In this paper, we carry out a systematic study on the interaction between ultrashort optical pulses and fiber Bragg grating structures operating in the linear regime. Our study is based on the joint time-frequency representation (spectrogram) of the reflection impulse response from the grating structures under analysis. By means of such a representation we get to visualize in a single image all the relevant information concerning the optical and dispersive behavior of the grating structures and more importantly, we obtain information on the pulse-grating interaction process, which otherwise is not accessible from any other method. Here, we analyze uniform and nonuniform fiber Bragg gratings. The effects of the apodization of the coupling coefficient and chirp of the grating period on the macroscopic optical properties of the considered gratings are investigated. Furthermore, we extend our analysis to more complicated in-fiber grating structures such as concatenated gratings, Fabry-Pérot-like grating structures, and superimposed gratings. The results of our study indicate that the time-frequency methods constitute a powerful tool for the analysis and design of fiber Bragg grating structures.
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