We present an ab initio formalism based on the Bethe-Salpeter equation (BSE) to describe exciton-polaritons, capturing photonic and matter components on the same footing and obtaining polariton dispersions at the same cost as standard, static BSE calculations. We show in MgO that, near the light cone, the Bohr radii of excitons dramatically shrink by 50% while retaining primarily ($>75\%$) excitonic character. Our calculations agree well with experiments in CdS and can capture drastic changes in the exciton wave function in structurally complex materials, including crystalline pentacene.

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• Exciton polariton
• Excitons
• Polaritons
• Quasiparticles & collective excitations
• Bethe-Salpeter equation
• First-principles calculations
• Green's function methods