Abstract
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous isotropic media described by real permittivities and permeabilities have a topological origin explained by the bulk-boundary correspondence. Importantly, the topological classification is determined by the helicity operator, which is generically non-Hermitian even in lossless optical media. The corresponding topological invariant, which determines the number of surface modes, is a {Bbb Z}_4 number (or a pair of {Bbb Z}_2 numbers) describing the winding of the complex helicity spectrum across the interface. Our theory provides a new twist and insights for several areas of wave physics: Maxwell electromagnetism, topological quantum states, non-Hermitian wave physics, and metamaterials.
Highlights
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago
Optics and electromagnetism provide one of the best platforms for studying fundamental relativistic wave phenomena, because classical Maxwell equations represent relativistic wave equations for massless spin-1 particles, i.e., photons within the firstquantization approach12–14. (This explains the mathematical similarities to the Dirac equation, even though Maxwell equations describe classical electromagnetic fields.) studies of surface electromagnetic waves at interfaces between different media resulted in the rapid development of several areas of modern photonics, such as plasmonics[15,16] and negative-index metamaterials[17,18,19]
We show that all surface Maxwell waves appearing at interfaces between media with different signs of ε and μ are topological in nature
Summary
Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. We show that all surface Maxwell waves appearing at interfaces between media with different signs of ε and μ are topological in nature. The winding of this spectrum across the interface exactly corresponds to the number of surface electromagnetic modes, which are zero-helicity transverse-electric (TE) or transverse-magnetic (TM) polarized waves.
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