Abstract

We show that Bloch oscillations are possible in dissipative optical waveguide lattices with a linearly varying propagation constant. These oscillations occur in spite of the fact that the Bloch wave packet experiences coupling gain and (or) loss. Experimentally, this process can be observed in different settings, such as in laser arrays and lattices of semiconductor optical amplifiers. In addition, we demonstrate that these systems can suppress instabilities arising from preferential mode noise growth.

© 2004 Optical Society of America

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  1. D. Botez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994).
    [CrossRef]
  2. K. Otsuka, Electron. Lett. 19, 723 (1983).
    [CrossRef]
  3. J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
    [CrossRef]
  4. M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
    [CrossRef]
  5. U. Peschel, T. Pertsch, and F. Lederer, Opt. Lett. 23, 1701 (1998).
    [CrossRef]
  6. T. Pertsch, P. Dannberg, W. Elflein, A. Bruer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  7. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  8. N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2002).
    [CrossRef]
  9. H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988).
  10. G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
    [CrossRef]
  11. H. G. Winful and R. K. Defreez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994), pp. 226–254.
    [CrossRef]
  12. T. Pertsch, U. Peschel, and F. Lederer, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1999), paper QThG8.
  13. D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
    [CrossRef]

2002 (2)

M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2002).
[CrossRef]

1999 (2)

T. Pertsch, P. Dannberg, W. Elflein, A. Bruer, 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]

1998 (1)

1991 (1)

G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[CrossRef]

1986 (1)

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

1984 (1)

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

1983 (1)

K. Otsuka, Electron. Lett. 19, 723 (1983).
[CrossRef]

Ackley, D. E.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Aitchison, J. S.

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

Botez, D.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

D. Botez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994).
[CrossRef]

Bruer, A.

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

Butler, J. K.

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Christodoulides, D. N.

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2002).
[CrossRef]

Clück, M.

M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
[CrossRef]

Dannberg, P.

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

DeFreez, R. K.

G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[CrossRef]

H. G. Winful and R. K. Defreez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994), pp. 226–254.
[CrossRef]

Dunlap, D. H.

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

Efremidis, N. K.

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2002).
[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. Bruer, and F. Lederer, Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

Kenkre, V. M.

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

Kogelnik, H.

H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988).

Kolovsky, A. R.

M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
[CrossRef]

Korsch, H. J.

M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
[CrossRef]

Lederer, F.

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

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

T. Pertsch, U. Peschel, and F. Lederer, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1999), paper QThG8.

Morandotti, R.

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

Otsuka, K.

K. Otsuka, Electron. Lett. 19, 723 (1983).
[CrossRef]

Pertsch, T.

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

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

T. Pertsch, U. Peschel, and F. Lederer, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1999), paper QThG8.

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]

T. Pertsch, U. Peschel, and F. Lederer, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1999), paper QThG8.

Silberberg, Y.

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

Wilson, G. A.

G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[CrossRef]

Winful, H. G.

G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[CrossRef]

H. G. Winful and R. K. Defreez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994), pp. 226–254.
[CrossRef]

Appl. Phys. Lett. (1)

J. K. Butler, D. E. Ackley, and D. Botez, Appl. Phys. Lett. 44, 293 (1984).
[CrossRef]

Electron. Lett. (1)

K. Otsuka, Electron. Lett. 19, 723 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. A. Wilson, R. K. DeFreez, and H. G. Winful, IEEE J. Quantum Electron. 27, 1696 (1991).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

M. Clück, A. R. Kolovsky, and H. J. Korsch, Phys. Rep. 366, 103 (2002).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. E (1)

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

T. Pertsch, P. Dannberg, W. Elflein, A. Bruer, 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]

Other (4)

H. Kogelnik, in Guided-Wave Optoelectronics, T. Tamir, ed. (Springer-Verlag, Berlin, 1988).

D. Botez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994).
[CrossRef]

H. G. Winful and R. K. Defreez, in Diode Laser Arrays, D. Botez and D. R. Scifres, eds. (Cambridge U. Press, Cambridge, England, 1994), pp. 226–254.
[CrossRef]

T. Pertsch, U. Peschel, and F. Lederer, in Quantum Electronics and Laser Science Conference (Optical Society of America, Washington, D.C., 1999), paper QThG8.

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Figures (3)

Fig. 1
Fig. 1

Evolution arising from a single waveguide excitation when α=1±i0.4 and β=1. Left panel, =0; right panel, =0.003.

Fig. 2
Fig. 2

Evolution arising from a single waveguide excitation when α=1±i0.4 and β=1. Left panel, =0; right panel, =0.003.

Fig. 3
Fig. 3

Path of a beam in the xy plane when βx=3/6 and βy=4/6 and α=1 (left panel) and α=1+i0.5 (right panel). The starting (and final) point of the oscillations is A. Note that in the conservative case the beam follows the initial path to return from B to A, whereas in the nonconservative case the beam returns to A from a different path.

Equations (11)

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

iu˙n-iun+αun+1+un-1+βnun=0,
unt=BJn4αβsinβt2expin2βt+πexpt,
P=1Ttt+TPtdt
T=2π/β.
un=exp-n-n0/A2
<-2αi.
gavg=02πgθdθ=2π<0,    or <0.
iu˙m,n-ium,n+Δ2um,n+βxm+βynum,n=0,
um,nt=BJmpxJnpyexpimqx+nqyexpt,
Tx=2π/βx,    Ty=2π/βy.
R=m,nmxˆ+nyˆum,n2m,num,n2,

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