  We develop a fundamental transfer-matrix formulation of the scattering of
electromagnetic (EM) waves that incorporates the contribution of the evanescent
waves and applies to general stationary linear media which need not be
isotropic, homogenous, or passive. Unlike the traditional transfer matrices
whose definition involves slicing the medium, the fundamental transfer matrix
is a linear operator acting in an infinite-dimensional function space. It is
given in terms of the evolution operator for a non-unitary quantum system and
has the benefit of allowing for analytic calculations. In this respect it is
the only available alternative to the standard Green's-function approaches to
EM scattering. We use it to offer an exact solution of the outstanding EM
scattering problem for an arbitrary finite collection of possibly anisotropic
nonmagnetic point scatterers lying on a plane. In particular, we provide a
comprehensive treatment of doublets consisting of pairs of isotropic point
scatterers and study their spectral singularities. We show that identical and
$\mathcal{P}\mathcal{T}$-symmetric doublets do not admit spectral singularities
and cannot function as a laser unless the real part of their permittivity
equals that of vacuum. This restriction does not apply to doublets displaying
anti-$\mathcal{P}\mathcal{T}$-symmetry. We determine the lasing threshold for a
generic anti-$\mathcal{P}\mathcal{T}$-symmetric doublet and show that it
possesses a continuous lasing spectrum.
