Optimal Design of THz NRD Rat-Race Circuit Using Function Expansion Based Topology Optimization Method With CMA-ES

Rat-race circuit devices are crucial components in the design of THz-wave circuits. Although nonradiative dielectric (NRD) waveguides having simple structures and extremely low loss are promising platforms for THz-wave circuits, it may difficult to realize conventional rat-race devices in NRD platform due to the appearance of unwanted LSE$_{01}$ mode in the output ports. Therefore, optimal design of these devices is very essential for THz-wave circuit applications. In this paper, we present topology optimal design of THz NRD rat-race circuit based on function expansion method and covariance matrix adaptation evolution strategy (CMA-ES). The proposed method overcomes the difficulty of appearing unwanted LSE$_{01}$ mode in the output ports, thus the optimized devices achieved the significant improvement in the device performance in comparison with that of conventional NRD rat-race devices. In addition to the NRD rat-race circuit, a 90$^{\circ }$ hybrid device is also designed in order to confirm the validity of the proposed design approach. A thorough discussion of the fabrication tolerance of proposed devices has also been conducted in detail.