Function photonic crystals

In this paper, we present a new kind of function photonic crystals (PCs), whose refractive index is a function of space position. Conventional PCs structure grows from two materials, A and B, with different dielectric constants εA and εB. Based on Fermat principle, we give the motion equations of light in one-dimensional, two-dimensional and three-dimensional function photonic crystals. For one-dimensional function photonic crystals, we give the dispersion relation, band gap structure and transmissivity, and compare them with conventional photonic crystals, and we find the following: (1) For the vertical and non-vertical incidence light of function photonic crystals, there are band gap structures, and for only the vertical incidence light, the conventional PCs have band gap structures. (2) By choosing various refractive index distribution functions n(z), we can obtain more wider or more narrower band gap structure than conventional photonic crystals.