Estudio de la respuesta óptica de sólidos mediante las Transformaciones de Hilbert: Aplicación de las reglas de Kramers-Krönig

Abstract

This work aims to develop a comprehensive catalog that consolidates optical dispersion models of materials, with particular emphasis on the intrinsic nature of each material and its relationship with optical response. Conductive and dielectric materials exhibit distinct behaviors in terms of light absorption and scattering due to their electrical conduction properties. These differences in conductivity significantly influence the interaction between the material and electromagnetic radiation, affecting absorption, reflection, and transmission processes, and consequently shaping the material’s overall optical response. The characterization of a physical system’s response to an external perturbation inherently involves a causal relationship. In this context, the theoretical foundation of this study is based on the Hilbert transforms, specifically the Kramers-Krönig relations, which provide a rigorous framework for understanding space-time causality through the optical response of materials. These relations allow the derivation of the real part of the response function from its imaginary component and explicitly define the cause-effect relationship between the applied perturbation and the system's response. This connection is essential for both the validation of theoretical models and the accurate interpretation of experimental data. Developed as a professional internship, this project represents a comprehensive learning experience that has enabled the prospective Bachelor of Physics to strengthen their skills, competencies, and practical and theoretical knowledge. By addressing a real and relevant problem in the field of physical optics, this work fosters not only the effective application of academic knowledge but also the development of essential research, analytical, and scientific writing abilities.