Application of Fourier differential quadrature for the analysis of photonic crystals

作者：Mahzoon M^*; Abiri H; Ghayour R

来源：Communications in Numerical Methods in Engineering, 2008, 24(11): 1363-1372.

DOI：10.1002/cnm.1037

• FDQ
• photonic crystal
• eigenvalue

A Fourier expansion-based differential quadrature (FDQ) method is used for computing the spectrum and eigenmodes of 2-D photonic crystals. The FDQ method is applied to the master equation of photonic crystals, which is in the form of an eigenvalue problem. It is shown that the complex periodic Bloch eigenfunction may be determined by this method. The region under consideration is a unit cell with periodic boundary conditions and consists of two different dielectric materials. Thus, there are discontinuities in the region. By adjusting the position of grid points properly, the accuracy of solution can be improved.
Since proper analytical interpolation functions are used in the DQ method, its accuracy is high compared with the conventional low-order finite difference and finite element methods, whereas the number of required grid points is quite smaller. In addition, the method is efficient as far as the CPU capacity and computational time are concerned because of the low number of grid points used.

• 出版日期2008-11