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Theoretical study and applications of Talbot effect

Array illuminator based on Talbot effect is an important optical element that has wide applications in optical interconnection, optical communication, and optical computing. This paper summarizes our recent results on this subject. Symmetry of the Talbot effect, that was reported in Optics Communication 115, 40 (1995), is now realized as the first step to revealing other rules for explanation of the Talbot effect for array illumination. The prime-number decomposing rule (Applied Optics 40, 607 (2001)) shows that the number of phase level of a Talbot array illuminator is related with the prime number. Along with the study of the characteristics of the Talbot array illuminator, the applications of the Talbot effect are also in progress. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages over the previous Fresnel encoding method. Furthermore, the hexagonal array illumination based on the Talbot effect was reported in Optics Letters 27, 228 (2002). Recently, a novel two-layered multifunctional computer generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters 28, 1513 (2003)), which can be multifunctional for potential use in secure system technology. We believe that the results reported in this paper should be useful tools for further exploration of the Talbot effect and design of novel optical devices that should benefit the practical applications.