Thermal energy dependent transient permittivity of epsilon-near-zero material

Transparent conductive oxides exhibit attractive optical nonlinearity with ultrafast response and giant refractive index change near the epsilon-near-zero (ENZ) wavelength, originating from the intraband dynamics of conduction electrons. The optical nonlinearity of ENZ materials has been explained by using the overall-effective-mass and the overall-scattering-time of electrons in the extended Drude model. However, their response to optical excitation is yet the last building block to complete the theory. In this paper, the concept of thermal energy is theoretically proposed to account for the total energy of conduction electrons exceeding their thermal equilibrium value. The time-varying thermal energy is adopted to describe the transient optical response of indium-tin-oxide (ITO), a typical ENZ material. A spectrally-resolved femtosecond pump-probe experiment was conducted to verify our theory. By correlating the thermal energy with the pumping density, both the giant change and the transient response of the permittivity of ITO can be predicted. The results in this work provide a new methodology to describe the transient permittivities of ENZ materials, which will benefit the design of ENZ-based nonlinear photonic devices.