Fig. 2
From: Topological non-Hermitian origin of surface Maxwell waves
Winding of the energy and helicity spectra in the Dirac and Maxwell equations. a Changing the sign of the mass m in the Dirac equation is equivalent to a π rotation (shown by the arrows) of the rest-energy spectrum E0 ≡ E(0) = m in the complex-mass plane, which results in a single zero-mass surface mode (shown by the star symbol) protected by the topological \({\Bbb Z}_2\) winding number1,2,3,27. The dot and star symbols with their colors correspond to the rest-energy spectra of the bulk and surface modes shown in Fig. 1a. b Changing the signs of the permittivity ε and permeability μ in Maxwell equations produces ±π/2 and π rotations of the helicity spectrum in the complex helicity (\({\frak S}\)) plane Eq. (2). This results in the appearance of one or two zero-helicity (transverse-electric and transverse-magnetic) surface modes15,16,17,18,19,34,35,36 (shown by the star symbols) described by the topological \({\Bbb Z}_4\) number (3). c The medium-index diagram showing the signs of the refractive index n and impedance Z in four possible types of media (see Supplementary Note 1)
