Confining light in all-dielectric anisotropic metamaterial particles for nano-scale nonlinear optics

High-index dielectrics can confine light into nano-scale leading to enhanced nonlinear response. However, increased momentum in these media can deteriorate the overlap between different harmonics which hinders efficient nonlinear interaction in wavelength-scale resonators in the absence of momentum matching. Here, we propose an alternative approach for light confinement in anisotropic particles. The extra degree of freedom in anisotropic media allows us to control the evanescent waves near the center and the radial momentum away from the center, independently. This can lead to a strong light confinement as well as an excellent field overlap between different harmonics which is ideal for nonlinear wavelength conversion. Controlling the evanescent fields can also help to surpass the constrains on the radiation bandwidth of isotropic dielectric antennas. This can improve the light coupling into these particles, which is crucial for nano-scale nonlinear optics. We estimate the second-harmonic generation efficiency as well as optical parametric oscillation threshold in these particles to show the strong nonlinear response in these particles even away from the center of resonances. Our approach is promising to be realized experimentally and can be used for many applications, such as large-scale parallel sensing and computing.