▎ 摘　　要

Consider electromagnetic waves in two-dimensional honeycomb structured media, whose constitutive laws have the symmetries of a hexagonal tiling of the plane. The properties of transverse electric polarized waves are determined by the spectral properties of the elliptic operator LA=-delta xA(x)delta x, where A(x) is h-periodic (h denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, A(x) is PC-invariant (A(x)=A(-x)) and 120 degrees rotationally invariant (A(Rx)=RA(x)R, where R is a 120degrees rotation in the plane). A summary of our results is as follows: (a) For generic honeycomb structured media, the band structure of LA has Dirac points, i.e. conical intersections between two adjacent Floquet-Bloch dispersion surfaces; (b) Initial data of wave-packet type, which are spectrally concentrated about a Dirac point, give rise to solutions of the time-dependent Maxwell equations whose wave-envelope, on long time scales, is governed by an effective two-dimensional time-dependent system of massless Dirac equations; (c) Dirac points are unstable to arbitrary small perturbations which break either C (complex-conjugation) symmetry or P (inversion) symmetry; (d) The introduction through small and slow variations of a domain wall across a line-defect gives rise to the bifurcation from Dirac points of highly robust (topologically protected) edge states. These are time-harmonic solutions of Maxwell's equations which are propagating parallel to the line-defect and spatially localized transverse to it. The transverse localization and strong robustness to perturbation of these edge states is rooted in the protected zero mode of a one-dimensional effective Dirac operator with spatially varying mass term; (e) These results imply the existence of unidirectional propagating edge states for two classes of time-reversal invariant media in which C symmetry is broken: magneto-optic media and bi-anisotropic media.