Shedding light on and comparing three different mathematical models of the optical conductivity concept

Abstract

The optical response in materials offers valuable insights into their properties, especially regarding interband transitions, distinct from direct current responses. By adjusting the frequency of electromagnetic radiation, interband transitions and energy band mappings can be explored, even in materials like graphene. Optical conductivity, which measures a material’s ability to conduct electricity under the influence of light, is pivotal across physics, materials science, and engineering. It quantifies a material’s efficiency in absorbing and transporting electromagnetic energy as photons. Typically described by Drude’s model, optical conductivity has applications in diverse fields, from designing specific optical properties in materials to optimizing solar cells and developing photonic devices. Plasmonics, meta-materials, and renewable energy research also benefit from understanding and controlling optical conductivity. The optical conductivity problem centers on comprehending materials’ electrical interactions with light across the optical spectrum, which is vital for various technologies. Theoretical models, simulations, and experiments address this problem, aiming to develop tunable materials and enhance theoretical models for accurate prediction of optical properties. Mathematical models, such as Maxwell’s equations, the Lorentz-Drude model, and the Hosam-Heba model, elucidate optical conductivity, aiding in understanding light-material interactions and predicting material behavior under electromagnetic radiation. Each model offers a unique perspective on optical conductivity, with different theoretical foundations and mathematical formulations that can be applied depending on the specific properties of the material being studied. Understanding and manipulating optical conductivity is foundational to utilizing light across various technological applications.