  We demonstrate new axisymmetric inverse-design techniques that can solve
problems radically different from traditional lenses, including
\emph{reconfigurable} lenses (that shift a multi-frequency focal spot in
response to refractive-index changes) and {\emph{widely separated}}
multi-wavelength lenses ($\lambda = 1\,\mu$m and $10\,\mu$m). We also present
experimental validation for an axisymmetric inverse-designed monochrome lens in
the near-infrared fabricated via two-photon polymerization. Axisymmetry allows
fullwave Maxwell solvers to be scaled up to structures hundreds or even
thousands of wavelengths in diameter before requiring domain-decomposition
approximations, while multilayer topology optimization with $\sim 10^5$ degrees
of freedom can tackle challenging design problems even when restricted to
axisymmetric structures.
