Abstract

We examine an all-optical bump-on-tail instability by considering the nonlinear interaction of two partially incoherent spatial beams. Using a radiation transport approach, we develop plasmalike dispersion relations for perturbation modes and show that a positive gradient in the power spectrum can trigger instability. Theoretical considerations are confirmed by experiment and numerical simulation.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
    [CrossRef] [PubMed]
  2. D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
    [CrossRef] [PubMed]
  3. D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]
  4. V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
    [CrossRef]
  5. R. Fedele and D. Anderson, J. Opt. B 2, 207 (2000).
    [CrossRef]
  6. B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
    [CrossRef]
  7. D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
    [CrossRef]
  8. A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).
  9. W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
    [CrossRef]
  10. A. Picozzi, Opt. Express 15, 9063 (2007).
    [CrossRef] [PubMed]
  11. D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008).
    [CrossRef] [PubMed]
  12. N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973).
  13. D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (2008).
    [CrossRef]
  14. A. N. Kaufman, J. Plasma Phys. 8, 1 (1972).
    [CrossRef]
  15. D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
    [CrossRef]
  16. S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
    [CrossRef] [PubMed]
  17. C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
    [CrossRef]
  18. C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
    [CrossRef]

2008

D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008).
[CrossRef] [PubMed]

D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

2007

2006

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

2004

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

2002

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

2001

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
[CrossRef]

2000

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

R. Fedele and D. Anderson, J. Opt. B 2, 207 (2000).
[CrossRef]

1999

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

1998

V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

1997

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

1972

A. N. Kaufman, J. Plasma Phys. 8, 1 (1972).
[CrossRef]

1964

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Anastassiou, C.

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Anderson, D.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

R. Fedele and D. Anderson, J. Opt. B 2, 207 (2000).
[CrossRef]

Anderson, D. Z.

V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

Carmon, T.

Christodoulides, D. N.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Coskun, T.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Coskun, T. H.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Dylov, D. V.

D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008).
[CrossRef] [PubMed]

Eugenieva, E.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Eugenieva, E. D.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

Fedele, R.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

R. Fedele and D. Anderson, J. Opt. B 2, 207 (2000).
[CrossRef]

Fleischer, J. W.

D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008).
[CrossRef] [PubMed]

D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
[CrossRef]

Giordmaine, J. A.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Hall, B.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Helczynski-Wolf, L.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

Jauslin, H. R.

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Kaufman, A. N.

A. N. Kaufman, J. Plasma Phys. 8, 1 (1972).
[CrossRef]

Kip, D.

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Krall, N. A.

N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973).

Lagrange, S.

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Lan, S.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Lisak, M.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Martienssen, W.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Martin, J.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Mitchell, M.

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Picozzi, A.

A. Picozzi, Opt. Express 15, 9063 (2007).
[CrossRef] [PubMed]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Pitois, S.

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

Rudakov, L. I.

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

Segev, M.

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Semenov, V.

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

Semenov, V. E.

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

Shih, M. F.

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Shkunov, V. V.

V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

Soljacic, M.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Spiller, E.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Steiglitz, K.

C. Anastassiou, J. W. Fleischer, T. Carmon, M. Segev, and K. Steiglitz, Opt. Lett. 26, 1498 (2001).
[CrossRef]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Trivelpiece, A. W.

N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973).

Vedenov, A. A.

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

Vishwanath, A.

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

Am. J. Phys.

W. Martienssen and E. Spiller, Am. J. Phys. 32, 919 (1964).
[CrossRef]

Dokl. Akad. Nauk SSSR

A. A. Vedenov and L. I. Rudakov, Dokl. Akad. Nauk SSSR 159, 767 (1964) A. A. Vedenov and L. I. Rudakov,[Sov. Phys. Dokl. 9, 1073 (1965)]).

J. Opt. B

R. Fedele and D. Anderson, J. Opt. B 2, 207 (2000).
[CrossRef]

J. Plasma Phys.

A. N. Kaufman, J. Plasma Phys. 8, 1 (1972).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

D. V. Dylov and J. W. Fleischer, Phys. Rev. A 78, 061804 (2008).
[CrossRef]

Phys. Rev. E

D. Anderson, L. Helczynski-Wolf, M. Lisak, and V. Semenov, Phys. Rev. E 69, 025601 (2004).
[CrossRef]

B. Hall, M. Lisak, D. Anderson, R. Fedele, and V. E. Semenov, Phys. Rev. E 65, 035602 (2002).
[CrossRef]

D. N. Christodoulides, E. D. Eugenieva, T. H. Coskun, M. Segev, and M. Mitchell, Phys. Rev. E 63, 035601 (2001).
[CrossRef]

Phys. Rev. Lett.

D. V. Dylov and J. W. Fleischer, Phys. Rev. Lett. 100, 103903 (2008).
[CrossRef] [PubMed]

M. Soljacic, M. Segev, T. Coskun, D. N. Christodoulides, and A. Vishwanath, Phys. Rev. Lett. 84, 467 (2000).
[CrossRef] [PubMed]

D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

V. V. Shkunov and D. Z. Anderson, Phys. Rev. Lett. 81, 2683 (1998).
[CrossRef]

S. Pitois, S. Lagrange, H. R. Jauslin, and A. Picozzi, Phys. Rev. Lett. 97, 033902 (2006).
[CrossRef] [PubMed]

C. Anastassiou, M. Segev, K. Steiglitz, J. A. Giordmaine, M. Mitchell, M. F. Shih, S. Lan, and J. Martin, Phys. Rev. Lett. 83, 2332 (1999).
[CrossRef]

Science

D. Kip, M. Soljacic, M. Segev, E. Eugenieva, and D. N. Christodoulides, Science 290, 495 (2000).
[CrossRef] [PubMed]

Other

N. A. Krall and A. W. Trivelpiece, Principles of Plasma Physics (McGraw-Hill, 1973).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Simulation of nonlinear bump-on-tail propagation for (a) Lorentzian and (b) Gaussian distributions. The total intensity and nonlinearity are kept constant ( Δ n n 0 = 1.74 × 10 4 ) , and only the shape of the statistics differs. Dashed circles highlight the initially unstable region.

Fig. 2
Fig. 2

Experimental results of all-optical bump-on-tail instability. Top, intensity (x space); bottom, power spectrum (k space). Shown are output pictures after (a),(b) linear and (c),(d) nonlinear propagation ( Δ n n 0 = 1.74 × 10 4 ) . The blue and red curves in (b) and (d) show holographic readouts of single-beam propagation for the straight (blue) and angled (red) distributions, respectively.

Fig. 3
Fig. 3

Comparison of flattening efficiency from theory, simulation, and experiment.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

f z + β k f r + Δ n ( I ) r f k = 0 ,
1 = γ β d k x f 0 k x k x g α β ,
g β α 2 = Δ k + α 2 4 γ I 0 β α 2 1 ,
g 2 α 2 β γ f 0 ( k x ) [ 1 + 3 ( α β g ) 2 k x 2 ] d k x .
g R = g P ( 1 + 3 2 α 2 λ D 2 ) ,
g I π 2 γ α γ I 0 β | ( f 0 k x ) | k x = g α β ,

Metrics