In this work we analyze the compression and equalization of pulses in the ps range by using an approach based on the
Radon-Wigner transform (RWT). The whole RWT display is obtained from a generalization of the Fourier transform,
namely the fractional Fourier transform (FRT), by varying the fractional order <i>p</i> from 0 (temporal information) to 1
(spectral information). From the inspection of the RWT the optimum fractional order <i>pC</i> originating the desired
processing condition can be obtained. However, as this signal representation depends on a scale factor which should be
introduced, the value of <i>pC</i> is also affected. This point is here analyzed taking into account the restrictions on the scale
factor which are imposed by the photonic devices involved in an experimental implementation; namely, an amount of
chromatic dispersion and an attainable phase modulation factor. We illustrate the method with some applications which
are of interest in fiber optic links such as second and third order chromatic dispersion compensation and pulse
transmission under a non linear regime. The theoretical model derived from an analytical expression of the FRT is
corroborated with numerical simulations.
The temporal Radon-Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT)
for a varying fractional order p, is here employed as a processing tool for pulses with FWHM of ps-tens of ps,
commonly found in fiber optic transmission systems. To synthesize the processed pulse, a selected FRT irradiance is
optically produced employing a photonic device that combines quadratic phase modulation and dispersive transmission.
For analysis purposes, the complete numerical RWT display generation, with 0 < p < 1, is proposed to select a particular
pulse shape related to a determined value of p. To this end, the amplitude and phase of the signal to be processed should
be known. In order to obtain this information we use a pulse characterization method based on two intensity detections
and consider the amplitude and phase errors of the recovered signal to evaluate their impact on the RWT production.
Numerical simulations are performed to illustrate the implementation of the proposed method. The technique is applied
to process optical communication signals, such as chirped Gaussian pulses, pulses distorted by group velocity dispersion
and self-phase modulated pulses. The processing of pulses affected by polarization effects is also explored by means of
the proposed method.
A method that combines amplitude modulation and dispersive transmission for producing high-repetition periodic pulse trains in multiple wavelengths is proposed. The conditions satisfied by the several involved parameters for obtaining well-conformed high-contrast pulse trains are based in a generalization of the temporal Talbot effect. The basic scheme is designed to consider dense wavelength-division multiplexing pulse sequence as the input signal. In this case, periodic pulse trains with different repetition rates and a multispectra content can be obtained. Numerical results are shown to corroborate this approach, illustrating how the involved approximations affect the irradiance distribution of the output pulses.