Pablo A. Costanzo-Caso

Radon-Wigner transform processing for optical communication signals

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.

Compression and equalization of arbitrary form pulses for optical fiber applications

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 p from 0 (temporal information) to 1 (spectral information). From the inspection of the RWT the optimum fractional order pC 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 pC 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.

Pulse processing in optical fibers using the temporal Radon-Wigner transform

It is presented the use of the temporal Radon-Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT) for a varying fractional order p, as a processing tool for pulses with FWHM of ps-tens of ps. For analysis purposes, the complete numerical generation of the RWT 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 are obtained using a pulse characterization technique. To synthesize the processed pulse, the selected FRT irradiance is optically produced employing a photonic device that combines phase modulation and dispersive transmission. The practical implementation of this device involves a scaling factor that depends on the modulation and dispersive parameters. It is explored the variation of this factor in order to obtain an enhancement of the particular characteristic sought in the pulse to be synthesized. To illustrate the implementation of the proposed method, numerical simulations of its application to compress signals commonly found in fiber optic transmission systems, are performed. The examples presented consider chirped Gaussian pulses and pulses distorted by group velocity dispersion and self-phase modulation.

Multiple wavelength periodic pulse-train conformation

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.

Temporal filtering for Montgomery self-imaging under dispersive transmission.

We present what we believe is a new method to introduce self-imaging properties under dispersive transmission of single or multiple light pulses with different temporal characteristics. By properly performing a temporal filtering into a given input signal it can produce an output signal having a spectral content satisfying the Montgomery condition, thereby allowing self-imaging of this signal under further dispersive transmission. An array of fiber loops performs the filtering operation on the input signal. We show some numerical simulations with a single light pulse as an input signal to verify the feasibility of the method and demonstrate the effects of the several involved parameters on both the pulse shape and the noise level.