2023 158 CSM

Application of the Fractional Fourier Transform to Functionally Graded Materials

By: Miriam Sanchez, Angela Perez

Department: Mathematics 

Faculty Advisor: Dr. Ornella Mattei

The Fractional Fourier Transform is a formal extension of the classical Fourier Transform that allows one to study the behavior of Functionally Graded Materials (FGM). In the context of optical systems, the latter are materials in which the refractive index changes continuously in space to simulate a series of infinitesimal layers in which reflection and propagation occur at the same time. Specifically, the Fractional Fourier Transform describes the behavior of FGM in which the material properties change according to a quadratic power law in the spatial component. Here we extend such a result to the case of time-modulated materials, which are materials in which the material properties change in time due to changes in the external applied fields.