Understanding the conditions for the optimum nonlinear refraction of epsilon-near-zero films based on transparent conducting oxides.

Transparent Conducting Oxides (TCOs) exhibit a large and ultrafast intensity-dependent refractive index in their Epsilon-Near-Zero (ENZ) spectral region, which depends dramatically on the material properties and measurement arrangement conditions. Therefore, attempts to optimize the nonlinear response of ENZ TCOs usually involve extensive nonlinear optical measurements. In this work, we show that significant experimental work can be avoided by carrying out an analysis of the material's linear optical response. The analysis accounts for the impact of thickness-dependent material parameters on the absorption and field intensity enhancement under different measurement conditions and estimates the incidence angle required for achieving the maximum nonlinear response for a given TCO film. We perform measurements of angle-dependent and intensity-dependent nonlinear transmittance for Indium-Zirconium Oxide (IZrO) thin films with different thicknesses and demonstrate a good agreement between the experiment and theory. Our results also indicate that the film thickness and the excitation angle of incidence can be adjusted simultaneously to optimize the nonlinear optical response, allowing a flexible design of TCO-based highly nonlinear optical devices.