A fast metasurface optimization strategy for finite-size metasurfaces modeled using integral equations is presented. The metasurfaces considered are constructed from finite patterned metallic claddings supported by grounded dielectric spacers. Integral equations are used to model the response of the metasurface to a known excitation and solved by Method of Moments. An accelerated gradient descent optimization algorithm is presented that enables the direct optimization of such metasurfaces. The gradient is normally calculated by solving the method of moments problem N+1 times where N is the number of homogenized elements in the metasurface. Since the calculation of each component of the N-dimensional gradient involves perturbing the moment method impedance matrix along one element of its diagonal and inverting the result, this numerical gradient calculation can be accelerated using the Woodbury Matrix Identity. The Woodbury Matrix Identity allows the inverse of the perturbed impedance matrix to be computed at a low cost by forming a rank-r correction to the inverse of the unperturbed impedance matrix. Timing diagrams show up to a 26.5 times improvement in algorithm times when the acceleration technique is applied. An example of a passive and lossless wide-angle reflecting metasurface designed using the accelerated optimization technique is reported.
翻译:演示了使用集成方程式模型的有限尺寸表面的快速表面优化战略。 所考虑的表层是用有固定模式的金属包裹在有固定的电动空间器的支持下建造的。 集成方程式用于模拟元表对已知刺激的反应, 并用时速法解决。 显示加速梯度优化算法, 使这种元表能够直接优化。 梯度的计算方法通常是通过解决时针问题N+1乘以N是元表层中同质元素数目的时针方法。 由于N- 度梯度的每个组成部分的计算涉及沿着其双向和反向结果的一个元素对瞬时法阻力矩阵进行扰动。 这种数字梯度计算可以使用Woodbury矩阵特性加速进行。 Woodbury 矩阵特性允许以低成本计算受扰动阻力矩阵的反向, 将级校正校正值校正值调整到未受扰动的阻碍矩阵。 定式图显示加速度技术应用时, 加速度技术的加速度和损度优化度技术将加速度优化。