Novel Planar Absorber Designs Using Genetic Algorithms Suomin Cui*1, Daniel S. Weile1 and John L. Volakis2 1 ECE Dept., University of Delaware, Newark, DE,19711 2 ElectroScience Laboratory, ECE Dept.,The Ohio State Univ.,Columbus, OH 43212 1. Introduction Electromagnetic absorbers are often used to reduce radar echo from anechoic chambers, aircraft and so on. For many applications, the absorber must be built conformable to a complex surface, or must have a flat interface with the air. The most common of these conformable absorber types is the multilayer, which is composed of flat layers of different lossy materials [1]. Unfortunately, multilayers exhibit narrow frequency response; therefore, few planar structures have been proposed to create high performance absorbers, especially for wide frequency bands. Instead, frequency selective surfaces (FSSs) have been used, including resistive screens [2], metal FSS screens [3] and active metal FSS screens [4]. Earlier studies have found that planar-implanted periodic material blocks exhibit frequency selective properties. Motivated by this, this study seeks to create absorbers by drilling holes (texturization) in lossy materials. Optimized results based on genetic algorithms demonstrate that this absorber model can vastly reduce reflections over a wide frequency band, and thus outperform multilayer coating and FSS-type absorbers when a predefined lossy material database is provided. To the best of the authors’ knowledge, this type of absorber has never been considered before. 2. The absorber models and design approach Because this study investigates the performance of a new conformable absorber model, this model should first be compared to absorber models available in the literature. Some of these models are listed below and serve to address the unique features of the described absorber. Multilayer coating: The performance of this absorber is determined by the number of layers, and the thickness and material composition of each layer. In this work, the layer material is selected from a predefined database of eight materials compiled from [3]. The relative dielectric constant ( ε = ε ′ − jε ′′ ) of each material (material type 1 to 8) is listed in Table I. Table I: Database of Materials Material

ε′ ε ′′

1 4.48 1.87

2 5.84 1.66

3 5.21 1.18

4 7.08 2.32

5 9.84 4.95

6 11.87 9.72

7 12.73 8.13

8 17.97 14.57

FSS-type absorbers: Examples of FSS-type absorbers are shown in Fig.1. As shown in Fig. 1(a), small metal patches are mounted on top of the lossy material— Case 1—or inside the material as shown in Fig. 1(b)—Case 2. The (square) FSS unit cell is displayed in Fig.1(c). The unit cell is divided into a uniform 6 × 6 array of square pixels. Each pixel may be covered by one metal patch which is denoted by 1 or may have no patch, denoted by 0 in Fig. 1(c). The reflectance of this class of absorbers is governed by the property of the lossy material, the thickness d for case

1 or thicknesses d1 and d 2 for case 2, as well as the distribution of the metal patches on the unit cell. Texture-type absorbers: The new absorbers, texture-type absorbers, are created by drilling holes on a one-layer coating. The holes may be drilled to the bottom (PEC layer) as shown in Fig. 2(a)—Case 1—or may be drilled partially as shown in Fig. 2(b)—Case 2. The top view is the same as in Fig. 1(c). A “1” in the pixel represents a hole whereas a “0” in the pixel represents the presence of material. The reflectance of these absorbers depends on the lossy material, the thicknesses shown in Fig. 2 and the distribution of the holes. To design the above absorbers to achieve optimally low reflectance, an electromagnetic simulator is needed to analyze the reflected power from the periodic structures. The spectral finite element-boundary integral (FE-BI) method [5] is adopted herewith due to its flexibility and efficiency for simulating inhomogeneous structures. (Of course, for multilayer coatings, an exact analytical solution exists). An optimizer must also be integrated with the FE-BI solver to design for the variables, including thicknesses (real variables), material choices from the available database (integer variables), and existence or nonexistence of metal or material (binary variables). As in our previous work with polygonal absorbers [6], a genetic algorithm is used for the design. More specifically, a standard binary GA enhanced with elitism and niching is adapted here. The design objective for the three absorbers is the same: minimize the maximum reflected power over a wide frequency band (20-25GHz) for both TM and TE polarizations. (Results for a more general design criterion will be presented at the conference.) The maximum thickness for each thickness is limited to 4 mm , with 5 bits used to represent each thickness. The population size is also set to 100 for all runs of the GA. 3. Designs for normal incidence for three models The multilayer coating was first optimized so that it could serve as a reference for further comparisons. The maximum reflected powers over the frequency band for the four-layer and eight-layer coatings were found to be -16.53dB and -16.79dB, respectively. Table II: Performance of the optimized FSS-type and texture-type absorbers (case 1) Model FSS-type Texture-type

