Localized polaritons and second-harmonic generation in a resonant medium with quadratic nonlinearity

We derive model equations for the propagation of ultrashort pulses in materials with resonant linear and quadratic nonlinear responses and find approximate soliton solutions describing all-bright and dark-bright polaritons. We report the specific phase matching condition for efficient 2nd harmonic generation, which involves detuning from the resonance. We also demonstrate that the 2nd harmonic emission by the polaritonic pulses can lead to reduction of their group velocity, having zero as a theoretical limit. Our analytical results are supported by numerical simulations.