Ultrahigh free-electron Kerr nonlinearity in all-semiconductor waveguides for all-optical nonlinear modulation of mid-infrared light

Nonlinear optical waveguides, particularly those harnessing the optical Kerr effect, are promising for advancing next-generation photonic technologies. Despite the Kerr effect’s ultrafast response, its reported weak nonlinearities to date have hindered practical applications. Here, we explore free-electron-induced Kerr nonlinearities in all-semiconductor waveguides, and we show that longitudinal bulk plasmons—inherently nonlocal excitations—can generate exceptionally strong Kerr nonlinearities. We specifically develop and share here a nonlinear eigenmode analysis integrated with semiclassical hydrodynamic theory to compute the linear and nonlinear optical responses originating from the quantum behavior of free electrons in heavily doped semiconductors. These waveguides achieve ultrahigh nonlinear refractive indices and nonlinear coefficients while supporting long-propagating modes. Additionally, we confirm the robustness of the nonlinear response under realistic conditions by considering viscoelastic and nonlinear damping mechanisms. Finally, we implement our all-semiconductor waveguides in a Mach-Zehnder interferometer, demonstrating efficient nonlinear modulation of its transmittance spectrum via the free-electron Kerr effect. This work evidences the transformative potential of free-electron nonlinearities in heavily doped semiconductors for photonic integrated circuits, paving the way for scalable on-chip nonlinear nanophotonic systems.