Alejandro Carballar

REAL-TIME FOURIER TRANSFORMER BASED ON FIBER GRATINGS

We use the well-known duality between paraxial diffraction in space and dispersion in time to propose a time-domain analog to spatial Fraunhofer diffraction. This analog permits the design of real-time optical Fourier-transformer systems. These systems are shown to be realizable by use of linearly chirped fiber gratings as dispersive media.

Internal field distributions in fiber Bragg gratings

We have developed a technique to calculate the amplitude of the electric field of a lightwave propagating through a fiber Bragg grating (FBG). The technique is based on a transfer matrix method developed for electric field calculations in multilayer thin films. The internal electric field distribution of FBG structures having uniform, tapered chirped, and phase-shifted index modulations has been calculated. Two-dimensional plots of the average internal power versus the distance along the grating axis and light frequency are presented.

Phase reconstruction from reflectivity in fiber Bragg gratings

We propose a method for phase, time delay, and impulse response reconstruction from the spectral power reflectance or reflectivity in fiber Bragg gratings (FBGs). This method is based on causality and stability conditions and uses the Hilbert and Wiener-Lee transforms. In order to obtain a complete study of the algorithm, we have applied it to uniform and nonuniform fiber Bragg gratings. Finally, we get a complete characterization of a experimental uniform fiber Bragg grating, from the measured reflectivity, by means of the phase reconstruction algorithm. Results show a good agreement between exact and reconstructed functions.

Experimental demonstration of ultrafast all-fiber high-order photonic temporal differentiators

We propose and demonstrate what we believe to be a new, simple, and compact all-fiber design for arbitrary-order ultrafast optical temporal differentiation. The proposed design allows us to implement any desired differentiation order using a maximum of two concatenated fiber gratings, both operating in transmission. A single specially apodized chirped fiber Bragg grating is required for implementing any even-order differentiator, whereas the immediately next odd-order differentiator can be implemented by concatenating a long-period fiber-grating first-order differentiator. Besides its simplicity, this scheme provides an optimized energetic efficiency. We experimentally demonstrate a set of high-order all-optical time differentiators (up to the fourth order) capable of accurately processing arbitrary optical waveforms with picosecond time features.

Fiber grating filter for WDM systems: an improved design

We report on a novel technique for the design of fiber gratings whose reflection characteristic closely approximates the ideal rectangular linear phase filter. The technique is based on the design of a suitable grating period variation, following the apodization function, in order to ensure the Bragg condition to remain constant along the grating length.

Phase reconstruction from reflectivity in uniform fiber Bragg gratings

We propose a method for phase, time-delay, and impulse-response reconstruction from spectral power reflectance or reflectivity and apply it to uniform fiber Bragg gratings. This method is based on causality conditions and uses Hilbert and Wiener-Lee transforms. Results show a good agreement between exact and reconstructed functions.

Arbitrary-Order Ultrabroadband All-Optical Differentiators Based on Fiber Bragg Gratings

We introduce a general approach for designing ultrabroadband arbitrary-order all-optical (all-fiber) time differentiators based on the use of fiber Bragg gratings (FBGs). Specifically, we numerically demonstrate that an Nth-order time differentiator can be implemented using a single specially apodized highly dispersive linearly chirped FBG operated in transmission. A concatenated reflection phase-shifted FBG is also required for implementing any odd-order differentiator. Our numerical simulations show that accurate and efficient time differentiation of optical signals with bandwidths up to a few hundreds of gigahertz can be realized using readily feasible FBG structures.

Field distributions inside fiber gratings

We have developed a technique to calculate the electric field distributions of a light wave propagating through a fiber grating (FG). The technique is based on a transfer matrix method developed for electric field calculations in multilayer thin films. We apply this method to several FG structures of practical interest in optical fiber networks based on wavelength-division multiplexing. Two-dimensional plots of the average internal power versus the distance along the grating axis and light frequency are presented. This representation allows a better understanding of the macroscopic behavior of these structures.

Fiber grating synthesis by use of time–frequency representations

We propose a method to reconstruct the grating period in fiber grating structures from the field reflection coefficient or the related impulse response. The method is based on the joint time-frequency signal analysis and uses the Wigner-Ville and the spectrogram distributions. Results show good agreement between exact and reconstructed functions.

Picosecond linear optical pulse shapers based on integrated waveguide Bragg gratings

We demonstrate a general linear pulse-shaping technique based on integrated III-V Bragg gratings (BGs). Such a technique allows for the synthesizing of complex waveforms with picosecond resolution using a compact single-waveguide design. This approach is experimentally demonstrated by fabricating and testing a series of integrated ultrafast optical pulse shapers based on BG geometries acting as time-domain code generators operating at 500 Gbits/s.