We review the simulation work for the far-field focus and dispersionless anticrossing bands in two-dimensional (2D) photonic crystals. In a two-dimensional photonic-crystal-based concave lens, the far-field focus of a plane wave
is given by the distance between the focusing point and the lens. Strong and good-quality far-field focusing of a transmitted
wave, explicitly following the well-known wave-beam negative refraction law, can be achieved. The spatial frequency
information of the Bloch mode in multiple Brillouin zones (BZs) is investigated in order to indicate the wave propagation in
two different regions. When considering the photonic transmission in a 2D photonic crystal composed of a negative
phase-velocity medium (NPVM), it is shown that the dispersionless anticrossing bands are generated by the couplings
among the localized surface polaritons of the NPVM rods. The photonic band structures of the NPVM photonic crystals are
characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands.
Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens