5. M. Krumpholz and L.P.B. Katehi, MRTD: New time domain schemes based on multiresolution analysis, IEEE Trans Microwave Theory Techn 44 (1996), 555–571. 6. S. Jaffard, Wavelet methods for fast resolution of elliptic problems, SIAM J Numerical Analysis 29 (1992), 965–986. © 2003 Wiley Periodicals, Inc. META-MATERIAL SURFACE DESIGN USING THE HIERARCHICAL GENETIC ALGORITHM Yuan Yuan, 1 Chi Hou Chan, 1 Kim Fung Man, 2 and Kwai Man Luk 1 1 Wireless Communications Research Laboratory City University of Hong Kong 83 Tat Chee Ave, Kowloon, Hong Kong SAR, China 2 Department of Electronic Engineering City University of Hong Kong 83 Tat Chee Ave, Kowloon, Hong Kong SAR, China Received 14 April 2003 ABSTRACT: In this paper, we design a meta-material surface emulat- ing a perfect magnetic conducting plane (PMC) using the hierarchical genetic algorithm (HGA). This is achieved by manipulating the unit-cell geometry of frequency-selective surface screens and the electrical prop- erties of the supporting dielectric medium in the optimization process. The properties of the structure are evaluated using a method of mo- ments (MoM)-based electromagnetic solver. By virtue of the HGA, prior information of the number of FSS screens and dielectric layers is not required. The designed PMC is employed as a dipole-antenna reﬂector for gain enhancement. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 226 –230, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11176 Key words: meta material; genetic algorithm; electromagnetic simula- tion INTRODUCTION Meta-material is a complex “artiﬁcial” material that does not exist in nature; one example is the perfect magnetic conductor (PMC), which can be very useful in a wide variety of microwave applica- tions. Recently, electromagnetic bandgap (EBG) structures have been widely investigated for mimicking a PMC [1, 2]. They are in the form of frequency-selective surfaces with multiple screens and multiple dielectric layers backed by a perfect electric conducting ground plane [3–5]. This conﬁguration is desirable for its low cost and easy realization. However, the design procedure is very chal- lenging as there are many parameters involved, for instance, the unit-cell geometry of each screen, and the thickness of the dielec- tric layers and their electric properties. More importantly, the number of FSS screens and dielectric layers needs to be speciﬁed a priori before adopting an optimization procedure. The hierarchical genetic algorithm (HGA) [8] is an emerging optimization algorithm, which can simultaneously precede struc- tural and parametric system optimization [6, 7]. The desirable properties of the meta-material surface are the magnitude and phase of the reﬂection coefﬁcient equal to unity and 0°, respec- tively. The reﬂection coefﬁcient is computed by the method of moments (MoM)-based electromagnetic solver [5] and is con- verted into a ﬁtness value based on the design speciﬁcation. Following the rule of “survival of the ﬁttest,” HGA can globally ﬁnd the best solution whose properties mostly match the design speciﬁcation. The realization of the frequency-selective-based PMC demonstrates the efﬁciency and suitability of HGA. In this paper, the design of a 5.8-GHz meta-material surface acting as a PMC using HGA is presented. The number of FSS screens and dielectric layers are not speciﬁed, but will be deter- mined by the optimization process. This PMC surface is employed as a reﬂector for a dipole antenna. For the dipole antenna’s resonance frequency shifting, the dipole should be placed at a little distance from the PMC. The measured gain of the dipole is increased by 3 dB in the broadside direction when compared to the same dipole radiating in free space. The same measured gain is obtained if the dipole is backed by a PEC reﬂector that is set at a quarter-wavelength distance away from the dipole. This measure- ment conﬁrms that the meta-material surface indeed acts as a PMC. HIERARCHICAL GENETIC ALGORITHM Hierarchical genetic algorithm (HGA) has a newly formulated chromosome structure inspired by the complex hierarchical chro- mosome structure in nature. The hierarchical chromosome consists of two levels of genes, the control and parametric genes, so that it can provide a unique solution for simultaneous parametric and system structural search. For the frequency-selective-surface-based meta-material, there are many design parameters that should be taken into consider- ation. These include the number of screen and dielectric layers, dielectric constant, thickness of each dielectric layer, and unit-cell geometry. Even for the conventional genetic algorithm, there are too many parameters to be optimized. However, the control genes Figure 1 Unit-cell geometry of the FSS screen. [Color ﬁgure can be viewed in the online issue, which is available at www.interscience.wiley. com.] Figure 2 Structure of the designed FSS-based meta-material surface to be operated at 5.8 GHz. [Color ﬁgure can be viewed in the online issue, which is available at www.interscience.wiley.com.] 226 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 39, No. 3, November 5 2003