Figure 1

(Color online) The band structure of a square lattice of dielectric cylinders. The lattice constant is $a$ and the radius of the cylinders is $0.3a$. $\Gamma M$ and $\Gamma X$ denote the [11, 10] directions, respectively. A partial gap is between the two horizontal lines.Reuse & Permissions

Figure 2

(Color online) Imaging of the transmitted fields across two slabs of dielectric cylinders. The black circles denote the cylinders (for clarity, not all cylinders are plotted).Reuse & Permissions

Figure 3

(Color online) Imaging of the intensity fields across two consecutive slabs of arrays of dielectric cylinders in two arrangements. The left and right panels, respectively, plot the real part of the field and the intensity.Reuse & Permissions

Figure 4

(Color online) Imaging of the intensity fields across two consecutive slabs of arrays of dielectric cylinders in two arrangements. The left and right panels respectively plot the real part of the field and the intensity. Shown here is the amphoteric diffraction at the interfaces between two adjacent slabs: (a) positive and (b) negative. In both (a) and (b), the adjacent slabs measure as $10\times 50$ and $12\times 50$.Reuse & Permissions

Figure 5

(Color online) Left panel: the field pattern of eigenmodes. Right panel: the energy flow of the eigenmodes. The eigenmodes along two directions are considered: (a) $\vec{K}=\left(0.9\pi ∕a,0.37\pi ∕a\right)$, i.e., along an angle of $22.5°$ exactly between $\Gamma X$ and $\Gamma M$ directions; the corresponding frequency is 0.185; (b) $\vec{K}=\left(0.7\pi ∕a,0.7\pi ∕a\right)$, i.e., along $\Gamma M$; the corresponding frequency is 0.192. The direction of the Bloch vectors are denoted by the blue arrows, while the red arrows denote the local energy flow including the direction and the magnitude. The circles refer to the cylinders. Both frequencies in (a) and (b) lie within the partial gap. Due to the periodicity, we only plot the energy flow within one unit cell. Note that although the features shown by (a) also hold for other Bloch vectors for which the corresponding frequencies lie within the partial gap regime, we only plot here for the case of $22.5°$.Reuse & Permissions

Figure 6

(Color online) Normalized transmission versus the slab size. The normalization is to take out the trivial geometrical spreading effects. The size is scaled by the lattice constant. Here the slab height is 40 lattice constant.Reuse & Permissions