COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2008; 24:1363–1372 Published online 20 August 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cnm.1037 Application of Fourier differential quadrature for the analysis of photonic crystals M. Mahzoon ∗, † , H. Abiri and R. Ghayour Department of Electrical and Electronics Engineering, Shiraz University, Shiraz, Iran SUMMARY 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. Copyright 2007 John Wiley & Sons, Ltd. Received 23 August 2006; Revised 14 March 2007; Accepted 4 July 2007 KEY WORDS: FDQ; photonic crystal; eigenvalue INTRODUCTION The differential quadrature (DQ) method, which was introduced by Bellman et al. in 1972 [1] to solve nonlinear partial differential equations, has gained popularity recently in the analysis of the mechanical behavior of plate structures [2]. The conventional DQ method is mostly effective for problems with geometrically regular domains, although it is applicable to some problems with irregular domains if a proper geometric transformation is procured [3, 4]. The concept of triangular DQ was proposed by Zhong [5], aiming to deal with problems on irregular and triangular domains. Using this method, transformation of the physical domain is avoided and simple algebraic equations are resulted. More recently, DQ method has been applied in the analysis of electromagnetic field problems [6]. ∗ Correspondence to: M. Mahzoon, Department of Electrical and Electronics Engineering, Shiraz University, Shiraz, Iran. † E-mail: mahzoon@sutech.ac.ir Copyright 2007 John Wiley & Sons, Ltd.