  In this paper we focus on high order finite element approximations of the
electric field combined with suitable preconditioners, to solve the
time-harmonic Maxwell's equations in waveguide configurations. The
implementation of high order curl-conforming finite elements is quite delicate,
especially in the three-dimensional case. Here, we explicitly describe an
implementation strategy, which has been embedded in the open source finite
element software FreeFem++ (http://www.freefem.org/ff++/). In particular, we
use the inverse of a generalized Vandermonde matrix to build a basis of
generators in duality with the degrees of freedom, resulting in an easy-to-use
but powerful interpolation operator. We carefully address the problem of
applying the same Vandermonde matrix to possibly differently oriented
tetrahedra of the mesh over the computational domain. We investigate the
preconditioning for Maxwell's equations in the time-harmonic regime, which is
an underdeveloped issue in the literature, particularly for high order
discretizations. In the numerical experiments, we study the effect of varying
several parameters on the spectrum of the matrix preconditioned with
overlapping Schwarz methods, both for 2d and 3d waveguide configurations.
