CONICET | Buscador de Institutos y Recursos Humanos

A generalization of the Fourier transform or spectrum of a signal, namely the fractional Fourier transform (FRT), allows to obtain the Radon-Wigner transform (RWT) when the fractional order p of the FRT is varied from 0 (only temporal information) to 1 (only spectral information or ordinary Fourier transform). In this way, the whole RWT display can be considered as a dual phase-space signal representation. Although originally employed for space optics applications, the RWT can be translated to the temporal domain using the spatial-time analogy so becoming a useful tool for different optical pulse processing operations. For the case of a pulse distorted and/or broadened under transmission in a certain optical channel, the complete RWT display of the pulse complex amplitude gives information about the specific fractional order p = pC which has associated an irradiance showing partial symmetry and compression effects. Thus, if the FRT of order pC can be applied to the distorted pulse, the obtained time-varying irradiance gives rise to a compressed and partially reshaped pulse. In this work we analyze a photonic implementation of the temporal FRT irradiance by combining chromatic dispersion transmission and phase modulation of the pulse to be processed. For analysis purposes, as the complete RWT should be obtained, it is very unpractical to get an experimental implementation since it would require both, a very precise adjustment and the continuous variation of the device parameters. For this reason the RWT should be numerically produced. The RWT computational generation implies to know amplitude and phase information of the pulse, something which is not the case in most applications. This problem can be solved in two different ways: i) Through an experimental amplitude and phase recoverying process, or ii) by a numerical modelling of the pulse. The second approach can be only applied if there is a partial knowledge of the fiber optic channel where the pulse was propagated. From the numerical RWT display one or several fractional orders pC are chosen for synthesizing a particular, required time waveform using our proposed setup. To illustrate this approach, different FRT irradiances are generated and combined in order to modulate a continuous wave laser source. In this way, the regeneration of a pulse is performed by selecting the FRT irradiances which, when combined, can shape the desired waveform; e.g. a symmetry operation on a deformed pulse can be readily done. On the other hand, conditions for deriving the fractional orders pC needed to regenerate an originally symmetrical pulse are theoretically obtained. A scaling operation of the FRT is also explored in order to have a more versatile and functional pulse regeneration. Some important applications concerning with long haul optical communications are illustrated such as: second and third order chromatic dispersion compensation and partial mitigation of some nonlinear effects.