Figure 5: (a) The band structure of a alumina vein structure for the TE polarization, with the thickness of the vein equal to . At the point, a conical dispersion intersects with an extra sheet. A closeup of the band diagram contour of the blue solid region is shown in the inset. (b) The field distributions for a Gaussian beam incidence deviate from what is expected for homogeneous medium (Figure 2(a)).