Abstract

We present a feedback control method for the stabilization of unstable patterns and for the control of spatio-temporal disorder. The control takes the form of a spatial modulation to the input pump, which is obtained via filtering in Fourier space of the output electric field. The control is powerful, flexible and non-invasive: the feedback vanishes once control is achieved. We demonstrate by means of computer simulation, the effect of the control in two different optical systems.

© 1997 Optical Society of America

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  1. E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
    [Crossref] [PubMed]
  2. C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
    [Crossref]
  3. M. C. Cross and P. C. Hohenberg , Rev. Mod. Phys.   65 , 851 ( 1993 ).
    [Crossref]
  4. L. A. Lugiato and C. Oldano , Phys. Rev. A   37 , 3896 ( 1988 ).
    [Crossref] [PubMed]
  5. W. J. Firth and A. J. Scroggie , Europhys. Lett.   26 , 521 ( 1994 ).
    [Crossref]
  6. R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
    [Crossref] [PubMed]
  7. R. Neubecker and G.-L. Oppo et al, Phys. Rev. A   52 , 791 ( 1995 ).
    [Crossref] [PubMed]
  8. G. D’Alessandro and W. J. Firth , Phys. Rev. A   46 , 537 ( 1992 ).
    [Crossref] [PubMed]
  9. G. K. Harkness et al, Phys. Rev. A   50 , 4310 ( 1994 ).
    [Crossref] [PubMed]
  10. G. K. Harkness et al, submitted to Phys. Rev. A , Rapid Communications.

1996 (1)

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

1995 (2)

R. Neubecker and G.-L. Oppo et al, Phys. Rev. A   52 , 791 ( 1995 ).
[Crossref] [PubMed]

C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
[Crossref]

1994 (2)

W. J. Firth and A. J. Scroggie , Europhys. Lett.   26 , 521 ( 1994 ).
[Crossref]

G. K. Harkness et al, Phys. Rev. A   50 , 4310 ( 1994 ).
[Crossref] [PubMed]

1993 (1)

M. C. Cross and P. C. Hohenberg , Rev. Mod. Phys.   65 , 851 ( 1993 ).
[Crossref]

1992 (1)

G. D’Alessandro and W. J. Firth , Phys. Rev. A   46 , 537 ( 1992 ).
[Crossref] [PubMed]

1990 (1)

E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
[Crossref] [PubMed]

1988 (1)

L. A. Lugiato and C. Oldano , Phys. Rev. A   37 , 3896 ( 1988 ).
[Crossref] [PubMed]

Babloyantz, A.

C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
[Crossref]

Cross, M. C.

M. C. Cross and P. C. Hohenberg , Rev. Mod. Phys.   65 , 851 ( 1993 ).
[Crossref]

D’Alessandro, G.

G. D’Alessandro and W. J. Firth , Phys. Rev. A   46 , 537 ( 1992 ).
[Crossref] [PubMed]

Firth, W. J.

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

W. J. Firth and A. J. Scroggie , Europhys. Lett.   26 , 521 ( 1994 ).
[Crossref]

G. D’Alessandro and W. J. Firth , Phys. Rev. A   46 , 537 ( 1992 ).
[Crossref] [PubMed]

Grebogi, C.

E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
[Crossref] [PubMed]

Harkness, G. K.

G. K. Harkness et al, Phys. Rev. A   50 , 4310 ( 1994 ).
[Crossref] [PubMed]

G. K. Harkness et al, submitted to Phys. Rev. A , Rapid Communications.

Hohenberg, P. C.

M. C. Cross and P. C. Hohenberg , Rev. Mod. Phys.   65 , 851 ( 1993 ).
[Crossref]

Hougardy, M.

C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
[Crossref]

Lourenço, C.

C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
[Crossref]

Lugiato, L. A.

L. A. Lugiato and C. Oldano , Phys. Rev. A   37 , 3896 ( 1988 ).
[Crossref] [PubMed]

Martin, R.

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

Neubecker, R.

R. Neubecker and G.-L. Oppo et al, Phys. Rev. A   52 , 791 ( 1995 ).
[Crossref] [PubMed]

Oldano, C.

L. A. Lugiato and C. Oldano , Phys. Rev. A   37 , 3896 ( 1988 ).
[Crossref] [PubMed]

Oppo, G.-L.

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

R. Neubecker and G.-L. Oppo et al, Phys. Rev. A   52 , 791 ( 1995 ).
[Crossref] [PubMed]

Ott, E.

E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
[Crossref] [PubMed]

Scroggie, A. J.

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

W. J. Firth and A. J. Scroggie , Europhys. Lett.   26 , 521 ( 1994 ).
[Crossref]

Yorke, J. A.

E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
[Crossref] [PubMed]

Europhys. Lett. (1)

W. J. Firth and A. J. Scroggie , Europhys. Lett.   26 , 521 ( 1994 ).
[Crossref]

Phys. Rev. A (4)

L. A. Lugiato and C. Oldano , Phys. Rev. A   37 , 3896 ( 1988 ).
[Crossref] [PubMed]

R. Neubecker and G.-L. Oppo et al, Phys. Rev. A   52 , 791 ( 1995 ).
[Crossref] [PubMed]

G. D’Alessandro and W. J. Firth , Phys. Rev. A   46 , 537 ( 1992 ).
[Crossref] [PubMed]

G. K. Harkness et al, Phys. Rev. A   50 , 4310 ( 1994 ).
[Crossref] [PubMed]

Phys. Rev. E (1)

C. Lourenço , M. Hougardy , and A. Babloyantz , Phys. Rev. E   52 , 1528 ( 1995 ).
[Crossref]

Phys. Rev. Lett. (2)

E. Ott , C. Grebogi , and J. A. Yorke , Phys. Rev. Lett.   64 , 1196 ( 1990 ).
[Crossref] [PubMed]

R. Martin , A. J. Scroggie , G.-L. Oppo , and W. J. Firth , Phys. Rev. Lett.   77 , 4007 ( 1996 ).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

M. C. Cross and P. C. Hohenberg , Rev. Mod. Phys.   65 , 851 ( 1993 ).
[Crossref]

Other (1)

G. K. Harkness et al, submitted to Phys. Rev. A , Rapid Communications.

Supplementary Material (2)

» Media 1: MOV (296 KB)     
» Media 2: MOV (476 KB)     

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Figures (2)

Fig. 1
Fig. 1

The figure displays the patterns shown in the animation, along with the feedback (shaded curve) which vanishes when stabilization is achieved. The feedback is normalised to the maximum wave-vector of the pattern. [Media 1]

Fig. 2
Fig. 2

Schematic diagram of the LCLV in a configuration modelling a Kerr-slice feedback with mirror, with an added control loop (dashed box). F denotes the plane-wave input field, and B the backward field. The Filtering is performed in the Fourier plane in the feedback loop. [Media 2]

Equations (5)

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t E ψ = E [ ( 1 + ) + 2 C ( 1 i Δ ) E 2 + 1 + Δ 2 ] + E I + i ( xx + yy ) E ψ
E I ( x , y ) = E I 0 ( 1 s 1 f 1 ( x , y ) )
f 1 ( x , y ) = F 1 UFE
b 1 a 1 + a 4 b 31 a 3 + a 2 b 2 a 2 + a 1 b 4 a 4 + a 3
E I ( x , y ) = E I 0 ( 1 s 1 f 1 ( x , y ) + s 2 f 2 ( x , y ) )

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