A two-dimensional phoxonic crystal (PxC) with optimal dual phononic and photonic complete band gaps (BGs) is proposed and analyzed numerically. Using finite element simulations, the thickness of the frame and the length of square silicon as well as the length of the square scatterer are found to be the three key factors influencing the dual BGs of PxC. Based on the orthogonal test design, 3-factor and 5-level experiments are designed to determine the relationships between the total bandwidths of the photonic and phononic BGs, respectively, with the three key factors. Using the two functional relationships as the unified objective function, the optimal thickness of the frame, and the length of square silicon and square scatterer are obtained to open the optimal dual BGs of PxC. It is expected that the combination of orthogonal test design and finite element simulations is a helpful way to design PxCs.

提出了具有最佳声子和光子双完整带隙（BG）的二维光子晶体（PxC）并进行了数值分析。使用有限元模拟，发现框架的厚度，方形硅的长度以及方形散射体的长度是影响PxC双BG的三个关键因素。基于正交测试设计，设计了三因素和五水平实验，分别确定了光子和声子BG的总带宽与三个关键因素之间的关系。使用这两个函数关系作为统一的目标函数，获得了框架的最佳厚度以及方形硅片和方形散射体的长度，以打开PxC的最佳双BG。