Abstract

We propose to use photon echoes in rare-earth-doped crystals to implement the Fourier-transform chirp algorithm. The process is considered for application to spectral analysis of fast radio-frequency signals. Compared with surface acoustic wave devices, the proposed scheme gives access to the larger bandwidths of rare-earth-doped crystals and greater flexibility. An experimental demonstration of the proposed process is reported.

© 2001 Optical Society of America

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References

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1999

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1996

1986

Afzelius, M.

Altner, S. B.

Anderson, K. E.

Babbit, W. R.

Babbitt, W. R.

Bai, Y. S.

Boggs, B.

Cabaret, L.

Cone, R. L.

Equall, R. W.

Graf, F. R.

Greiner, C.

Gustafsson, U.

Harris, T. L.

Kröll, S.

Le Gouët, J.-L.

Lin, H.

Lorgeré, I.

Maniloff, E.

Ménager, L.

Merkel, K. D.

Mohan, R. K.

Mossberg, T. W.

Ohlsson, N.

Plagemann, B. H.

Renn, A.

Ritcey, J. A.

Sun, Y.

Wagner, K. H.

Wang, T.

Wang, X.

Wild, U. P.

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Figures (3)

Fig. 1
Fig. 1

(a) Complete exciting sequence and echo signal in the demonstration experiment and (b) laser frequency chirps during the sequence; A, first chirp, rate 2r; B, second chirp, rate -2r; C, third chirp, rate r, modulated by square pulses; D, echo signal; PM, photomultiplier.

Fig. 2
Fig. 2

Schematic of the experimental setup.

Fig. 3
Fig. 3

Echo signal detected for input pulse train frequencies of (a) 5, (b) 3, and (c) 1  MHz, averaged over 16 acquisitions. Solid curves, experimental records; dotted curves, calculated FTs.

Equations (2)

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E˜rt=Etexpiπrt2exp-iπrt2expiπrt2,
Et=E1*-tE2tE3t,

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