The theory of fractals has already been applied to many fields in science, such as physics, biology, and chemistry. One of the most commonly used fractals in these applications is the Cantor set. Novel fiber Bragg gratings are proposed that combine the present technology of fiber Bragg gratings with the theory of Cantor sets. The principal goal of this work is to analyze how Cantor sets, applied to gratings, can alter their reflectivity spectra. Specifically, it is observed that, as the order of the Cantor set increases, the bandpass reflectivity spectra of these gratings broaden and evolve into more-complex patterns. Also, self-similarity properties can be observed in the spectra of these gratings. Numerical examples demonstrate variations in the spectra of these structures as the fractal order increases.
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