Electromagnetic retrieval of missing fibers in periodic fibered laminates via sparsity concepts.

Electromagnetic modeling and imaging of fibered laminates with some fibers missing is investigated, this extending to similarly organized photonic crystals. Parallel circular cylinders are periodically set in a homogeneous layer (matrix) sandwiched between two homogeneous half-spaces. Absent fibers destroy the periodicity. An auxiliary periodic structure (supercell) provides a subsidiary model considered using method tailored to standard periodic structures involving the Floquet theorem to decompose the fields. Imaging approaches from the Lippman-Schwinger integral field formulation as one-shot MUltiple SIgnal Classification (MUSIC) with pointwise scatterers assumptions and an iterative, sparsity-constrained solution are developed. Numerical simulations illustrate the direct model and imaging.