Near-Zero-Index (NZI) media have recently received significant attention for enhanced nonlinear optical processes such as the intensity dependent refractive index (IDRI). For NZI materials in the infrared, this effect is generally described as a result of free-electron effects such as excess carrier and hot-electron generation. Yet, many works model the response through the Kerr effect, a bound-electron polarization process exhibiting an instantaneous response and polarization sensitivity that are not observed in NZI materials. The similar dispersions in absorption for NZI and resonant materials enables the Kerr index to be a reasonable approximation, but its origin limits the predictive ability of the model. For example, the non-degenerate Kerr model predicts a diverging n_2 as the material loss tends towards zero. However, this condition would eliminate the absorption of the pump resulting in a vanishing nonlinear interaction. To aid the description of nonlinearities in NZI media, we have developed carrier kinetic models for the IDRI rooted in free electron effects. From this, our model shows that for low loss films, the quality factor n_2/FWHM in fact increases with additional loss, largely due to an significant increase in n_2 which outpaces the increase in breadth. This suggests the difficult task to reduce the loss in NZI materials may not be necessary for applications where the maximum IDRI or modulation is desired. As a result, the carrier kinetic models can more accurately predict the behavior of materials, e.g. in response to varying loss, as well as optimize pumping conditions and couple multiple excitation schemes.
|