  In this paper we introduce methods for electromagnetic wave propagation,
based on splines and on T-splines. We define spline spaces which form a De Rham
complex and, following the isogeometric paradigm, we map them on domains which
are (piecewise) spline or NURBS geometries. We analyse their geometric
structure, as related to the connectivity of the underlying mesh, and we give a
physical interpretation of the fields degrees-of-freedom through the concept of
control fields. The theory is then extended to the case of meshes with
T-junctions, leveraging on the recent theory of T-splines. The use of T-splines
enhance our spline methods with local refinement capability and numerical tests
show the efficiency and the accuracy of the techniques we propose.
