  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.
