Extended Drude Model for Intraband-Transition-Induced Optical Nonlinearity

No existing model has completely explained the physics of the optical nonlinearity for epsilon-near-zero materials, which have recently emerged as candidates for design and fabrication of active nanophotonic devices. We propose to extend the Drude model by adopting a weighted electron effective mass, which takes into account the electron distribution in the nonparabolic conduction band. The extended Drude model is able to interpret the cause of the nonlinearity and provide a functional relationship between the refractive index and wavelength. Both the band nonparabolicity and the temperature-dependent mobility are responsible for the intraband-transition-induced optical nonlinearity. The spectrally resolved nonlinear refractive index and nonlinear susceptibilities are obtained from this model. The results can be applied to other transparent conducting oxides and will help in the design and modeling of spectral responses of nonlinear plasmonic devices.