Abstract

Recently, the classical Talbot effect (self-imaging of optical wave fields) has attracted a renewed interest, as the concept has been generalized to the domain of pulsed wave fields by several authors. In this paper we discuss the self-imaging of three-dimensional images. We construct pulsed wave fields that can be used as self-imaging �pixels� of a three-dimensional image and show that their superpositions reproduce the spatial separated copies of its initial three-dimensional intensity distribution at specific time intervals. The derived wave fields will be shown to be directly related to the fundamental localized wave solutions of the homogeneous scalar wave equation � focus wave modes. Our discussion is illustrated by some spectacular numerical simulations. We also propose a general idea for the optical generation of the derived wave fields. The results will be compared to the work, published so far on the subject.

© 2002 Optical Society of America

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J. Mod. Opt.

Z. Bouchal and M. Bertolotti, �Self-reconstruction of wave packets due to spatio-temporal couplings,� J. Mod. Opt. 47, 1455 - 1467 (2000).

J. Opt. A: Pure Appl. Opt.

J. Salo and M. M. Salomaa, �Diffraction-free pulses at arbitrary speeds,� J. Opt. A: Pure Appl. Opt. 3, 366-373 (2001).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Laser Phys.

P. Saari, H. S�najalg, �Pulsed Bessel beams,� Laser Phys. 7, 32-39 (1997).

Microwave and Opt. Technol. Lett.

H. Wang, C. Zhou, L. Jianlang and L. Liu, �Talbot effect of a grating under ultrashort pulsed-laser illumination,� Microwave and Opt. Technol. Lett. 25, 184-187 (2000)

Opt. Commun.

Zs. Bor and B. R�cz, �Group velocity dispersion in prisms and its application to pulse compression and traveling-wave excitation,� Opt. Commun. 54, 165-170 (1985).

Z. Bouchal and J. Wagner, �Self-reconstruction effect in free propagation of wavefield,� Opt. Commun. 176, 299-307 (2000).

P. Saari, J. Aaviksoo, A. Freiberg, K. Timpmann, �Elimination of excess pulse broadening at high spectral resolution of picosecond duration light emission,� Opt. Commun. 39, 94-98 (1981).

Opt. Lett.

Opt.Commun.

J. Wagner and Z. Bouchal, �Experimental realization of self-reconstruction of the 2D aperiodic objects,� Opt.Commun. 176, 309-311 (2000).

Phys. Rev. E

K. Reivelt and P. Saari, �Optically realizable localized wave solutions of homogeneous scalar wave equation,� Phys. Rev. E (to be published) [accepted for publication].

Phys. Rev. Lett.

P. Saari and K. Reivelt, �Evidence of X-shaped propagation-invariant localized light waves,� Phys. Rev. Lett. 79, 4135-4138 (1997).

J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, �Diffraction-free beams,� Phys. Rev. Lett. 58, 1499�1501 (1987).

P. Di Trapani, D. Caironi, G. Valiulis, A. Dubietis, R. Danielius and A. Piskarskas, �Observation of Temporal Solitons in Second-Harmonic Generation with Tilted Pulses,� Phys. Rev. Lett. 81, 570-573 (1998).

Proc. SPIE

Z. Bouchal, �Self-reconstruction ability of wave field,� Proc. SPIE, vol. 4356, 217-224, (2001).

Progr. In Electromagn. Research

I. Besieris, M. Abdel-Rahman, A. Shaarawi, and A. Chatzipetros, �Two fundamental representations of localized pulse solutions of the scalar wave equation,� Progr. In Electromagn. Research 19, 1 (1998).

Pure Appl. Opt.

J. Turunen and A. T. Friberg, �Self-imaging and propagation-invariance in electromagnetic fields,� Pure Appl. Opt. 2, 51-60 (1993).

Other

O. Svelto, Principles of Lasers (3rd ed. Plenum Press 1989).

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