Topology optimization for the design of microwave resonator considering frequency-dependent property

Microwave resonators are devices used for electron spin resonance spectroscopy which is expected to be one of the essential ingredients for future quantum technologies. The performance of the microwave resonators depends on the magnetic flux density norm in the sample space of the devices. Conventional microwave resonators have been designed to increase the magnetic flux density norm by resonance in the sample space. However, since the structures have been made by trial and error, there would be further improvement in performance of the devices. Thus, in this research, microwave resonators are designed by level set-based topology optimization. First, the design model and the governing equations of electromagnetic wave propagation problem are explained. Second, we propose a topology optimization method for the design of microwave resonators where two objective functions are defined. Third, the optimization problem is formulated to avoid local solutions because of frequency-dependent property. Finally, a numerical example is provided to confirm the usability and validity of the proposed method.