Efficient second-harmonic generation in micrometer-thick slabs with indefinite permittivity

We theoretically predict efficient optical second-harmonic generation (SHG) from a micrometer-thick slab consisting of a quadratic nonlinear anisotropic medium whose linear principal permittivities have, at the fundamental wavelength, real parts of different signs (indefinite permittivity) and magnitude smaller than 1. We show that, by illuminating the slab with a $p$-polarized fundamental wave (with intensity of a few $\mathit{MW}/{\mathrm{cm}}^{2}$), highly efficient scattering of the second-harmonic field occurs in conditions at which the slab is linearly fully transparent for the fundamental wave. The high efficiency of the SHG process stems from the enhancement of the longitudinal field, perpendicular to the slab surface, produced by the very small value of the slab dielectric permittivities. We investigate the role played by medium losses, showing that, even in the strong-absorption regime, the described process yields a second-harmonic field which is much stronger than that produced by a standard (not indefinite) nonlinear slab.