Enhancement of the cubic nonlinearity in epsilon-near-zero media: nondegenerate optical Kerr effect

Nonlinear media whose permittivity $\varepsilon$ can be reduced to nearly zero allow an additional enhancement of a nonlinear optical response. It is commonly accepted that the cubic nonlinearity is enhanced at a certain wavelength $\lambda_\text{ENZ}$ if $\mathrm{Re}\, [\varepsilon(\lambda_\text{ENZ})]=0$. It is shown in this work that the enhancement of the nonlinear refractive index $n_2$ generally occurs at a different wavelength $\lambda'$. This anomalous shift is manifested when the wavelength $\lambda_\text{ENZ}$ of a material is near the resonance of the nonlinear susceptibility. An analytical condition for the enhancement of the nondegenerate optical Kerr effect is obtained.