Talbot effect for dispersion in linear optical fibers and a wavelet approach
Rosu Barbus, Haret-Codratian
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 trans-mission (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 disper-sion. Although dispersion deals with continuous functions, such as gaussian and supergaussian pulses, whereas in diﬀraction one frequently deals with discontin-uous 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 simi-lar for supergaussian pulses. Finally, a high-precision measurement of irrational distances employing the fractal index determined with the wavelet transform is pointed out.
Fecha de publicación2006
Palabras claveTalbot eﬀect
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