Miguel A. Muriel

An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg gratings

Presents an efficient method for the design of complex fiber Bragg gratings. The method relies on the synthesis of the impulse response of the grating by means of a differential layer-peeling algorithm. The algorithm developed takes into account all the multiple reflections inside the grating, giving an exact solution to the inverse scattering problem. Its low algorithmic complexity enables the synthesis of long fiber gratings. The method is illustrated by designing several filters with interest for optical fiber communication systems: dispersionless bandpass filters and second- and third order dispersion compensators.

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.

Temporal self-imaging effects: theory and application for multiplying pulse repetition rates

A time-domain equivalent of the spatial Talbot or self-imaging phenomenon appears when a periodic temporal signal propagates through a dispersive medium under first-order dispersion conditions. The effect is of great interest because it can be applied for multiplying the repetition rate of an arbitrary periodic pulse train without distorting the individual pulse features and essentially without loss of energy. In this way, pulse sequences in the terahertz regime can be generated from typical mode-locked pulse streams (with a few gigahertz repetition rates). The Talbot-based repetition-rate-multiplication technique can be implemented by using a linearly chirped fiber grating (LCFG) as the dispersive medium. As compared with other alternatives, an LCFG can be designed to provide the required bandwidth and dispersion characteristics in significantly more compact forms. Here, by using a signal-theory-based approach, we carry out a general theoretical analysis of the temporal self-imaging phenomenon and derive analytical expressions for all cases of interest (integer and fractional self-imaging effects). We also show how to design a LCFG for implementing the repetition-rate-multiplication technique and discuss the impact of nonidealities in the gratings response on the multiplication process. Results of our study are relevant from both a physical and a practical perspective.

Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings

Based on time-space duality, we deduce a time-domain equivalent to the Fraunhofer (far-field) approximation in the problem of spatial diffraction. We can use this equivalence to carry out a real-time optical spectrum analysis, which is shown to be realizable by using, as the dispersive media, filtering devices based on chirped distributed resonant coupling. In particular, we present the design of linearly chirped fiber gratings (reflection configurations) and linearly chirped intermodal couplers (transmission configurations) to work as real-time spectrum analyzers. The proposed systems are shown to work properly by means of simulation tools. Furthermore, we use joint time-frequency signal representations to get a better understanding of the physical processes that determine the behavior of these systems. In this way, we demonstrate that the propagation of a given signal through a chirped fiber grating (or a chirped intermodal coupler), under the temporal Fraunhofer conditions, translates into a temporal separation of the spectral components of the signal. The results of our study indicate potential important applications based on this effect.

Technique for multiplying the repetition rates of periodic trains of pulses by means of a temporal self-imaging effect in chirped fiber gratings

We show that a temporal effect that is equivalent to the spatial self-imaging (Talbot) effect applies to the reflection of periodic signals from linearly chirped fiber gratings. The effect can be used for multiplying the repetition frequency of a given periodic pulse train without distorting the individual pulse characteristics. The practical limit on the frequency-multiplication factor depends only on the temporal width of the individual pulse. Thus we demonstrate that a suitable combination of well-known techniques for short-pulse generation, such as pulse mode locking, and the technique proposed here allows us to obtain short-pulse trains with ultrahigh repetition rates (in the terahertz regime). Results from simulations show good agreement with those predicted by theory.

Real-time spectrum analysis in microstrip technology

We report on a time-domain analog in microwave lines to the spatial Fraunhofer (far-field) diffraction in paraxial conditions. Microstrip lines are used to design filtering configurations acting as spectrum analyzers. They are based on linearly chirped distributed Bragg coupling between the fundamental microstrip mode and the same but counterpropagating mode. Linearly chirped continuous impedance modulation in a microstrip line with varying upper plane strip-width is shown to yield a mode-coupling location and group delay linearly distributed in frequency. Under the condition of a temporal equivalent to the spatial Fraunhofer inequality, the energy spectral density of the input signal is directly recoverable from the average output (reflected) power. It is only necessary to take into account a linear axis-change, given by the dispersion coefficient (group-delay slope) of the structure, from time to Fourier frequency. Both pulsed and nonpulsed RF signals are studied. Sequential time-gated segments of the input have to be processed in the nonpulsed case. The maximum frequency resolution achievable in this situation is discussed. The devices developed here could have important potential applications in the field of temporal signal processing, such as filtering using time-division techniques.

A new transfer matrix formalism for the analysis of fiber ring resonators: compound coupled structures for FDMA demultiplexing

A method of analyzing fiber-ring resonators which is based on the transfer matrix technique is presented. The method is described and used to analyze known structures and compound coupled-ring resonators. Application of these structures as demultiplexers in FDMA (frequency-division multiple-access) systems is discussed. >

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.

Transmission bistability in a double-coupler fiber ring resonator.

The transmission bistability of a two-coupler nonlinear ring resonator is demonstrated and described by using a geometrical method that provides a qualitative understanding of the operation characteristics of the device. Results showing the influence of the coupling constants and the linear phase are presented.

Apodized coupled resonator waveguides.

In this paper we propose analyse the apodisation or windowing of the coupling coefficients in the unit cells of coupled resonator waveguide devices (CROWs) as a means to reduce the level of secondary sidelobes in the bandpass characteristic of their transfer functions. This technique is regularly employed in the design of digital filters and has been applied as well in the design of other photonic devices such as corrugated waveguide filters and fiber Bragg gratings. The apodisation of both Type-I and Type-II structures is discussed for several windowing functions.