Applying the Optical Theorem in a Finite-Difference Time-Domain Simulation of Light Propagation
Date Issued
2009
Date
2009
Author(s)
Tsai, Cheng-Hao
Abstract
In this thesis, we discuss how to apply the optical theorem to the finite-difference time-domain method (FDTD). Because it is easier to write the FDTD code in two dimensions, we only investigate the two-dimensional optical theorem. First, we rewrite the form of the optical theorem to conveniently put into execution in the FDTD simulation and introduce some techniques which are used in the FDTD method to practice the optical theorem. There are (1) scattered-field / total-field technique (SFTF), which can separate the scattered field from the total field, (2) the near-to-far field transformation (NTFF), which could calculate the far field from the near-field data, and (3) the perfectly matched layer absorbing boundary condition (PML), which could absorb the electromagnetic wave. Then, we apply the optical theorem to calculate the scattering cross section of the non-absorbing cylinder which has the analytical solution called the Mie theory. With the changes of the grid size, the inaccuracies have the trend approaching to the second order-accuracy of the FDTD method. We also compare the inaccuracy between the different methods which are used to calculate the scattering cross section. The first method is the sum of RCS method. The second and third methods are to apply the definition of the scattering cross section and the definition of the extinction cross section in the near-field region. Finally, we observe that the inaccuracy of the optical theorem is larger than the others and suspect that it is induced by the anisotropy of the FDTD square grids.
Subjects
finite-difference time-domain method
optical theorem
extinction cross section
Type
thesis
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