  A theoretical description of radiation-matter coupling for
semiconductor-based photonic crystal slabs is presented, in which quantum wells
are embedded within the waveguide core layer. A full quantum theory is
developed, by quantizing both the electromagnetic field with a spatial
modulation of the refractive index and the exciton center of mass field in a
periodic piecewise constant potential. The second-quantized hamiltonian of the
interacting system is diagonalized with a generalized Hopfield method, thus
yielding the complex dispersion of mixed exciton-photon modes including losses.
The occurrence of both weak and strong coupling regimes is studied, and it is
concluded that the new eigenstates of the system are described by
quasi-particles called photonic crystal polaritons, which can occur in two
situations: (i) below the light line, when a resonance between exciton and
non-radiative photon levels occurs (guided polaritons), (ii) above the light
line, provided the exciton-photon coupling is larger than the intrinsic
radiative damping of the resonant photonic mode (radiative polaritons). For a
square lattice of air holes, it is found that the energy minimum of the lower
polariton branch can occur around normal incidence. The latter result has
potential implications for the realization of polariton parametric interactions
in photonic crystal slabs.
