Microscopic Theory of the Refractive Index

Abstract

We examine the refractive index from the viewpoint of modern first-principles materials physics. We first argue that the standard formula, $n^2={\epsilon }_{\mathrm{r}}{\mu }_{\mathrm{r}}$, is generally in conflict with fundamental principles on the microscopic level. Instead, it turns out that an allegedly approximate relation, $n^2={\epsilon }_{\mathrm{r}}$, which is already being used for most practical purposes, can be justified theoretically at optical wavelengths. More generally, starting from the fundamental, Lorentz-covariant electromagnetic wave equation in materials as used in plasma physics, we rederive a well-known, three-dimensional form of the wave equation in materials and thereby clarify the connection between the covariant fundamental response tensor and the various cartesian tensors used to describe optical properties. Finally, we prove a general theorem by which the fundamental, covariant wave equation can be reformulated concisely in terms of the microscopic dielectric tensor.

consistent with published version in Optik - International Journal for Light and Electron Optics (2017)

References in corpus (9)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model
• Holographic Optics and Negative Refractive Index
• Relativistic covariance of Ohm's law
• Microscopic Theory of the Refractive Index
• Functional Approach to Electrodynamics of Media
• Covariant Response Theory and the Boost Transform of the Dielectric Tensor
• Ab initio materials physics and microscopic electrodynamics of media
• Response Theory of the Electron-Phonon Coupling

Cited by in corpus (9)

• Microscopic Theory of the Refractive Index
• Why history matters: ab initio rederivation of Fresnel equations confirms microscopic theory of refractive index
• Covariant Response Theory and the Boost Transform of the Dielectric Tensor
• Ab initio materials physics and microscopic electrodynamics of media
• Response Theory of the Electron-Phonon Coupling
• Linear electromagnetic wave equations in materials
• General form of the full electromagnetic Green function in materials physics
• Wavevector-dependent optical properties from wavevector-independent proper conductivity tensor
• Microscopic theory of refractive index applied to metamaterials: Effective current response tensor corresponding to standard relation $n^2={\epsilon }_{\mathrm{eff}}{\mu }_{\mathrm{eff}}$