harmonic line generated by nonlinear oscillator and is absent on the spectrum of linear oscillator). The x-axis represents the frequency and has dimension 1015 Hz.

Equations (8)

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r ¨ + 1 m e U ( r ) r ξ m r 1 m F m b ( r ) = e m E ( t ) ,
U ( r ) ( r r 0 ) 2 ,
r ¨ + 2 U 0 r 0 2 m ( 1 r 0 r 2 1 r 3 ) ξ m r = e m E ( t ) ,
I ( t ) = I L ( 1 e x p ( t / t t r t r ) ) 2 ,
r ¨ + γ r ˙ + ω 0 2 r = e E 0 m e e i ω t ,
r ( 0 ) = 0 , r ˙ ( 0 ) = 0
r = e E 0 m ( ω 2 ω 0 2 ) cos ( ω t ) ω γ sin ( ω t ) ( ω 2 ω 0 2 ) 2 + ω 2 γ 2 e E 0 m e 1 2 γ t ( ω 2 ω 0 2 ) cos ( ω t ) ( ω 2 + ω 0 2 ) 2 ω γ sin ( ω t ) ( ω 2 ω 0 2 ) 2 + ω 2 γ 2 ,
E ( t , ω ) r ¨ ( t , ω ) e E 0 m e ω 2 cos ( ω t ) ω 2 ω 0 2 + e E 0 m e e 1 2 γ t ω 2 cos ( ω t ) ω 2 ω 0 2 .

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