  Resonators composed of two mirrors, such as Fabry-Perot cavities, provide a
simple but effective approach to achieve wave transmission with high finesse.
Further increase of the quality factor requires reflectors with higher
conductivity or multi-mirror solutions. However, the analytical complexity of
resonators with more than two mirrors prevents the design of optimal structures
without recurring to numerical methods. This work considers an alternative
approach to this problem by using cavities which do not produce any
electromagnetic scattering. We demonstrate that these invisible cavities can be
placed inside one another, resulting in a `matryoshka-doll'-like resonator. The
standing-wave distribution of the inner resonator can be controlled without
disturbing that of the outer one, whereas the whole system remains
non-scattering.
