evolution strategy to the design of frequency-selective surfaces, Int J RF Microwave Computer Aided Eng 15 (2005), 173–180. 26. A. Akdagli and M.E. Yuksel, Application of differential evolution algorithm to the modeling of laser diode nonlinearity in a radio- overfiber network, Microwave Opt Technol Lett 48 (2006), 1130 – 1133. 27. C. Yildiz, A. Akdagli, and M. Turkmen, Simple and accurate synthesis formulas obtained by using a differential evolution algorithm for coplanar striplines, Microwave Opt Technol Lett 48 (2006), 1133– 1137. © 2007 Wiley Periodicals, Inc. ANALYSIS OF ELECTROMAGNETIC BAND-GAP WAVEGUIDE STRUCTURES USING BODY-OF-REVOLUTION FINITE- DIFFERENCE TIME-DOMAIN METHOD Ming-Sze Tong, 1 Ronan Sauleau, 2 Anthony Rolland, 2 and Tae-Gyu Chang 1 1 School of Electrical and Electronics Engineering, Chung-Ang University, 221 Heukseok-dong, Dongjak-gu, Seoul 156 –756, Korea 2 Institute of Electronics and Telecommunications of Rennes, University of Rennes I, Campus de Beaulieu, 263 Avenue du Ge ´ ne ´ ral Leclerc, 35042 Rennes, France Received 12 February 2007 ABSTRACT: Study of electromagnetic band-gap (EBG) structures has become a hot topic in computational electromagnetics. In this article, some EBG structures integrated inside a circular waveguide are studied. They are formed by a series of air-gaps within a circu- lar dielectric-filled waveguide. A body-of-revolution finite-difference time-domain (BOR-FDTD) method is adopted for analysis of such waveguide structures, due to their axial symmetric properties. The opening ends of the waveguide are treated as a matched load using an unsplit perfectly matched layer technique. Excitations on a waveguide in BOR-FDTD are demonstrated. Numerical results of various air-gap lengths with respect to the period of separation are given, showing an interesting tendency of EBG behavior. A chirping- and-tapering technique is applied on the EBG pattern to improve the overall performance. The proposed EBG structures may be applied into antenna structures or other system for unwanted signal suppres- sion. Results show that the BOR-FDTD offers a good alternative in analyzing axial symmetric configurations, as it offers enormous sav- ings in computational time and memory comparing with a general 3D-FDTD algorithm. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 2201–2206, 2007; Published online in Wiley Inter- Science (www.interscience.wiley.com). DOI 10.1002/mop.22668 Key words: EBG structures; circular dielectric-filled waveguide; BOR- FDTD method 1. INTRODUCTION One of the interesting areas that have recently been broadly con- ducted in computational electromagnetics (CEM) is the study of electromagnetic band-gap (EBG) structures. Typically, an EBG material acts as a band-stop filtering device to suppress electro- magnetic (EM) waves inside a certain frequency range. This is conventionally done through a periodic pattern of distributed ele- ments. The concept originated in optics [1, 2], and thereafter successfully transformed into microwave areas by proper fre- quency downscaling (e.g. [3, 4]). Circular waveguides have been commonly used in microwave engineering due to their high power capability and low power loss during transmission [5, 6]. Dielectric waveguide is deemed as a good candidate in guided wave structures, since the traveling EM waves are well confined inside the dielectrically filled substrate of the device during transmission. Their axial symmetric nature ensures an even field distributions along the azimuthal () direction at a cross section. Because of the nonexistence of a secondary conducting medium other than the outer metallic shell, waveguides support generally non-TEM (transverse electromagnetic) mode operations, such as transverse elec- tric (TE) or transverse magnetic (TM) modes. In terms of analyzing tool, a body-of-revolution finite-dif- ference time-domain (BOR-FDTD) method is adopted for anal- ysis [7, 8], due to the axial symmetric properties existing in circular waveguide structures. The BOR-FDTD method has been demonstrated as a robust and versatile numerical tool for solving axial symmetric problems as found in [9 –11], though they can also be solved using other frequency domain methods [12–14]. BOR-FDTD is a cylindrically based algorithm, and it expands the angular dependence using Fourier series. The com- putational domain is thus compressed from a three-dimensional (3-D) volume into a two-dimensional (2-D) –z plane. On the other hand, an unsplit perfectly matched layer (U-PML) tech- nique [15] is used to model the two end-walls of the waveguide as a matched load. In this article, some EBG structures integrated inside circular waveguides are taken for studies. They are constructed by aligning a series of periodic air-gaps longitudinally inside a dielectrically filled circular waveguide. Two operational modes, viz., TE 11 and TM 01 , are used for excitations. Frequency characteristics in terms of scattering parameters are extracted for analysis. It is observed that the given EBG structures exhibit a good band-gap behavior. Additionally, to further improve the performance of bandwidth in stop-band and the low frequency side-lobes, a chirping-and-taper- ing technique [16] is applied on the EBG air-gap pattern. 2. THEORY 2.1. BOR-FDTD Method Derivation of BOR-FDTD starts with the general time-dependent Maxwell’s curl equations:   H  = 0   r E  /t +  e E  and   E  =-  0  r H  /t -  m H  (1) This assumes linear and anisotropic media inside the computa- tional domain; where [ r ], [ r ], [ e ], [ h ] are the diagonal tensors of the relative permittivity, relative permeability, electric conduc- tivity, and magnetic conductivity, respectively. The Maxwell’s equations are expanded in cylindrical coordinates to handle cylin- drical structures more efficiently. For axial symmetric structures, viz., BOR structures, the electric and magnetic fields can be expanded using infinite Fourier series [17]: E   , , z ; t  =  m=0   E   , z ; t  even cosm + E  ,z;t odd sinm (2a) H  ,,z;t =  m=0  H  ,z;t even cosm + H  ,z;t odd sinm (2b) where m is the mode number in the -direction, and the field terms with subscripts even and odd are the coefficients of cos(m) and sin(m), respectively. Solutions for Maxwell’s curl equations are obtainable by a proper selection of angular field variations, e.g., DOI 10.1002/mop MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 49, No. 9, September 2007 2201