Matrix theory and entropy of the partially-coherent temporal Talbot effect

Author： Chantada Laura Fernández-pousa Carlos Gómez-reino Carlos

ISSN： 1362-3044

Source： Journal of Modern Optics, Vol.54, Iss.4, 2007-03, pp. : 501-514

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Abstract

The temporal Talbot effect is a well-established passive, coherent and all-optical technique for multiplying the repetition rate of the intensity of pulse trains in guided media after first-order dispersive propagation. In this paper we report on a matrix analysis of this technique under partial coherence. This formalism takes into account the two aspects that affect the intensity patterns after partially-coherent Talbot propagation: the intrinsic coherence of the carrier wave and the spectral content of the pulse trains. The matrix representation also provides a simple description of the intensity after partially-coherent Talbot propagation by means of a reduced number of variables. After diagonalization, the impact of partial coherence can be described by means of the informational entropy, which leads to the measure of the effective number of degrees of freedom that describe the intensity. Using the Szegö theorem, we also present approximate analytical expressions for the entropy in the limit of narrow pulses.