Low-Power Threshold\nOptical Bistability Enabled by\nHydrodynamic Kerr Nonlinearity of Free Carriers in Heavily Doped Semiconductors

We develop an efficient numerical model based on the\nsemiclassical\nhydrodynamic theory for studying Kerr nonlinearity in degenerate electron\nsystems such as heavily doped semiconductors. This model provides\ndirect access to the electromagnetic responses of the quantum nature\nof the plasmons in heavily doped semiconductors with complex geometries,\nwhich is nontrivial for conventional frameworks. Using this model,\nwe demonstrate nanoscale optical bistability at an exceptionally low-power\nthreshold of 1 mW by leveraging Kerr-type hydrodynamic nonlinearities\nsupported by the heavily doped semiconductor’s free carriers.\nThis high nonlinearity is enabled by a strong coupling between metallic\ngap plasmons and longitudinal bulk plasmons in the semiconductor due\nto quantum pressure. These findings offer a viable approach to studying\nKerr-type nonlinearity and lay the groundwork for developing efficient\nand ultrafast all-optical nonlinear devices.