Maxwell’s electromagnetism extended to smaller scales

A general framework for incorporating and correcting for nonclassical electromagnetic phenomena in nanoscale systems.

In 1865, James Clerk Maxwell published ‘A Dynamical Theory of the Electromagnetic Field,’ where he suggests that the electric and magnetic field travels through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium that is the cause of electric and magnetic phenomena.

In the paper, Maxwell derives an electromagnetic wave equation with a velocity for light in close agreement with measurements made by experiment and deduces that light is an electromagnetic wave.

Those equations (originally 20, (elegantly reduced to four today) are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies exemplars of extremely interface-localized fields rely on their validity. However, this classical description neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres.

Consequently, a general and unified framework for nanoscale electromagnetism remains absent.

In a new study, MIT scientists finally open up a path to understanding and modeling nanoscale electromagnetic phenomena. Scientists presented a model that extends the validity of the macroscopic electromagnetism into the nano regime.

In other words, scientists introduced a model that generalizes the boundary conditions by incorporating the electronic length scales in the form of so-called Feibelman d-parameters.

The d-parameters assume a job that is analogous from that of the permittivity, yet for interfaces. As far as numerical displaying, it is essential to match every two-material interface with related Feibelman d-parameters and illuminate Maxwell’s conditions with the new boundary conditions.

During the experiment, scientists examined film-coupled nanoresonators, a quintessential multiscale architecture. The experimental setup was chosen because of its nonclassical nature.

Recently graduated postdoc and lead author Yi Yang says said, “Even so, When we built our experiment, we were lucky enough to run into the right geometry that enabled us to observe the pronounced nonclassical features, which were unexpected and excited everyone. These features eventually enabled us to measure the d-parameters, which are hard to compute for some important plasmonic materials like gold (as in our case).”

MIT Professor Marin Soljacic is enthusiastic: “We expect this work to have a substantial impact. The framework we present opens a new chapter for cutting-edge nanoplasmonics—the study of optical phenomena in the nanoscale vicinity of metal surfaces—and nanophotonics—the behavior of light on the nanometer scale—and for controlling the interaction of nanometer-scale objects with light.”

Scientists presented their findings in the journal Nature.

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