Nonlinear Optical Interactions in \varepsilon -Near-Zero Materials: Second and Third Harmonic Generation

Second and third harmonic generation in materials that display near-zero permittivity values are discussed. The enormous field enhancement due to the continuity of the longitudinal component of the displacement field enhances the nonlinear response drastically. Nonlinear surface terms due to symmetry breaking and phase-locked harmonic components should not be neglected in such extreme environments.