Inverse scattering of two-dimensional photonic structures by layer stripping

Design and reconstruction of two-dimensional (2D) and three-dimensional photonic structures are usually carried out by forward simulations combined with optimization or intuition. Reconstruction by means of layer stripping has been applied in seismic processing as well as in design and characterization of one-dimensional photonic structures such as fiber Bragg gratings. Layer stripping is based on causality, where the earliest scattered light is used to recover the structure layer by layer. Our setup is a 2D layered nonmagnetic structure probed by plane-polarized harmonic waves entering normal to the layers. It is assumed that the dielectric permittivity in each layer only varies orthogonal to the polarization. Based on obtained reflectance data covering a suitable frequency interval, time-localized pulse data are synthesized and applied to reconstruct the refractive index profile in the leftmost layer by identifying the local, time-domain Fresnel reflection at each point. Once the first layer is known, its impact on the reflectance data is stripped off and the procedure repeated for the next layer. Through numerical simulations it will be demonstrated that it is possible to reconstruct structures consisting of several layers. The impact of evanescent modes and limited bandwidth is discussed. (C) 2011 Optical Society of America