| Title | Maxwell's Electromagnetism Extended To Smaller Scales | |
| Date | Friday December 13 2019, @09:47AM | |
| Author | Fnord666 | |
| Topic | ||
| from the both-macro-and-micro dept. | ||
More than one hundred and fifty years have passed since the publication of James Clerk Maxwell's "A Dynamical Theory of the Electromagnetic Field" (1865). What would our lives be without this publication? It is difficult to imagine, as this treatise revolutionized our fundamental understanding of electric fields, magnetic fields, and light. The twenty original equations (nowadays elegantly reduced into four), their boundary conditions at interfaces, and the bulk electronic response functions (dielectric permittivity and magnetic permeability ) are at the root of our ability to manipulate electromagnetic fields and light.
Therefore, wondering what our life would be without Maxwell's equations means to try to envision our life without most of current science, communications and technology.
On large (macro) scales, bulk response functions and the classical boundary conditions are sufficient for describing the electromagnetic response of materials, but as we consider phenomena on smaller scales, nonclassical effects become important. A conventional treatment of classical electromagnetism fails to account for the mere existence of effects such as nonlocality [1], spill-out [2], and surface-enabled Landau damping. Why does this powerful framework break down towards nanoscales [3]? The problem is that electronic length scales are at the heart of nonclassical phenomena, and they are not part of the classical model. Electronic length scales can be thought of as the Bohr radius or the lattice spacing in solids: small scales that are relevant for the quantum effects at hand.
Today, the path to understand and model nanoscale electromagnetic phenomena is finally open. In the breakthrough Nature paper "A General Theoretical and Experimental Framework for Nanoscale Electromagnetism," Yang et al. present a model that extends the validity of the macroscopic electromagnetism into the nano regime, bridging the scale gap. On the theoretical side, their framework generalizes the boundary conditions by incorporating the electronic length scales in the form of so-called Feibelman d-parameters.
The d-parameters play a role that is analogous to that of the permittivity ε, but for interfaces. In terms of numerical modelling, all one needs to do is to pair each two-material interface with associated Feibelman d-parameters and solve the Maxwell's equations with the new boundary conditions.
Journal Reference:
Yi Yang, Di Zhu, Wei Yan, Akshay Agarwal, Mengjie Zheng, John D. Joannopoulos, Philippe Lalanne, Thomas Christensen, Karl K. Berggren, Marin Soljačić. A general theoretical and experimental framework for nanoscale electromagnetism. Nature, 2019; 576 (7786): 248 DOI: 10.1038/s41586-019-1803-1
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