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.

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References

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Other (10)

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

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

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

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

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

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

R Neubecker, 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]

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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