Abstract

The large dispersive properties and the narrow frequency bandwidth of the two-wave mixing in a liquid-crystal light valve is used to realize an adaptive holographic interferometer in the Raman–Nath regime. We report experimental observation of picometer periodic displacements and estimate the theoretical signal-to-noise ratio and the minimum quantum-noise-limited detectable displacement.

© 2009 Optical Society of America

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2009 (1)

See, e. g., A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, J. Appl. Phys. 105, 031101 (2009).

2008 (1)

U. Bortolozzo, S. Residori, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

2005 (1)

2002 (1)

A. A. Kamshilin and A. I. Grachev, Appl. Phys. Lett. 81, 2923 (2002).
[CrossRef]

1997 (4)

A. Brignon, I. Bongrand, B. Loiseaux, and J. P. Huignard, Opt. Lett. 22, 1855 (1997).
[CrossRef]

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

V. Petrov, C. Denz, J. Petter, and T. Tschudi, Opt. Lett. 22, 1902 (1997).
[CrossRef]

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

1990 (1)

1987 (1)

1981 (1)

Apostol, I.

Boccara, A. C.

Bongrand, I.

Bortolozzo, U.

U. Bortolozzo, S. Residori, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef] [PubMed]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 43, pp. 497-530.
[CrossRef]

Brignon, A.

de Montmorillon, L. A.

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

Delaye, P.

M. Lesaffre, F. Jean, F. Ramaz, A. C. Boccara, M. Gross, P. Delaye, and G. Roosen, Opt. Express 15, 1030 (2007).
[CrossRef] [PubMed]

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

Denz, C.

Di Girolamo, S.

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 43, pp. 497-530.
[CrossRef]

Grachev, A. I.

A. A. Kamshilin and A. I. Grachev, Appl. Phys. Lett. 81, 2923 (2002).
[CrossRef]

Gross, M.

Hahn, J.

Huignard, J. P.

Jean, F.

Kamshilin, A. A.

See, e. g., A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, J. Appl. Phys. 105, 031101 (2009).

S. Di Girolamo, A. A. Kamshilin, R. V. Romashko, Y. N. Kulchin, and J. C. Launay, Opt. Express 15, 545 (2006).
[CrossRef]

A. A. Kamshilin and A. I. Grachev, Appl. Phys. Lett. 81, 2923 (2002).
[CrossRef]

Khoo, I. C.

I. C. Khoo, Liquid Crystals, Wiley Series in Pure and Applied Optics (Wiley, 2007).
[CrossRef]

Kulchin, Y. N.

See, e. g., A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, J. Appl. Phys. 105, 031101 (2009).

S. Di Girolamo, A. A. Kamshilin, R. V. Romashko, Y. N. Kulchin, and J. C. Launay, Opt. Express 15, 545 (2006).
[CrossRef]

Launay, J. C.

S. Di Girolamo, A. A. Kamshilin, R. V. Romashko, Y. N. Kulchin, and J. C. Launay, Opt. Express 15, 545 (2006).
[CrossRef]

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

Lesaffre, M.

Loiseaux, B.

Marrakchi, A.

Petrov, M.

Petrov, M. P.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

Petrov, V.

Petrov, V. M.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

Petter, J.

Popa, D.

Ramaz, F.

Residori, S.

U. Bortolozzo, S. Residori, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef] [PubMed]

Romashko, R. V.

See, e. g., A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, J. Appl. Phys. 105, 031101 (2009).

S. Di Girolamo, A. A. Kamshilin, R. V. Romashko, Y. N. Kulchin, and J. C. Launay, Opt. Express 15, 545 (2006).
[CrossRef]

Roosen, G.

M. Lesaffre, F. Jean, F. Ramaz, A. C. Boccara, M. Gross, P. Delaye, and G. Roosen, Opt. Express 15, 1030 (2007).
[CrossRef] [PubMed]

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

Sokolov, I. A.

Spicer, J. B.

Stepanov, S. I.

Tschudi, T.

Vlad, V. I.

Wagner, J. W.

Xu, L. P.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

Yariv, A.

A. Yariv, Optical Waves in Crystals (John Wiley & Sons, 2003).

Zouboulis, I. S.

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

Appl. Phys. Lett. (1)

A. A. Kamshilin and A. I. Grachev, Appl. Phys. Lett. 81, 2923 (2002).
[CrossRef]

J. Appl. Phys. (2)

See, e. g., A. A. Kamshilin, R. V. Romashko, and Y. N. Kulchin, J. Appl. Phys. 105, 031101 (2009).

L. A. de Montmorillon, P. Delaye, J. C. Launay, and G. Roosen, J. Appl. Phys. 82, 5913 (1997).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. P. Petrov, V. M. Petrov, I. S. Zouboulis, and L. P. Xu, Opt. Commun. 134, 569 (1997).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

U. Bortolozzo, S. Residori, and J. P. Huignard, Phys. Rev. Lett. 100, 203603 (2008).
[CrossRef] [PubMed]

Other (3)

I. C. Khoo, Liquid Crystals, Wiley Series in Pure and Applied Optics (Wiley, 2007).
[CrossRef]

A. Yariv, Optical Waves in Crystals (John Wiley & Sons, 2003).

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E.Wolf, ed. (Elsevier Science, 2002), Vol. 43, pp. 497-530.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Experimental setup. The input laser is split into a reference and a signal that, before arriving at the LCLV, is sent to a vibrating object. NF, neutral density filters; PZT, piezoelectrically driven mirror.

Fig. 2
Fig. 2

Relative detection limits for m = 1 , 0 , 1 as a function of (a) n 2 , K = 5 and (b) K, n 2 = 4.5 cm 2 W . P S = 3.2 mW in both plots.

Fig. 3
Fig. 3

Signal V lock in detected on the 1 order as a function of the displacement δ and for Ω 2 π = 1 kHz , n 2 = 4.5 cm 2 W , K = 5 , P S = 3.2 mW ; (a) linear and (b) log scale. Solid curve is the fit with the theoretical curve J 0 ( 2 k 0 δ ) J 1 ( 2 k 0 δ ) .

Fig. 4
Fig. 4

Laser-induced membrane displacement; on/off indicates the switching of the laser.

Equations (5)

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

I = E R e i ( k ̃ r r ̃ + k 0 Δ ω 0 t ) + E S e i ( k ̃ s r ̃ + θ ω 0 t ) 2 ,
P m = P R e α D ( K 2 J m 2 + J m + 1 2 + 2 K J m J m + 1 sin ( θ ) ) ,
P ̂ m ( Ω ) = 4 P R e α D K J m J m + 1 J 1 ( 2 k 0 δ ) sin ( Ω t ) ,
SNR = 2 η P R ω 0 Δ ν e α D 2 K J m J m + 1 K 2 J m 2 + J m + 1 2 2 k 0 δ ,
δ lim ( rel ) = K 2 J m 2 + J m + 1 2 K J m J m + 1 e α D 2 .

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