Photonic and chiral photonic crystals—materials engineered with nanometric to micrometric periodic structures—are of great significance to science, industry, and national defense. Their ability to control and manipulate light enables various technological applications, including optical communication devices, lasers, sensors, solar cells, and thermal management systems. In materials science, some defects can be intentionally added to these periodic structures to create new materials with advanced properties, such as precisely controlling light in specific areas and accurately routing light signals. The ability to control waves in a small space can allow for more compact device designs. Studying how light interacts with periodic structures that contain defects will offer a cost-effective method for optical testing of designs—a crucial step in developing these new materials. This project will contribute to the study of inverse electromagnetic scattering theory in complex periodic media. The main objective is to simulate wave–material interactions and reconstruct defects using measurements of the scattered waves at a certain distance. This research also supports quality control of optical devices fabricated from purely periodic structures. Graduate and undergraduate students will participate in and receive training as part of this research. This project investigates the direct and inverse scattering problems governed by Maxwell's equations in an infinite locally perturbed bi