Thickness(mm)

d = 1.291 d = 2.323

Material choice 3 5

Maximum reflected power -18.34dB -26.00dB

First, we considered two possible absorber configurations given in Fig.1 and 2. Figure 1 refers to an FSS-type absorber whereas Fig. 2 proposes a texture-type absorber. Note also that each figure depicts two possible configurations. For the FSStype absorber, the FSS is placed either on the surface of the dielectric or in the middle as shown. The two cases given in Figure 2 refer to textures constructed with either full depth or partially filled holes. The geometrical complexities of the two absorber models are comparable. However, as seen from the convergence history and the reflectivity results (see Fig. 3, case 1 for both absorber types) the texture-type absorber leads to much better absorbers. Specifically, the reflectivity is down to -25dB for the texture-type absorber, but reaches only -18dB for the FSS-type absorber. Table II gives the specific designs,

including the designed thickness, material choice and the performance for each design. Fig.4 shows the frequency responses for the two designed absorbers. The convergence history and attainable absorption for the case 2 designs are given in Fig. 5 and 6, respectively. Specifically, Fig.5 shows the convergence histories for FSS-type and texture-type absorbers. Again, we observe the much better performance of the texture-type design (-18.42dB vs. -27.13dB for the FSS-type absorber, a difference of 8.5dB). The corresponding geometries are listed in Table III and Fig. 6 depicts the frequency responses for both case 2 absorbers. Table III :Performance of the designed FSS-type and texture-type absorbers (case 2) Model

Thickness(mm)

Material choice

Maximum reflected power

FSS-type

d1 = 2.581, d 2 = 1.549 d1 = 3.226, d 2 = 2.452

1

-18.42dB

5

-27.13dB

Texture-type

Comparing the numerical results for the three absorber models, including the multilayer coatings, the FSS-type absorbers and the texture-type absorbers for the frequency band at normal incidence, we can conclude that for a given database, the latter two models, can obtain lower reflectivites than the coating absorbers. The texture-type absorbers actually achieve the lowest reflected power among all three designs. For the database shown in Table I, the specific attainable reflectivities are for the eight-layer coating, the FSS-type and texture-type absorbers are -16.79 dB, 18.45dB and -27.13dB, respectively. 4. Conclusion A new class of planar absorbers were proposed in this paper. This absorber is created by drilling textures within or on top of the coating. Genetic algorithms were applied to optimize the absorbers and thus achieve low reflectance over a wide frequency band. Numerical results demonstrate that the new absorber outperforms the multilayer coating and the absorber using FSS-screens. These new absorbers have been designed for various requirements, and a richer design set will be presented to show their superior reflectivity responses at the talk. References 1. D. S. Weile, E. Michielssen, and D. E. Goldberg, "Genetic algorithm design of Pareto optimal broadband microwave absorbers," IEEE Trans. Electromag. Compat, vol. 38, pp. 518-525, 1996. 2. D. J. Kern and D. H. Werner, "A genetic algorithm approach to the design of ultrathin electromagnetic bandgap absorbers," Microwave and Opt. Tech. letters, vol. 38, pp. 61-64, 2003. 3. S. Chakravarty, R. Mittra, and N. B. Williams, "Application of a microgenetic algorithms (MGA) to the design of broad-band microwave absorbers using multiple frequency selective surface screen buried in dielectrics," IEEE Trans. on Microwave Theory and Techniques, vol. 50, pp. 284-296, 2002. 4. A. Tennant and B. Chambers, "A single-layer tuneable microwave absorber using an active FSS," IEEE Microwave and Wireless Components Lett., pp. 46-47, 2004. 5. T. F. Eibert and J. L. Volakis, "Fast spectral domain algorithm for a hybrid finite element/bounday integeral modeling of doubly periodic structures," IEE Proc.Microwave,Antennas and Propagation, vol. 147, pp. 329-334, 2000.

6. S. Cui and D. S. Weile, "Robust design of absorbers using genetic algorithms and the finite element-boundary integral method," IEEE Trans. Antennas and Propagation, vol. 51, pp. 3249-3258, 2003.

Fig.1 The FSS-type absorber models & FSS screen geometry (a) Case 1: FSS is on top of material (b) Case 2: FSS is inside of material (c) FSS screen geometry.

d1

d

d2

6 mm

6 mm

6mm 6mm

Fig. 2 The texture-type absorber models (a) Case 1: holes drilled to the bottom; (b) Case 2: holes drilled partway. -6 Best objective function value (dB)

-8 -10 -12 FSS-type absorber (case 1)

-14 -16

-18.34dB

-18 -20 -22

Texure-type absorber(case 1)

-24

-26.dB

-26 -28 0

10

20

30 40 50 60 70 Generation Number

80

90 100

Fig.3 Convergence histories for Case 1

Fig.4 Frequency responses for the designed absorbers

Best objective function value (dB)

-12 -14 FSS-type absorber (case 2)

-16

-18.42dB

-18 -20 -22 -24

Texture-type absorber (case 2)

-26

-27.13dB

-28 0

10

20

30 40 50 60 70 Generation Number

80

Fig.5 Convergence histories for Case 2

90 100

Fig.6 Frequency responses for the designed absorbers