Designing the Structure of a One-Dimensional Photonic Crystal with a Given Spectrum of the Reflection Coefficient

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A method for solving the inverse problem of designing the structure of a one-dimensional photonic crystal is proposed and experimentally implemented. It is known that a one-dimensional photonic crystal with a spatial sinusoidal modulation of the refractive index, has a narrow photonic bandgap at a frequency related to the spatial frequency of this sinusoid. A reverse engineering method is proposed for one-dimensional photonic crystals with an arbitrary given reflection spectrum by expanding this spectrum into elementary photonic band gaps and then summing them. The application of this method to fabricate examples of photonic crystals with simple shapes of spectral reflection curves is demonstrated.