Electronic-Based Model of the Optical Nonlinearity of Low-Electron-Density Drude Materials

Low-electron-density Drude (LEDD) materials such as indium tin oxide (ITO) are receiving considerable attention for their combination of CMOS compatibility, unique epsilon-near-zero (ENZ) behavior, and giant ultrafast nonlinear thermo-optic response. However, current understanding of the electronic and optical response of LEDD materials is limited due to the simplistic modeling that extends only the known models of noble metals without considering the interplay among the lower electron density, relatively high Debye energy, and the nonparabolic band structure. We bridge this knowledge gap and provide a complete understanding of the nonlinear electronic-thermal-optical response of LEDD materials. In particular, we rely on state-of-the-art electron dynamics modeling, as well as a time-dependent permittivity model for LEDD materials under optical pumping within the adiabatic approximation. We find the electron temperature may reach values much higher than realized before, even exceeding the Fermi temperature, in which case the effective chemical potential dramatically decreases and even becomes negative, thus, transient giving the material some characteristics of a semiconductor. We further show that the nonlinear optical response of LEDD materials originating from the changes to the real part of the permittivity is associated with changes of the population. This resolves the argument about the rise time of the permittivity, showing that it is instantaneous. In this vein, we show that referring to the LEDD permittivity as having a Kerr or ``saturable'' nonlinearity is unsuitable since its permittivity dynamics is absorptive rather than nonresonant and does not originate from population inversion. Finally, we analyze the probe-pulse dynamics and unlike previous work, we obtain a quantitative agreement with the results of recent experiments.