Valenzuela-Sau Jesús Daniel, Munguía-Arvayo Ramón, Gastélum-Acuña Sandra, Gaspar-Armenta Jorge, Nápoles-Duarte José, García-Llamas Raúl
J Opt Soc Am A Opt Image Sci Vis. 2017 Aug 1;34(8):1369-1375. doi: 10.1364/JOSAA.34.001369.
The transverse magnetic Gaussian beam diffraction from a finite number, equally spaced and rectangular cross section dielectric cylinder row is studied. The infinitely long cylinders' axes are perpendicular to the beam's direction of propagation. The cylinder row, with dielectric constant ε=nc2, is treated as a periodic inhomogeneous film, with period a and thickness w, bounded by two semi-infinite homogeneous media. With this restriction, the method is valid only for square or rectangular cross section cylinders. The supercell and the plane wave expansion methods are used to calculate the eigenfrequencies and eigenvectors supported for a one-dimensional photonic crystal. Then, these eigenfrequencies and eigenvectors are used to expand the field in the inhomogeneous film. Numerical results are presented for a greater than λ (the incident light wavelength), w (the cylinder width), and w (Gaussian beam waist). Two cases are studied. In the first (second) case, the unit cell contains one cylinder (a cylinder row), which simulates the scattering from a single cylinder (an inhomogeneous thin film). The total integrated scattering in transmission (reflection) shows three well-defined minima (maxima), which are due to interference effects. Its positions can be approximately obtained with the formula λ=4nw/k, with k=3, 4, and 6. The total integrated scattering in transmission decreases linearly as a function of the cylinder number.
研究了有限数量、等间距且具有矩形横截面的介质圆柱排对横向磁高斯光束的衍射。无限长圆柱的轴线垂直于光束的传播方向。介电常数为ε = nc²的圆柱排被视为周期非均匀薄膜，周期为a，厚度为w，由两个半无限均匀介质界定。在此限制下，该方法仅对方形或矩形横截面的圆柱有效。采用超胞法和平面波展开法计算一维光子晶体支持的本征频率和本征向量。然后，利用这些本征频率和本征向量在非均匀薄膜中展开场。给出了a大于λ（入射光波长）、w（圆柱宽度）和w（高斯光束束腰）时的数值结果。研究了两种情况。在第一种（第二种）情况下，单胞包含一个圆柱（一排圆柱），其模拟了单个圆柱（非均匀薄膜）的散射。透射（反射）中的总积分散射显示出三个清晰的极小值（极大值），这是由干涉效应引起的。其位置可用公式λ = 4nw/k近似得到，其中k = 3、4和6。透射中的总积分散射随圆柱数量呈线性下降。
