Wave guiding and mode coupling at the Dirac point in photonic crystal fibers

This work provides an alternative confirmation of Dirac localization in the photonic crystal fiber proposed in Light Sci. Appl. 4, e304 (2015)LSAIAZ2047-753810.1038/lsa.2015.77. In weakly guiding fibers, Maxwell equations can be reduced to the wave equation, which can then be further reduced to the Helmholtz equation for time-harmonic waves. The Dirac point in the band structure of the Helmholtz equation in periodic media is analyzed. Wave localization at the Dirac point is numerically demonstrated, which confirms the finding of Light Sci. Appl. 4, e304 (2015)LSAIAZ2047-753810.1038/lsa.2015.77. Coupling of Dirac modes is numerically simulated, and the results show remote coupling is feasible. Coupling strength is shown to decrease in an algebraic form with distance. This feature of coupling can be attributed to the massless property of Dirac quasiparticles, which is a precise analog of Klein tunneling of massless relativistic electrons in graphene.