(a) Regions I and II, with width ω₁ and ω₂ respectively, which are connected by the bridge with length d. The bridge consists of a finite repetition of alternating layers of material A with thickness d_A and materials B with thickness d_B. (b) A typical transmission coefficient as a function of ω/Δcalculate by scattering matrix method. Reprinted with permission from Ref. [24]. Copyright (2003) by IOP Publishing.