Low-Power Threshold Optical Bistability Enabled by Hydrodynamic Kerr Nonlinearity of Free Carriers in Heavily Doped Semiconductors.

We develop an efficient numerical model based on the semiclassical hydrodynamic theory for studying Kerr nonlinearity in degenerate electron systems such as heavily doped semiconductors. This model provides direct access to the electromagnetic responses of the quantum nature of the plasmons in heavily doped semiconductors with complex geometries, which is nontrivial for conventional frameworks. Using this model, we demonstrate nanoscale optical bistability at an exceptionally low-power threshold of 1 mW by leveraging Kerr-type hydrodynamic nonlinearities supported by the heavily doped semiconductor's free carriers. This high nonlinearity is enabled by a strong coupling between metallic gap plasmons and longitudinal bulk plasmons in the semiconductor due to quantum pressure. These findings offer a viable approach to studying Kerr-type nonlinearity and lay the groundwork for developing efficient and ultrafast all-optical nonlinear devices.