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Discovering The Topological Origin Of Surface Electromagnetic Waves

Scientists from the RIKEN Cluster for Pioneering Research in Japan have uncovered the topological origin of surface electromagnetic waves. In a new paper published in Nature Communications, researchers proved that surface electromagnetic waves can have a purely topological origin. Scientists believe this information could be extremely useful in a number of applications, including the development of metamaterials and plasmonics.

The researcher’s work was based in large part on Maxwell’s electromagnetic theory. This scientific theory was formed 150 years ago but still resonates just as strongly today. It helped provide scientists with a comprehensive description of electromagnetic waves. Additionally, Maxwell’s theory anticipated numerous field and relativity theories that would not become a reality until the 20th century.

Surface waves are an essential part of topological quantum systems. Topological quantum systems are tough enough to withstand continuous deformations, as well as small perturbations. Back in 2016, scientists uncovered nontrivial topological phases in condensed-matter quantum systems. They also discovered the existence of topological surface modes at interfaces between topologically-different materials. This work earned them the Nobel Prize in physics.

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A Dash of Maxwell’s: A Maxwell’s Equations Primer – Part One

Solving Maxwell’s Equations for real-life situations, like predicting the RF emissions from a cell tower, requires more mathematical horsepower than any individual mind can muster. These equations don’t give the scientist or engineer just insight, they are literally the answer to everything RF.

The new work by researchers builds on that, proving that surface electromagnetic waves at interfaces between homogenous isotropic media have an exclusively topological origin when obtained within Maxwell’s classical electromagnetism.

Scientists believe their work helps to better understand the origin of surface electromagnetic waves. It also helps to explain the reasons why these waves appear at specific interfaces. At these interfaces, one of the medium parameters, such as dielectric permittivity or magnetic permeability, changes its sign. Additionally, the number of surface modes is decided based on the number of bulk-medium parameters that change their sign at the interface. This is known in topological formalism as “bulk-boundary correspondence.”

“There is a crucial difference between the topological description of surface Maxwell waves and that of previously known topological surface modes. So far, topological properties and classification of various wave systems have relied on mathematical properties of the Hamiltonian (i.e., energy) operator characterizing the system.

In contrast, the topological properties of Maxwell’s waves are described by the so-called helicity operator, which characterizes the chirality—or handedness—of circularly-polarized electromagnetic waves. Thus, our theory also extends the range of applicability of the topological approach to other wave systems. It shows that the topological classification can be associated not only with the Hamiltonian but also with other operators corresponding to conserved physical quantities.”

Konstantin Bliokh, Research Scientist at Theoretical Quantum Physics Laboratory

Scientists believe their work will lead to a greater understanding of electromagnetism, and how its properties can be used in an assortment of applications.

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