  In this work we study the convergence properties of the one-level parallel
Schwarz method with Robin transmission conditions applied to the
one-dimensional and two-dimensional Helmholtz and Maxwell's equations.
One-level methods are not scalable in general. However, it has recently been
proven that when impedance transmission conditions are used in the case of the
algorithm applied to the equations with absorption, under certain assumptions,
scalability can be achieved and no coarse space is required. We show here that
this result is also true for the iterative version of the method at the
continuous level for strip-wise decompositions into subdomains that can
typically be encountered when solving wave-guide problems. The convergence
proof relies on the particular block Toeplitz structure of the global iteration
matrix. Although non-Hermitian, we prove that its limiting spectrum has a near
identical form to that of a Hermitian matrix of the same structure. We
illustrate our results with numerical experiments.
