In recent years, topology optimization has proved itself to be state of the art in the design of mechanical structures. At the same time, energy harvesting has gained a lot of attention in research and industry. In this work, we present a novel topology optimization of a multi-resonant piezoelectric energy-harvester device. The goal is to develop a broadband design that can generate constant power output over a range of frequencies, thus enabling reliable operation under changing environmental conditions. To achieve this goal, topology optimization is implemented with a combined-objective function, which tackles both the frequency requirement and the power-output characteristic. The optimization suggests a promising design, with satisfactory frequency characteristics.

We introduce an inverse design methodology for a new class of eigenfrequency-invariant metamaterial-resonators, targeting nuclear magnetic resonance detection at ultra-high $$\mathbf {B_0}$$ B 0 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.

This work presents an efficient inverse design process for electron paramagnetic resonance (EPR) loop-gap detectors. The primary goal is to achieve a high-intensity magnetic field in the sample and resonance characteristics at two distinct frequencies, improving experiment performance, selectivity, and versatility. By employing topology optimisation, we obtained the optimal shapes of the auxiliary loops, enhancing both sensitivity and magnetic concentration at the target frequencies. The resulting double-resonant LGR design is compact, features minimal sample heating, and supports high-quality factor operation. Simulation results demonstrate significant improvements in field localisation and signal-to-noise ratio (SNR), highlighting the potential of this method to advance spectroscopy techniques. The proposed optimisation framework paves the way for the development of multi-functional resonators with tailored performance for diverse magnetic resonance applications.