Multiband FSS with Fractal Characteristic Based on Jerusalem Cross Geometry

This paper proposes a new Frequency Selective Surface (FSS) with modifications on the Jerusalem Cross (JC) geometry to provide a multiband response. Fractal levels are created by introducing concentric self-similar JC copies in the original unit cell. This modification results in new dipoles at the structure which allows for the appearance of new bands proportional to these diploles’ lengths, while maintaining total unit cell size. Three fractal levels of the JC FSS are studied in this paper, and third level presents five resonant frequencies which are f1=1.78 GHz, f2=6.42 GHz, f3=8.69 GHz, f4=10.94 GHz and f5=12.98 GHz. Simulation results for the insertion loss (S21), surface current distribution and measurement results are presented.


I. INTRODUCTION
Recently, interest in the potential application of fractal geometries has increased.Some fractal shapes are highly convoluted geometries, giving the possibility to embed resonant elements into small areas.In some applications, self-similarity [1,2] property of certain fractals can be exploited to create multi-resonant behavior [3].The self-similarity can be described as the replication of the geometry of the initial element with different scale in the same structure [4].This paper proposes the use of fractal characteristics to design a set of four orientation insensitive (OI) multi-band Frequency Selective Surfaces (FSSs).FSSs are bi-dimensional structures, composed by periodic arrays of metallic elements that are printed on one or more dielectric substrates [5].When an incident electromagnetic wave encounters a FSS, resonance effects can occur on the grid elements in a given frequency band, depending on the elements' geometry and periodicity, and the properties of the dielectric substrate [5].For some frequencies, the induced currents in the cells are constructive and all incident power is transmitted through the structure [6].

Multiband FSS with Fractal Characteristic
Based on Jerusalem Cross Geometry FSSs applications have also been presented in the fields of millimeter-wave quasi-optical filters and diplexers, dichroic surfaces for reflectors and large aperture antennas' subreflectors and absorbers [7][8][9][10].Fractal geometries have been extensively implemented in the design of multiband antennas and FSSs.
This paper investigates the behavior of a modification in the Jerusalem Cross FSS (JC-FSS) [11][12][13].The JC-FSS presents dual stop-band frequency response and orientation-insensitiveness (resonance occurs for both vertical and horizontal polarizations) due to its symmetrical geometry [6].
The first resonant frequency is mainly caused by the cross dipole with length l d , as well as the second resonant frequency is related to the perpendiculars dipoles with length l 0 .

A. Modified Jerusalem Cross
The proposed unit cells of the modified JC-FSS (MJC-FSS) are shown in Fig.This procedure gives the structure fractal characteristics because of its self-similarity.Other parameter that indicates the fractal characteristics is the fractal dimension [1,3].When the fractal dimension is non-integer, the geometry can be classified as a fractal [20].According to the box counting method [1,3], the fractal dimension for the third interaction of the MJC-FSS is non-integer and approximately 1.5, which indicates that the structure can be fractal.In the JC-FSS, the cross dipole is responsible for the first resonant frequency and the perpendicular dipoles for the second one; therefore, it is expected that the new dipoles result in the appearance of new resonant frequencies.This way, the first fractal level, shown in Fig. 2    The Table 1 summarizes the simulated and measured resonant frequencies.Because of coupling effects, the resonant frequency of a dipole can be shifted when a new dipole is inserted.However, on this design, these shifts were small.When new dipoles were inserted, the f 1 had a maximum shift of 2.5%, f 2 had a maximum shift of 4.7%, f 3 had a maximum shift of 4.3% and f 4 had a maximum shift of 7.6% considering the measured values.These small shifts indicate that the coupling between the dipoles is low; therefore, an independent control of frequency in each fractal level is possible.
Comparing the simulated and measured results at the third fractal level, there was a shift of 2.7% at the first resonant frequency, 0.8% at the second resonant frequency, 2.8% at the third resonant frequency, 3.4% at the fourth resonant frequency, 5.7% at the fifth resonant frequency.A good agreement is observed between measured and simulated results.The shift at the f 1 , f 4 and f 5 can be attributed to the small gain of the horn antennas used to measure this frequency bands and to standing wave effects.
Papers [21][22][23] also investigate fractal FSSs.In [21], the proposed fractal FSS provides only one resonant band.In [22,23], FSSs fractal based on Sierpinski and Cross dipole presented three resonant bands spaced by scalar factor of two, which is determined by the FSS geometry.The structure developed in this paper is able to achieve five or more bands which can be easily adjusted varying the dipoles length.
Table 1 Measured and simulated resonant frequency characteristics.Fig. 5 shows the measured results for the proposed FSSs considering incident angle of 0º, 15º, 30º and 45º for the four structures.One can observe that there is an small shift in the resonant frequencies when the incident angle varies from 0º to 45º.It can be observed more clearly in Fig. 6 which shows each resonant frequency as a function of the incident angle.

