  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. We propose a
reverse engineering method for one-dimensional photonic crystals with an
arbitrary given reflection spectrum by expanding this spectrum into elementary
photonic band gaps and then summing them. This paper shows the application of
this method to fabricate examples of photonic crystals with simple shapes of
spectral reflection curves.
