  Second harmonic generation (SHG) with a material of large transparency is an
attractive way of generating coherent light sources at exotic wavelength range
such as VUV, UV and visible light. It is of critical importance to improve
nonlinear conversion efficiency in order to find practical applications in
quantum light source and high resolution nonlinear microscopy, etc. Here an
enhanced SHG with conversion efficiency up to the order of 0.01% at SH
wavelength of 282 nm under 11 GW/cm2 pump power via the excitation of anapole
in lithium niobite (LiNbO3, or LN) nanodisk through the dominating d33
nonlinear coefficient is investigated. The anapole has advantages of strongly
suppressing far-field scattering and well-confined internal field which helps
to boost the nonlinear conversion. Anapoles in LN nanodisk is facilitated by
high index contrast between LN and substrate with properties of near-zero-index
via hyperbolic metamaterial structure design. By tailoring the multi-layers
structure of hyperbolic metamaterials, the anapole excitation wavelength can be
tuned at different wavelengths. It indicates that an enhanced SHG can be
achieved at a wide range of pump light wavelengths via different design of the
epsilon-near-zero (ENZ) hyperbolic metamaterials substrates. The proposed
nanostructure in this work might hold significances for the enhanced
light-matter interactions at the nanoscale such as integrated optics.
