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Talbot effect for dispersion in linear optical fibers | | H.C. Rosu
; J.P. Trevino
; H. Cabrera
; J.S. Murguia
; | | Date: |
8 Oct 2005 | | Abstract: | We 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. 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 dispersion | | Source: | arXiv, physics/0510067 | | Services: | Forum | Review | PDF | Favorites | |
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