Abstract
The exciton-polariton modes of a quantum dot lattice embedded in a planar optical cavity are theoretically investigated. Umklapp terms, in which an exciton interacts with many cavity modes differing by reciprocal lattice vectors, appear in the Hamiltonian due to the periodicity of the dot lattice. We focus on Bragg polariton modes obtained by tuning the exciton and the cavity modes into resonance at high symmetry points of the Brillouin Zone. Depending on the microcavity design these polaritons modes at finite in-plane momentum can be guided and can have long lifetimes. Moreover, their effective mass can be extremely small, of the order of $10^{-8} m_0$ ($m_0$ is the bare electron mass), and they constitute the lightest exciton-like quasi-particles in solids.
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