Figure 1

Band structures of longitudinally modulated periodic photonic lattices.

(a) is the case with V(x, z) = 0, where the red, green and blue solid thin curves are the bands indexed by (n, q) = (1, 0), (2, 0) and (3, 0), respectively, while the colored dashed curves are the corresponding shifted bands. A1 and A2, B1 and B2 and C1 and C2 are crossing points where . The vertical dashed lines indicate the positions of the resonant transverse wave vector . (b) is the longitudinally extended FB band structure and (c) is the corresponding reduced band structure of a lattice with T = 1300 μm and (d) is the reduced band structure of a lattice with T = 500 μm, respectively, where the red, green and blue bold solid curves are the bands indexed by n = 1, 2 and 3, respectively. The point R in (c) is the resonant point at which the transverse velocity of FB modes in different bands is the same. The other lattice parameters are D = 10 μm, δn = 5 × 10⁻⁴ and n₀ = 2.3, which are the same for (a–d). The operating wavelength is set at 0.6328 μm.