Enhancement of the Cubic Nonlinearity in Epsilon-Near-Zero Media: Nondegenerate Optical Kerr Effect

Nonlinear media whose permittivity epsilon 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(ENZ) if Re epsilon(lambda(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(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.