Abstract

It is shown that a frequency mode-locked laser with a sinusoidal sweep of modulation frequency around a mode-locking condition represents an ideal optical system for observing in the spectral domain the phenomena of dynamic localization and Bloch oscillations of electrons in an ideal solid placed in an external ac electric field.

© 2005 Optical Society of America

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  1. C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
    [CrossRef]
  2. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  3. G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
    [CrossRef]
  4. T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  5. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  6. V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
    [CrossRef]
  7. B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
    [CrossRef]
  8. B. Fischer, B. Vodonos, S. Atkins, and A. Bekker, Opt. Lett. 27, 1061 (2002).
    [CrossRef]
  9. S. Atkins, A. Rosen, A. Bekker, and B. Fischer, Opt. Lett. 28, 2228 (2003).
    [CrossRef] [PubMed]
  10. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
    [CrossRef]
  11. M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
    [CrossRef]
  12. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.
  13. H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
    [CrossRef]
  14. S. Longhi and P. Laporta, Appl. Phys. Lett. 73, 720 (1998).
    [CrossRef]
  15. S. Longhi, Phys. Rev. E 63, 037201 (2001).
    [CrossRef]
  16. S. Longhi, Phys. Rev. E 64, 047201 (2001).
    [CrossRef]
  17. S. Longhi and P. Laporta, Phys. Rev. A 60, 4016 (1999).
    [CrossRef]
  18. X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
    [CrossRef]

2004 (1)

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

2003 (1)

2002 (2)

M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef]

B. Fischer, B. Vodonos, S. Atkins, and A. Bekker, Opt. Lett. 27, 1061 (2002).
[CrossRef]

2001 (2)

S. Longhi, Phys. Rev. E 63, 037201 (2001).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 047201 (2001).
[CrossRef]

2000 (1)

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

1999 (4)

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

S. Longhi and P. Laporta, Phys. Rev. A 60, 4016 (1999).
[CrossRef]

1998 (3)

S. Longhi and P. Laporta, Appl. Phys. Lett. 73, 720 (1998).
[CrossRef]

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

1996 (1)

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

1995 (1)

X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
[CrossRef]

1986 (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Agarwal, V.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Atkins, S.

Bekker, A.

Bräuer, A.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Bright, J. N.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

Coquillat, D.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Dannberg, P.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

de Sterke, C. M.

M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

del Ro, J. A.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Dignam, M. M.

M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef]

Dunlap, D. H.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Elflein, W.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Fischer, B.

Fishman, S.

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

Gil, B.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Hammon, T. E.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

Haus, H. A.

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

Ippen, E. P.

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

Jahnke, R.

X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
[CrossRef]

Jones, D. J.

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

Kavokin, A.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Kenkre, V. M.

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Krug, P. A.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

Laporta, P.

S. Longhi and P. Laporta, Phys. Rev. A 60, 4016 (1999).
[CrossRef]

S. Longhi and P. Laporta, Appl. Phys. Lett. 73, 720 (1998).
[CrossRef]

Lederer, F.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Lenz, G.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Longhi, S.

S. Longhi, Phys. Rev. E 63, 037201 (2001).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 047201 (2001).
[CrossRef]

S. Longhi and P. Laporta, Phys. Rev. A 60, 4016 (1999).
[CrossRef]

S. Longhi and P. Laporta, Appl. Phys. Lett. 73, 720 (1998).
[CrossRef]

Malpuech, G.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Niu, Q.

X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
[CrossRef]

Pertsch, T.

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
[CrossRef]

Rosen, A.

S. Atkins, A. Rosen, A. Bekker, and B. Fischer, Opt. Lett. 28, 2228 (2003).
[CrossRef] [PubMed]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

Scalbert, D.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

Talanina, I.

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

Vladimirova, M.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Vodonos, B.

Wang, W. S.

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

Zaho, X.-G.

X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
[CrossRef]

Zamfirescu, M.

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

S. Longhi and P. Laporta, Appl. Phys. Lett. 73, 720 (1998).
[CrossRef]

J. Lightwave Technol. (1)

H. A. Haus, D. J. Jones, E. P. Ippen, and W. S. Wang, J. Lightwave Technol. 14, 622 (1996).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

X.-G. Zaho, R. Jahnke, and Q. Niu, Phys. Lett. A 202, 297 (1995).
[CrossRef]

Phys. Rev. A (1)

S. Longhi and P. Laporta, Phys. Rev. A 60, 4016 (1999).
[CrossRef]

Phys. Rev. B (1)

D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
[CrossRef]

Phys. Rev. E (4)

S. Longhi, Phys. Rev. E 63, 037201 (2001).
[CrossRef]

S. Longhi, Phys. Rev. E 64, 047201 (2001).
[CrossRef]

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, Phys. Rev. E 57, 2365 (1998).
[CrossRef]

B. Fischer, A. Rosen, A. Bekker, and S. Fishman, Phys. Rev. E 61, R4694 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

M. M. Dignam and C. M. de Sterke, Phys. Rev. Lett. 88, 046806 (2002).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, Phys. Rev. Lett. 83, 963 (1999).
[CrossRef]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

V. Agarwal, J. A. del Ro, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, Phys. Rev. Lett. 92, 097401 (2004).
[CrossRef]

Other (1)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), Chap. 27.

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Figures (2)

Fig. 1
Fig. 1

Spectral and temporal FM laser dynamics after the mode locker is switched on in the dynamic mode-locking regime: (a) evolution of laser spectrum F m ; (b) evolution of spectral width (in units of ω R ); (c) laser spectrum at n = 6050 (solid curve) and at n = 6100 (dashed curve); (d) evolution of laser intensity ψ ( t , n ) 2 ; (e) evolution of average laser power P , showing the onset of relaxation oscillations; (f) field intensity at n = 6000 . Parameter values are δ ω 0 Ω = 1 , δ ω 0 ω R = 0.01 , ω g ω R = 356 , Δ = 0.1 , γ = 2 × 10 5 , l = 0.05 , and g 0 l = 1.5 .

Fig. 2
Fig. 2

Same as Fig. 1 but in the dynamic localization regime. Parameter values are as in Fig. 1, except for δ ω 0 Ω = 2.405 . In (c) the spectra are taken at n = 33,788 (solid curve) and at n = 33,728 (dotted curve). In (f) the field intensity is taken at n = 34,150 .

Equations (6)

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

n ψ = ( g l + D g t 2 ) ψ + i Δ cos [ ω R t + η ( n ) ] ψ ,
d g d n = γ ( g g 0 + g P ) ,
d F m d n = 2 π i m [ δ ω ( n T R ω R ) ] F m + ( g l D g m 2 ω R 2 ) F m + i ( Δ 2 ) ( F m + 1 + F m 1 ) .
ψ ( t , n ) = P 0 exp [ i W ( n ) sin ( ω R t + ϕ ) ] = P 0 m = J m ( W ) exp [ i m ω R ( t + ϕ ω R ) ] ,
u ( n ) = Δ 0 n d n cos [ η ( n ) ] ,
v ( n ) = Δ 0 n d n sin [ η ( n ) ] .

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