Fractal level
Comparing the incident angle of 45º and normal incidence at the third fractal level, there is a shift of 6.3% at the first resonant frequency, 7.1% at the second resonant frequency, 2.26% at the third resonant frequency, 0.1% at the fourth resonant frequency and 2.7% at the fifth resonant frequency.
As the frequency shift is small when the plane wave incident angle is varied, the structures have a good angular stability.Fig. 8 shows the current distribution for all the resonant frequencies of the fractal level 3 of MJC-FSS for vertical polarization.The regions with the darker colors indicate where there is a greater concentration of current.It is observed that in 1.85 GHz, the current induced in the central dipole is more intense, meaning that it is the main responsible structure for this resonant frequency (Fig. 8a).
The same analysis is done for the other frequencies as shown in Figure 8 The new dipoles insertions cause a frequency shift of less than 7.6% of its measured central frequency.Thus, the MJC-FSS fractal levels can be a potentially interesting option for applications that require a response in multiband frequency.

Fig. 1
Fig. 1 shows two unit cells of the JC-FSS.This geometry consists of a central cross-dipole with length l d and dipoles placed perpendicularly at the end of each dipole with length l 0 .The unit cells are separated by a distance g, and all dipoles have a width w.The unit cell is a patch element, thus the black region represents the metallic part of the structure.This structure presents a stop band response because the FSS contains patch elements.

Fig .1Geometry of
Fig .1Geometry of the Jerusalem Cross.

2 .
The Fig.2(a)shows the first fractal level of this modification.It consists in inserting a rescaled concentric JC-FSS inside of the original JC-FSS.This results in the appearance of dipoles with the same orientation of the original dipoles.These new dipoles have length l 2 , slightly smaller than l 1 , and they are separated by a distance d.For the other fractal levels, the same procedure is carried out.Fractal levels 2 and 3 are shown in Fig.2(b) and 2(c).
(a), is expected to present three resonant frequencies, the second fractal level, shown in Fig. 2 (b), should present four resonant frequencies and the third fractal level, shown in Fig. 2(c), should present five resonant frequencies.The traditional JC-FSS and the fractal levels of MJC-FSS studied here were designed according to the dimensions: l d = 20.5, l 0 = 16.1, l 1 = 11.2, l 2 = 8.96, l 3 = 7.16, w = 1, d = 1 and g = 1 mm.Each dipole resonates when its physical length is approximately half-wavelength; however, the dimensions were optimized using the parameter sweep function of the CST Microwave Studio.IV.RESULTS AND DISCUSSIONA.Insertion Loss (|S21|)This section presents the measured and simulated results for the proposed FSSs considering a normal incidence angle of a plane wave.In order to validate the simulations, a 9x9 array of the JC-FSS and of the three fractal levels of the MJC-FSS were fabricated as shown in Fig.3.The substrate used was FR-4 (h = 1 mm, εr = 4,4, tanδ = 0.02) with dimensions of 20 cm x 20 cm.

Fig. 3
Fig. 3 Photograph of the FSS prototypes: (a) JC-FSS, (b) fractal level 1, (c) fractal level 2 and (d) fractal level 3.The experimental results are obtained using an Agilent E5071C Vector Network Analyzer and a pair of SAS-571 double ridge guide horn antenna.The measurement setup includes a panel with a slot of 20cm x 20cm to hold the FSS, shown in Figure 4. Absorbers are used to prevent undesired reflection.The pair of antennas was used to measure over 1-14 GHz.

Fig. 5 (Fig. 5 (
Fig.5 (a) shows the simulated and measured results of S 21 for the JC-FSS for normal incident angle.As expected, two resonant frequencies appear as mentioned in previous section

Fig. 8
Fig. 8 Simulated current distribution for the five resonant frequencies of the MJC-FSS third fractal level