dorsal/arxiv
View SchemaTalbot effect for dispersion in linear optical fibers and a wavelet approach
| Authors | H. C. Rosu, J. P. Trevino, H. Cabrera, J. S. Murguia |
|---|---|
| Categories | |
| ArXiv ID | physics/0510067 |
| URL | https://arxiv.org/abs/physics/0510067 |
| DOI | 10.1142/S0217979206034364 |
| Journal | Int. J. Mod. Phys. B 20 (2006) 1860-1876 |
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. 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
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"abstract": "We shortly recall the mathematical and physical aspects of Talbot\u0027s\nself-imaging effect occurring in near-field diffraction. In the rational\nparaxial approximation, the Talbot images are formed at distances z=p/q, where\np and q are coprimes, and are superpositions of q equally spaced images of the\noriginal binary transmission (Ronchi) grating. This interpretation offers the\npossibility to express the Talbot effect through Gauss sums. Here, we pay\nattention to the Talbot effect in the case of dispersion in optical fibers\npresenting our considerations based on the close relationships of the\nmathematical representations of diffraction and dispersion. Although dispersion\ndeals with continuous functions, such as gaussian and supergaussian pulses,\nwhereas in diffraction one frequently deals with discontinuous functions, the\nmathematical correspondence enables one to characterize the Talbot effect in\nthe two cases with minor differences. In addition, we apply, for the first time\nto our knowledge, the wavelet transform to the fractal Talbot effect in both\ndiffraction and fiber dispersion. In the first case, the self similar character\nof the transverse paraxial field at irrational multiples of the Talbot distance\nis confirmed, whereas in the second case it is shown that the field is not self\nsimilar for supergaussian pulses. Finally, a high-precision measurement of\nirrational distances employing the fractal index determined with the wavelet\ntransform is pointed out",
"arxiv_id": "physics/0510067",
"authors": [
"H. C. Rosu",
"J. P. Trevino",
"H. Cabrera",
"J. S. Murguia"
],
"categories": [
"physics.optics"
],
"doi": "10.1142/S0217979206034364",
"journal_ref": "Int. J. Mod. Phys. B 20 (2006) 1860-1876",
"title": "Talbot effect for dispersion in linear optical fibers and a wavelet approach",
"url": "https://arxiv.org/abs/physics/0510067"
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