頻率選擇表面(FSS)材料電磁模擬與分析

頻率選擇表面 (Frequency Selective Surface, FSS) 是一種由人工結構組成的表面材料，通常呈現平面或曲面的形式。它由規則排列的金屬圖案組成，這些圖案常見形狀包括環形、方形、十字形等幾何圖案，並以陣列方式分布在基板上。FSS 能夠精確調控特定頻段的電磁波，對某一頻率範圍內的電磁波實現選擇性反射、透過或吸收，功能類似濾波器。此技術廣泛應用於軍事、通訊、電子屏蔽以及智能建築等多個領域。   

本教學範例將示範如何利用 Sim4Life 軟體，建模並模擬一種二維週期性圓形環陣列的頻率選擇表面(FSS)結構，進一步分析當平面電磁波入射時，該結構的反射係數特性。

• Lumped Elements: 維持預設設定

• Grid: 分別設定 loop、sub 與 Wire box 物件的網格劃分最的步長與解析度。相關設定如下圖所示:

(3) 建立 1 個 EM-FDTD Single 電磁求解器，命名為 EM - wo，用來模擬在 FSS 單元晶格不存在時平面電磁波的行進  

• 右鍵點選 EM - EM FDTD 求解器中的 Grid，選擇 Lock Grid 鎖住目前的網格設定
• 右鍵點選 EM - EM FDTD 求解器，選擇 Clone 複製求解器相關的設定參數
• 將新建立的  EM-FDTD Single 電磁求解器，命名為 EM - wo

(2) 接下來我們開啟 Scripter 視窗，利用 Sim4Life 的 Python API 函式撰寫 python 腳本，由 R、T 兩個點感測器提取電場數據並計算 FSS 的 S 參數 (S11, S21)

• S₂₁ = |Ex|_EM / |Ex|_EM-wo 
• S₂₁(dB) = 20*log(S₂₁)   

• S₁₁ = 1 – S₂₁² 
• S₁₁(dB) = 20*log(S₁₁)

範例程式碼:
# -*- coding: utf-8 -*-
# This script was auto-generated by Sim4Life version 7.2.1.11125

import numpy as np
import s4l_v1.analysis as analysis
import s4l_v1.document as document
import s4l_v1.model as model
import s4l_v1.units as units
from s4l_v1 import Unit
import matplotlib.pyplot as plt

# Creating the analysis pipeline
# Adding a new SimulationExtractor with cell
simulation = document.AllSimulations["EM"]
simulation_extractor = simulation.Results()

# Adding a new EmSensorExtractor
em_sensor_extractor_R = simulation_extractor["R"]
em_sensor_extractor_R.UpdateAttributes()
em_sensor_extractor_R.Update()
document.AllAlgorithms.Add(em_sensor_extractor_R)

# Adding a new EmSensorExtractor
em_sensor_extractor_T = simulation_extractor["T"]
em_sensor_extractor_T.UpdateAttributes()
em_sensor_extractor_T.Update()
document.AllAlgorithms.Add(em_sensor_extractor_T)

# Adding a new Ex abs mag extractor
em_sensor_extractor_T_E = em_sensor_extractor_T.Outputs["EM E(f)"]
em_sensor_extractor_T_E.Update()
em_sensor_extractor_T_E_data = em_sensor_extractor_T_E.Data
em_sensor_extractor_T_E_data_Axis = em_sensor_extractor_T_E_data.Axis
em_sensor_extractor_T_E_data_Ex_mag = np.abs(em_sensor_extractor_T_E_data.GetComponent(0))

em_sensor_extractor_R_E = em_sensor_extractor_R.Outputs["EM E(f)"]
em_sensor_extractor_R_E.Update()
em_sensor_extractor_R_E_data = em_sensor_extractor_R_E.Data
em_sensor_extractor_R_E_data_Axis = em_sensor_extractor_R_E_data.Axis
em_sensor_extractor_R_E_data_Ex_mag = np.abs(em_sensor_extractor_R_E_data.GetComponent(0))

# Adding a new SimulationExtractor without cell
simulation_wo = document.AllSimulations["EM - wo"]
simulation_extractor_wo = simulation_wo.Results()

# Adding a new EmSensorExtractor
em_sensor_extractor_R_wo = simulation_extractor_wo["R"]
em_sensor_extractor_R_wo.UpdateAttributes()
em_sensor_extractor_R_wo.Update()
document.AllAlgorithms.Add(em_sensor_extractor_R_wo)

# Adding a new EmSensorExtractor
em_sensor_extractor_T_wo = simulation_extractor_wo["T"]
em_sensor_extractor_T_wo.UpdateAttributes()
em_sensor_extractor_T_wo.Update()
document.AllAlgorithms.Add(em_sensor_extractor_T_wo)

# Adding a new Ex abs mag extractor
em_sensor_extractor_T_E_wo = em_sensor_extractor_T_wo.Outputs["EM E(f)"]
em_sensor_extractor_T_E_wo.Update()
em_sensor_extractor_T_E_data_wo = em_sensor_extractor_T_E_wo.Data
em_sensor_extractor_T_E_data_Axis_wo = em_sensor_extractor_T_E_data_wo.Axis
em_sensor_extractor_T_E_data_Ex_mag_wo = np.abs(em_sensor_extractor_T_E_data_wo.GetComponent(0))

em_sensor_extractor_R_E_wo = em_sensor_extractor_R_wo.Outputs["EM E(f)"]
em_sensor_extractor_R_E_wo.Update()
em_sensor_extractor_R_E_data_wo = em_sensor_extractor_R_E_wo.Data
em_sensor_extractor_R_E_data_Axis_wo = em_sensor_extractor_R_E_data_wo.Axis
em_sensor_extractor_R_E_data_Ex_mag_wo = np.abs(em_sensor_extractor_R_E_data_wo.GetComponent(0))

x_axis_GHz = em_sensor_extractor_T_E_data_Axis*1.e-9

S21 = em_sensor_extractor_T_E_data_Ex_mag/em_sensor_extractor_T_E_data_Ex_mag_wo
S21_dB = 20.*np.log10(S21)

S11_lst = []
for i in range(len(S21)):
    S11_lst.append(np.sqrt( 1. - S21[i]**2 ))
S11 = np.array(S11_lst)
S11_dB = 20.*np.log10(S11)

fig, ax = plt.subplots()
ax.plot(x_axis_GHz, S21_dB, label="S21", color='b')
ax.plot(x_axis_GHz, S11_dB, label="S11", color='r')
# ax.set_ylim([-25, 0])
ax.grid()
ax.legend()
ax.set_xlabel("Frequency [GHz]")
ax.set_ylabel("dB")

inputs = S21_dB
plot_viewer = analysis.viewers.PlotViewer(inputs=inputs)
plot_viewer.Plotter.ComplexOptions = plot_viewer.Plotter.ComplexOptions.enum.Real
plot_viewer.Plotter.ShowAll = True
plot_viewer.UpdateAttributes()
document.AllAlgorithms.Add(plot_viewer)

參考文獻: Equivalent circuit model for array of circular loop FSS structures at oblique angles of incidence