  Epsilon-near-zero (ENZ) materials, i.e., materials with vanishing real part
of the permittivity, have become an increasingly desirable platform for
exploring linear and nonlinear optical phenomena in nanophotonic and on-chip
environments. ENZ materials inherently enhance electric fields for properly
chosen interaction scenarios, host extreme nonlinear optical effects, and lead
to other intriguing phenomena. To date, studies in the optical domain mainly
focused on nanoscopically thin films of ENZ materials and their interaction
with light and other nanostructured materials. Here, the optical response of
individual nanostructures milled into an ENZ material are explored both
experimentally and numerically. For the study, 3D structured light beams are
employed, allowing for the full utilization of polarization-dependent field
enhancements enabled by a tailored illumination and a vanishing permittivity.
This study reveals the underlying intricate interaction mechanisms and showcase
the polarization-dependent controllability, paving the way towards experiments
in the nonlinear optical regime where the presented effects will enable
polarization-controlled nonlinear refractive index based ultra-fast switching
on the single nanostructure level.
