Abstract

We obtain the correlation pattern between two amplitude-modulated input images of 36 and 280 random black and white pixels, using the standard degenerate four-wave-mixing geometry of 852-nm optical beams in a 1-mm-thick cesium-vapor cell. The total optical input power is 3.2 mW to obtain 0.4 nW of power in the correlation pattern. We verified that the buildup time of the four-wave-mixing signal is ~30 ns. Using the random patterns, we analyze the performance of the cesium optical correlator in terms of the number of pixels that can be processed and the number of photons per pixel used. We show how to scale our experimental results for the efficiency of the cesium correlator to images containing a larger number of pixels.

© 1994 Optical Society of America

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References

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1994 (1)

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

1993 (3)

1992 (3)

H. Rajbenbach, Appl. Opt. 31, 5666 (1992).
[CrossRef] [PubMed]

R. Thoma, N. Hampp, Opt. Lett. 17, 1158 (1992).
[CrossRef] [PubMed]

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

1989 (1)

1980 (2)

S. G. Odulov, M. S. Soskin, Sov. Phys. Dokl. 25, 380 (1980).

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

1978 (2)

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 34, 813 (1978).
[CrossRef]

D. M. Pepper, J. AuYeung, D. Fekete, A. Yariv, Opt. Lett. 3, 7 (1978).
[CrossRef] [PubMed]

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Abrams, R. L.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

Ai, B.

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

AuYeung, J.

Beddard, G. S.

Bell, M.

Biaggio, I.

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

Bloch, D.

Bloom, D. M.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 34, 813 (1978).
[CrossRef]

Chiu, T. H.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

A. Partovi, A. M. Glass, T. H. Chiu, D. T. H. Liu, Opt. Lett. 18, 906 (1993).
[CrossRef] [PubMed]

Connors, L. M.

Ducloy, M.

Economou, N. P.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 34, 813 (1978).
[CrossRef]

Fekete, D.

Fichet, M.

Foote, P. D.

Glass, A. M.

A. Partovi, A. M. Glass, T. H. Chiu, D. T. H. Liu, Opt. Lett. 18, 906 (1993).
[CrossRef] [PubMed]

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

Glassner, D. S.

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

Hall, T. J.

Hampp, N.

Hellwarth, R. W.

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

R. W. Hellwarth, in NSF Workshop on Optical Nonlinearities, Fast Phenomena and Signal Processing, N. Peyghambarian, ed. (National Science Foundation, Washington D.C., 1986), pp. 67–79.

Jonathan, J. M. C.

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

Knize, R. J.

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

Knox, W. H.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

Lam, J. F.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

Liao, P. F.

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 34, 813 (1978).
[CrossRef]

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

Lind, R. C.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

Liu, D. T. H.

McFadyen, G. G.

O'Bryan, H. M.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

Odulov, S. G.

S. G. Odulov, M. S. Soskin, Sov. Phys. Dokl. 25, 380 (1980).

Olson, D. H.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

Oria, M.

Partanen, J. P.

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

Partovi, A.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

A. Partovi, A. M. Glass, T. H. Chiu, D. T. H. Liu, Opt. Lett. 18, 906 (1993).
[CrossRef] [PubMed]

Pepper, D. M.

Powell, K.

Proudley, G. M.

Rajbenbach, H.

Reid, G. D.

Soskin, M. S.

S. G. Odulov, M. S. Soskin, Sov. Phys. Dokl. 25, 380 (1980).

Steel, D. G.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

Thoma, R.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

White, J.

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Yariv, A.

Zydzik, G. J.

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (4)

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

A. Partovi, A. M. Glass, D. H. Olson, G. J. Zydzik, H. M. O'Bryan, T. H. Chiu, W. H. Knox, Appl. Phys. Lett. 62, 464 (1993).
[CrossRef]

P. F. Liao, D. M. Bloom, N. P. Economou, Appl. Phys. Lett. 34, 813 (1978).
[CrossRef]

B. Ai, D. S. Glassner, R. J. Knize, J. P. Partanen, Appl. Phys. Lett. 64, 951 (1994).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Commun. (1)

R. J. Knize, J. M. C. Jonathan, B. Ai, D. S. Glassner, J. P. Partanen, Opt. Commun. 94, 245 (1992).
[CrossRef]

Opt. Lett. (4)

Sov. Phys. Dokl. (1)

S. G. Odulov, M. S. Soskin, Sov. Phys. Dokl. 25, 380 (1980).

Other (3)

I. Biaggio, B. Ai, R. J. Knize, J. P. Partanen, R. W. Hellwarth, in Conference on Lasers and Electro-Optics, Vol. 8 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 171–172.

R. W. Hellwarth, in NSF Workshop on Optical Nonlinearities, Fast Phenomena and Signal Processing, N. Peyghambarian, ed. (National Science Foundation, Washington D.C., 1986), pp. 67–79.

R. L. Abrams, J. F. Lam, R. C. Lind, D. G. Steel, P. F. Liao, in Optical Phase Conjugation, R. A. Fisher, ed. (Academic, New York, 1983), p. 211.

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Figures (3)

Fig. 1
Fig. 1

Schematic of the optical correlator. The lens has a focal length f of 127 mm. BS1 and BS2 are 50/50 beam splitters. BS1 is used to make the two input beams parallel and to view the input images I1 and I2. The intensity of beam 3 at the position of the Cs cell is 0.6 mW/cm2. Beams 1 and 2 are vertically polarized with powers of 2.3 and 0.85 mW, respectively. Beam 3 is horizontally polarized, and the horizontal polarizer in the path of the signal beam after BS2 suppresses scattered light from the two image-bearing beams.

Fig. 2
Fig. 2

Arrangement of input images and output signals as they would appear in the plane of I1 (the front focal plane of the lens) if image I2 were also imprinted in this plane and beam splitters BS1 and BS2 were absent (see Fig. 1). The left (right) image is that of the transparency I1 (I2) in Fig. 1. The backward beam (beam 3 in Fig. 1) gives a bright spot in the same front focal plane at the origin of the coordinate axes labeled x,y. The dashed circle gives the region in the focal plane that defines the acceptance angle θ0 of the Cs vapor and has a diameter of 2f tan(θ0/2) = 2.5 mm, where f is the focal length of the lens. The dotted–dashed rectangle encloses the output correlation pattern as it appears in the focal plane.

Fig. 3
Fig. 3

Intensity detected at the correlator signal plane of Fig. 1 as a function of the position x′, y′ defined in Fig. 2. The position of the highest peak gives the position of the smaller image inside the larger image through relation (1). The remainder of the correlation pattern arises from partial random correlations. The maximum intensity in the correlation peak is 0.4 μW cm−2, and its half-width at half-maximum is 20 μm.

Equations (1)

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E c ( x , y ) ~ E 1 ( x + u , y + v ) E 2 * ( u , v ) d u d v E 1 E 2 *

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