Scattering of a Gaussian beam from a row of cylinders with rectangular cross section

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_c = n²_c, is treated as a periodic inhomogeneous film, with period a_x and thickness w_y, 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_x greater than λ (the incident light wavelength), w_x (the cylinder width), and w_g (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_k = 4n_cw_y∕k, with k = 3, 4, and 6. The total integrated scattering in transmission decreases linearly as a function of the cylinder number.