Modeling the strong coupling in a GaN polariton waveguide: Impact of the Sommerfeld enhancement of the exciton spectrum

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The waveguide geometry is a new playground for the physics of polariton fluids. The exciton and guided photons can be brought to the strong coupling regime, in analogy with vertical microcavities. The low waveguide losses allow for long propagation distances, up to hundreds of microns. Recent achievements with waveguide polaritons include the formation of bright temporal solitons in GaAs heterostructures [1], in-plane polariton amplification and polariton lasing in a bulk ZnO waveguide [2]. The investigation of such non-linear physics relies on an understanding of the linear spectroscopy of the polaritons [3], i.e. a robust and quantitative analysis of the dispersions unveiling the exciton-photon anti-crossing.Here we report the experimental measurement and the modeling of the dispersion of polaritons in a bulk GaN slab waveguide grown on Si (Fig 1a). Fourier-space imaging of the emission at diffraction gratings (Fig. 1b) allows reconstructing the dispersion of the polariton modes (Fig. 1c). The measured dispersion is well reproduced by a model that separates the contributions of the excitons and the unbound electron-hole pairs to the energy dependence of the refractive index, i.e. the exciton-photon coupling and the natural dispersion of a bare waveguide. The highly bent bare photon dispersion (dotted line) emphasizes the important contribution of unbound pairs to the dielectric susceptibility, i.e. the Sommerfeld corrections to the dielectric function. The deduced Rabi splitting will be compared to other simpler models for the exciton susceptibility, from 10 to 300K. This modeling is crucial for the future design and development of GaN waveguide polariton physics and devices.References[1] Walker et al., Appl. Phys. Lett. 102, 012109 (2013) and Nat. Comm. 6, 8317 (2015)[2] Jamadi et al. Light: Science & Applications 7, 82 (2018), arxiv:1708.00501 [3] Ciers et al., Phys. Rev. Applied 7, 034019 (2015)Financial support: French National Research Agency (ANR-15-CE30-0020-02, ANR-11-LABX-0014)

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