Fig. 3: Illustrations of EUV-polariton characteristics.

a Down-conversion from pump (k_p, blue pulse) to signal (k_s, green pulse) photon transfers ~100 eV = ℏc(|k_p|–|k_s|) into diamond, launching an EUV-polariton. Repeated absorption of the energy into electronic excitations and re-emission as a photon hybridize both states (cyclical coupling depicted in red-blue). The resulting EUV-polariton, ultimately, decays into either of its constituents, a photon (γ, violet) or a free electron (e, black)—matching the kinematics of XPDC or Compton scattering, respectively. b Polaritonic dispersion relation shown schematically for upper (E₊) and lower (E₋) polariton branch; dotted lines indicate the uncoupled photonic (ω_γ) and electronic (ω_e) excitations. Their hybridization opens an avoided crossing (Rabi splitting) of 2 V around ω_e = ω_γ. c Polariton dispersion mapped across the scattering plane (2θ, χ) of XPDC; the previous branches E_+/− (cf. inset b) transform into dispersion surfaces that anti-cross at the phase-matching condition (green, dashed circle). The seam mirrors the two-fold modulation observed in the scattering pattern (bottom layer)—both cases show ΔΩ = 1.07°.