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

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Abstract
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.