Strong attenuation within the photonic band gaps of multiconnected networks

We study the photonic band structures and the attenuation behavior of waves in configuration-periodic square networks where nearest-neighbor nodes are connected by more than one segment. It is shown that even though the period of the unit cell of a square network cannot be defined by the lengths of the segments and the nodes may not be arranged periodically in space, one can still use the Floquet-Bloch theorem in this network system if the theorem is modified. We find that the attenuation can be extremely large even though there is no absorption in the networks and its strength does not have a quasiparabolic profile as a function of wave frequency inside a gap. Large gaps and narrow passbands created by resonances and antiresonances are found.