Determination of the refractive index of photonic-crystal material from scattering measurements

Summary form only given. The rapid progress of nanotechnology now allows the development of devices based on the properties of photonic crystals, for instance, optical filters, switches and wave guides. Two-dimensional photonic crystals built as arrays of parallel dielectric circular rods by additive nanolithography using a Si-based precursor have been fabricated and investigated. Their dimensions (diameter and spacing of the rods) are defined in the production process, but the determination of the refractive indices of the rod material presents a formidable task. Bulk material measurements would require a costly production of suitable layers and their results probably would not agree with the in situ values for thin rods. An experimental method is proposed based on a rigorous theory of scattering of a Gaussian beam by a finite row of parallel dielectric circular cylinders. The incoming and the diffracted field are represented by Fourier-Bessel expansions and the translation properties of Bessel functions are used. Thus, the scattering problem is reduced to the solution of a large system of complex linear equations.