Talbot effect for dispersion in linear optical fibers and a wavelet approach

Simple item page
dc.creatorRosu, H. C.
dc.creatorTrevino, J. P.
dc.creatorCabrera, H.
dc.creatorMurguia, J. S.
dc.date2005-10-08
dc.date2005-12-10
dc.date.accessioned2026-07-07T06:48:21Z
dc.date.available2026-07-07T06:48:21Z
dc.descriptionWe shortly recall the mathematical and physical aspects of Talbot's self-imaging effect occurring in near-field diffraction. In the rational paraxial approximation, the Talbot images are formed at distances z=p/q, where p and q are coprimes, and are superpositions of q equally spaced images of the original binary transmission (Ronchi) grating. This interpretation offers the possibility to express the Talbot effect through Gauss sums. Here, we pay attention to the Talbot effect in the case of dispersion in optical fibers presenting our considerations based on the close relationships of the mathematical representations of diffraction and dispersion. Although dispersion deals with continuous functions, such as gaussian and supergaussian pulses, whereas in diffraction one frequently deals with discontinuous functions, the mathematical correspondence enables one to characterize the Talbot effect in the two cases with minor differences. In addition, we apply, for the first time to our knowledge, the wavelet transform to the fractal Talbot effect in both diffraction and fiber dispersion. In the first case, the self similar character of the transverse paraxial field at irrational multiples of the Talbot distance is confirmed, whereas in the second case it is shown that the field is not self similar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed out
dc.description15 text pages + 7 gif figs, accepted at Int. J. Mod. Phys. B, final version of a contribution at ICSSUR-Besancon (May/05). Color figs available from the first author
dc.identifierhttps://arxiv.org/abs/physics/0510067
dc.identifierhttp://arxiv.org/abs/physics/0510067
dc.identifierInt. J. Mod. Phys. B 20 (2006) 1860-1876
dc.identifierdoi:10.1142/S0217979206034364
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103971
dc.subjectOptics
dc.titleTalbot effect for dispersion in linear optical fibers and a wavelet approach
dc.typetext

Files

Collections

arXiv