a question about defining K vector for photonic crystals.

I have a question about defining K vector path for photonic crystal lattices when I use super cell technique. (for band structure calculations)
For example, suppose a square array of dielectric rods embedded in a background of air.

O O O O
O O O O
O O O O
O O O O

When I want to define the band structure of this lattice using the simple unit cell, I can easily see the bands and also the gap between the bands 1 and 2. (as mentioned in several books and articles.) To draw the bands, I move the K vector along the first irreducible Brillioun zone.

But for example when I use a 2*2 super cell(and move along the same K vector as before) I encounter a different band structure. In the new bands, the band gap occurs for the same frequency range as for the unit cell. But the bands are different.. I know why.. because I have not moved along the appropriate K vector path.. but I can't find the correct path for K vector to find the same band structure as for the unitcell.. Can anyone help me or may introduce me an article or something for that?

If I understand what you are doing, you will need to use the k-vector path from your one-unit-cell simulation. Otherwise, the bands will look a bit different.