We present a systematic analysis, within the scope of electromagnetic theory, of the
spectral moments method (SMM) and develop several ways to compute the linear
response of any type of system. We show that the method can be used in diffraction
studies regardless of the number, nature and form of the diffracting objects. Multiple
diffraction is naturally taken into account in the computation. The method can thus
be applied to determine propagation through any type of media. It is based on the
computation of Green functions, solutions of discretized Maxwell's equations.
Fourier transforms of Green functions are developed in continued fraction. Two
approaches will be presented. In the first “global” approach, all space is discretized,
the coefficients of continued fractions are computed directly from the dynamic
matrix obtained by the discretization of Maxwell's equations and from sources and
receivers. In the second “local” approach, only the diffracting system is discretized.
This paper is devoted to the global approach. We study two important problems in
electromagnetism, i.e. propagation of a plane wave through a heterogeneous layer
and scattering of an isolated object. We present two computation techniques for
plane wave propagation: one uses a small grid, is very rapid but the results are
approximate; the other uses a large grid, is less rapid but the results are exact. We
show that computing the reflectivity and/or transmissivity of photonic lattices is
now a very simple problem. For scattering, we mainly report a series of tests on
some canonical systems, such as cylinders or spheres, showing that SMM results are
in very good agreement with the analytical results. Several types of absorbing
boundary conditions are tested. We report results on backscattering cross-sections
and the impulsional response of different one-, two- and three-dimensional systems.