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A theoretical description of radiation-matter coupling forsemiconductor-based photonic crystal slabs is presented, in which quantum wellsare embedded within the waveguide core layer. A full quantum theory isdeveloped, by quantizing both the electromagnetic field with a spatialmodulation of the refractive index and the exciton center of mass field in aperiodic piecewise constant potential. The second-quantized hamiltonian of theinteracting system is diagonalized with a generalized Hopfield method, thusyielding the complex dispersion of mixed exciton-photon modes including losses.The occurrence of both weak and strong coupling regimes is studied, and it isconcluded that the new eigenstates of the system are described byquasi-particles called photonic crystal polaritons, which can occur in twosituations: (i) below the light line, when a resonance between exciton andnon-radiative photon levels occurs (guided polaritons), (ii) above the lightline, provided the exciton-photon coupling is larger than the intrinsicradiative damping of the resonant photonic mode (radiative polaritons). For asquare lattice of air holes, it is found that the energy minimum of the lowerpolariton branch can occur around normal incidence. The latter result haspotential implications for the realization of polariton parametric interactionsin photonic crystal slabs.

Quantum theory of exciton-photon coupling in photonic crystal slabs with embedded quantum wells