Conditions for waveguide decoupling in square-lattice photonic crystals

We study coupling and decoupling of parallel waveguides in two-dimensional square-lattice photonic crystals. We show that the waveguide coupling is prohibited at some wavelengths when there is an odd number of rows between the waveguides. In contrast, decoupling does not take place when there is even number of rows between the waveguides. Decoupling can be used to avoid cross talk between adjacent waveguides.