Abstract

We report observation and control of the spatial–spectral distributions of coherent, dynamic Rabi sideband radiation. The Rabi sidebands result from the interaction of a shaped picosecond probe laser of intensity 1010Wcm2, with neutral excited atomic oxygen generated in a laser-induced microplasma. The spatial–spectral distribution is measured and compared for picosecond laser pulses having either an asymmetric temporal shape or a Gaussian temporal shape. The resulting spatial–spectral distributions are in quantitative agreement with theoretical predictions that account for the radial intensity distribution of the picosecond probe pulse.

© 2011 Optical Society of America

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References

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  1. I. I. Rabi, Phys. Rev. 51, 652 (1937).
    [CrossRef]
  2. R. W. Boyd, in Nonlinear Optics (Academic, 2008), p. 640.
  3. B. R. Mollow, Phys. Rev. 188, 1969 (1969).
    [CrossRef]
  4. F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
    [CrossRef]
  5. F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
    [CrossRef]
  6. D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
    [CrossRef]
  7. D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1984).
    [CrossRef]
  8. R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
    [CrossRef]
  9. R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
    [CrossRef]
  10. M. Plewicki, R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Opt. Lett. 35, 778 (2010).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Fourier Optics (Roberts, 2005).

2011 (1)

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

2010 (1)

2009 (1)

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

2008 (1)

R. W. Boyd, in Nonlinear Optics (Academic, 2008), p. 640.

2005 (1)

J. W. Goodman, Fourier Optics (Roberts, 2005).

1984 (1)

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1984).
[CrossRef]

1981 (1)

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

1975 (1)

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
[CrossRef]

1974 (1)

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[CrossRef]

1969 (1)

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

1937 (1)

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

Boyd, R. W.

R. W. Boyd, in Nonlinear Optics (Academic, 2008), p. 640.

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1984).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Compton, R.

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

M. Plewicki, R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Opt. Lett. 35, 778 (2010).
[CrossRef] [PubMed]

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

Ezekiel, S.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
[CrossRef]

Filin, A.

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

M. Plewicki, R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Opt. Lett. 35, 778 (2010).
[CrossRef] [PubMed]

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Fourier Optics (Roberts, 2005).

Grove, R. E.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
[CrossRef]

Harter, D. J.

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1984).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Hercher, M.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[CrossRef]

Levis, R. J.

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

M. Plewicki, R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Opt. Lett. 35, 778 (2010).
[CrossRef] [PubMed]

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

Mollow, B. R.

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Narum, P.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Plewicki, M.

Rabi, I. I.

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

Raymer, M. G.

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Romanov, D. A.

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

M. Plewicki, R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Opt. Lett. 35, 778 (2010).
[CrossRef] [PubMed]

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

Schuda, F.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[CrossRef]

Stroud, C. R.

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[CrossRef]

Wu, F. Y.

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
[CrossRef]

J. Phys. B (1)

F. Schuda, C. R. Stroud, and M. Hercher, J. Phys. B 7, L198 (1974).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (2)

I. I. Rabi, Phys. Rev. 51, 652 (1937).
[CrossRef]

B. R. Mollow, Phys. Rev. 188, 1969 (1969).
[CrossRef]

Phys. Rev. A (2)

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. A 83, 053423 (2011).
[CrossRef]

D. J. Harter and R. W. Boyd, Phys. Rev. A 29, 739 (1984).
[CrossRef]

Phys. Rev. Lett. (3)

R. Compton, A. Filin, D. A. Romanov, and R. J. Levis, Phys. Rev. Lett. 103, 205001 (2009).
[CrossRef]

F. Y. Wu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
[CrossRef]

D. J. Harter, P. Narum, M. G. Raymer, and R. W. Boyd, Phys. Rev. Lett. 46, 1192 (1981).
[CrossRef]

Other (2)

R. W. Boyd, in Nonlinear Optics (Academic, 2008), p. 640.

J. W. Goodman, Fourier Optics (Roberts, 2005).

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Figures (2)

Fig. 1
Fig. 1

Schematic of the spatial–spectral Rabi sideband experimental setup. L1, L2, L3, and L4, lenses of f = 25 , 25, 10, and 30 cm , respectively; DL, delay line; BS, 60 / 40 beam splitter; G, diffraction grating; CL, cylindrical lens; SLM, spatial light modulator.

Fig. 2
Fig. 2

Model of the optical interference forming the Rabi sideband spatial–spectral distribution. (a), (b) Probe beam profiles used for the simulation of the spatial–spectral distribution (similar profiles were used in the experiment). (c), (d) Simulated spatial– spectral distributions for both probe temporal profiles. The spectrum (white solid curve) at points along the lens plane are calculated from the sum of fields emitted by point emitters (black dots), excited by a radially Gaussian laser pulse. The lens plane corresponds to the position of L2 in Fig. 1. The dashed white curves correspond to the first zeros of the Bessel function obtained using Eq. (3). (e), (f) Experimentally obtained spatial–spectral distributions. The longitudinal coordinate is defined as c t .

Equations (3)

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Ω 0 ( x 0 , t ) = μ E ( t , x 0 ) = Ω 0 max exp ( x 0 2 / ( 2 r 2 ) ) × ( exp ( t 2 / ( 2 τ l 2 ) ) θ ( t ) + exp ( t 2 / ( 2 τ t 2 ) ) θ ( t ) ) ,
t l ( x 0 , Ω ) = τ l 2 ln ( Ω 0 2 / ( Ω 2 Δ 2 ) ) ( x 0 / r ) 2 , t t ( x 0 , Ω ) = τ t 2 ln ( Ω 0 2 / ( Ω 2 Δ 2 ) ) ( x 0 / r ) 2 .
δ ω n ( x ) = const B n ( 1 + ( 1 / z ) 2 ( r / ( c τ ) ) 2 x 2 ) 1 ,

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