  We will discuss a one-dimensional approximation for the problem of wave
propagation in networks of thin fibers. The main objective here is to describe
the boundary (gluing) conditions at branching points of the limiting
one-dimensional graph. The results will be applied to Mach-Zehnder
interferometers on chips and to periodic chains of the interferometers. The
latter allows us to find parameters which guarantee the transparency and
slowing down of wave packets.
