Document
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Talbot effect for dispersion in linear optical fibers and a wavelet approach
related by: authorship_47823
volume: 20
type: Entity
type: Document
accesstype: All Open Access, Green
type: Continuant
type: Thing
estado: published
has publication venue: International Journal of Modern Physics B
related by: authorship_47821
page start: 1860
most specific type: Conference Paper
type: Conference Paper
issue: 11-13
EI dscopus: 2-s2.0-33744507313
type: Generically Dependent Continuant
origen: scopus
abstract: We shortly recall the mathematical and physical aspects of Talbot%27s self-imaging effect occurring in near-field diffraction. In the rational paraxial approximation, the Talbot images are formed at distances ζ = 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. © World Scientific Publishing Company.
doi: 10.1142/S0217979206034364
page end: 1876
related by: authorship_47824
date time value: conference paper date 7486
crisid: 7486
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 ζ = 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. © World Scientific Publishing Company.
freetext keyword: Gauss sums; Talbot effect; Wavelet transform
related by: authorship_47822
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RDF description of Talbot effect for dispersion in linear optical fibers and a wavelet approach - http://orbis.uaslp.mx/vivo/individual/scopus7485
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date: 2026-08-28T22:55:35
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International Journal of Modern Physics B
type: Information Content Entity
type: Thing
type: Continuant
type: Generically Dependent Continuant
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publication venue for: Talbot effect for dispersion in linear optical fibers and a wavelet approach

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Conference Paper
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