We introduce an inverse design methodology for a new class of eigenfrequency-invariant metamaterial-resonators, targeting nuclear magnetic resonance detection at ultra-high B0 field, and operating at two specified frequencies selected from within the 100-1500 MHz range. The primary optimisation goal is to maximise the magnetic field intensity and uniformity within a liquid sample, while the electric energy should be kept to a minimum level to reduce dielectric heating or quadrupolar moment excitation effects. Due to the symmetric geometry requirement of the cavity, a demultiplexer is also designed to direct each discrete resonant signal to another predetermined output port of the resonator. In order to reduce the geometrical dependency of the resonance frequency, a bespoke metamaterial is used for the cavity host. Therefore, an additional optimisation problem for a unit cell domain is defined to seek a proper material layout for the host region of the resonators. Given the sensitivity of the frequency domain, the optimisation process is effectively regulated through the utilisation of both a Helmholtz filter and a projection method. It is found that considerable improvements of the resonator quality factor can be obtained through this optimisation process.

The simulation data can be handled using COMSOL software.