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

Jesús Daniel Valenzuela-Sau, Ramón Munguía-Arvayo, Sandra Gastélum-Acuña, Jorge Gaspar-Armenta, José Nápoles-Duarte, Raúl García-Llamas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 εc = n2c, is treated as a periodic inhomogeneous film, with period ax and thickness wy, 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 ax greater than λ (the incident light wavelength), wx (the cylinder width), and wg (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 λk = 4ncwy∕k, with k = 3, 4, and 6. The total integrated scattering in transmission decreases linearly as a function of the cylinder number.

Original languageEnglish
Pages (from-to)1369-1375
Number of pages7
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number8
StatePublished - Aug 2017

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© 2017 Optical Society of America.


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