  Using eigenmode analysis and full 3D FEM modelling, we demonstrate that a
closed cavity built of an array of elementary harmonic oscillators with
negative mutual couplings exhibits a dispersion curve with lower order modes
corresponding to higher frequencies. Such cavity arrays may help to achieve
large mode volumes for boosting sensitivity of the axion searches, where the
mode volume for the composed array scales proportional to the number of
elements, but the frequency remains constant.
  The negatively coupled cavity array is demonstrated with magnetically
coupling coils, where the sign of next-neighbour coupling (controlled with
their chirality) sets the dispersion curve properties of the resonator array
medium. Furthermore, we show that similar effects can be achieved using only
positively coupled cavities of different frequencies assembled in periodic
cells. This principle is demonstrated for the multi-post re-entrant system,
which can be realised with an array of straight metallic rods organised in
chiral structures.
