hi, every body
1. as it is known to investigate the bad-gap characteristics of 2-D periodic structures a dispersion diagram along Γ-X-M path is used
2. dispersion of a 2-D periodic structure is actually a "surface" not a 1-D diagram, however in a dispersion diagram along Γ-X-M path we just consider the edges of Brillouin zone
3. apparently it can be shown that a existence of a bandgap in 1-D dispersion diagram is "sufficient condition" to have a band gap in dispersion surface, any body can prove that?