We present a metamaterial element designed as an efficient radiator for waveguide-fed metasurface antennas. The metamaterial element is an electrically-small, complimentary electric-LC (cELC) resonator designed to exhibit large radiated power while maintaining low ohmic losses. The shape of the element is tapered to simultaneously achieve broadband operation and suppression of cross polarization radiation. Full-wave numerical studies at the K-band are conducted to examine its performance when etched into a microstrip line. In this configuration, the element shows a radiation efficiency of 90.2% and a fractional bandwidth of 8.7%. To investigate the potential benefits of the proposed element in two-dimensional platforms, the radiative characteristics of the element are calculated when the element is embedded in a dielectric-filled parallel-plate waveguide. This efficient metamaterial element has potential application as a building block for metasurface devices used in imaging, sensing, wireless power transfer, and wireless communication systems.
© 2016 Optical Society of America
Metasurfaces have garnered much attention over the last decade for their ability to manipulate electromagnetic waveforms in unprecedented manners [1,2]. In addition to their ability to support unique electromagnetic responses, metasurfaces are planar and easy to fabricate, making them well-suited for applications over much of the electromagnetic spectrum. At microwave frequencies, waveguide-coupled metasurfaces are of interest since they are easy to integrate with existing technologies and offer compact form factors. Such metasurfaces have been used as apertures to control electromagnetic radiation, including formation of subwavelength focal spots; propagating or evanescent Bessel beams; steered directive beams; and frequency-diverse waveforms [3–11]. Such extreme control over radiation patterns can revolutionize a wide array of applications such as imaging, power harvesting, and satellite communication among others [5–13].
Regardless of applications, the performance of a metasurface heavily depends on its constituent building blocks. In [5–11,14] the rectangular complementary ELC (cELCs) was used as the metamaterial radiator. Rectangular cELCs, and their non-complementary counterparts , have been widely used in different metamaterial designs including microwave absorbing detectors, planar filters, and absorbers at THz frequencies [16–18]. This ubiquitous usage is due to their duality as the electric counterpart of the split-ring resonator (SRR) metamaterial element . Like the SRR, the resonance frequency and quality factor of the ELC can be shifted by modifying its geometrical properties. Complementary ELCs can be easily integrated into waveguides at microwave frequencies, controlling either the propagation properties of the guided modes [20,21], or forming radiating structures fed by the guided modes [5–11]. In addition, their response can be dynamically tuned by a variety of mechanisms—such as diodes or liquid crystal—granting dynamic beam-forming or wave front shaping to the composite metasurface.
While rectangular cELCs have shown great promise in various applications, their performance as radiating elements can suffer from inherent ohmic and/or dielectric losses. For electrically-large metasurface antennas, low radiated power from each element is not necessarily a disadvantage since power radiated from the overall electrically-large aperture is of primary concern; however, it is always desirable to minimize unwanted power dissipation. As the operating frequency increases, all losses become increasingly problematic. Furthermore, suppression of the unwanted cross polarization component can become a critical design criterion in 2D implementations [6,7].
In this paper, we propose an alternative cELC geometry that considerably improves radiation efficiency. Identifying the mechanisms responsible for radiation and losses, we tailor the shape of the element to boost radiated power while keeping the ohmic losses low. The design process and physics behind the element's operation are confirmed with full-wave simulations. We discuss how the unique features of this metamaterial element make it well-suited to waveguide-fed metasurfaces, especially in 2D geometries.
2. Proposed metamaterial element
We begin by identifying the radiation mechanism of a cELC metamaterial element embedded in a waveguide. In more traditional waveguide-fed radiative platforms, energy leaks through irises or slots. Such openings can be modeled effectively as magnetic currents (representing the tangential components of the electric field) [22,23]. For an iris to radiate ample power, the tangential electric field formed on the opening should be large since the radiated power is proportional to the square of the current magnitude. In the case of an electrically-small radiator, the use of a resonator provides a straightforward approach to increase the magnetic current and, consequently, the radiated power. This is done by introducing inductive and capacitive elements into the design. Depending on the application, many types of LC resonators can be considered. In practice, the LC resonator should be chosen by taking into account ohmic and dielectric losses in the element. To maximize radiated power, it is also important to ensure that all the resonant field components interfere constructively with each other. By taking all of these factors into consideration in the element design, we propose a new metamaterial element aimed at high radiation power while minimizing losses.
We first consider a rectangular cELC which is commonly used in metasurface designs. This element, embedded in a microstrip line, is shown in Fig. 1(a) and is analyzed here using a full-wave electromagnetic solver, CST Microwave Studio. The substrate is 1.52-mm-thick Rogers 4003 ( = 3.38, = 0.0027). The resonance frequency is chosen to be 22 GHz, the center frequency of the K-band. The width of the microstrip line is chosen to have a characteristic impedance of 50 Ω at the operating frequency. The element couples to the fundamental mode of the guided wave and radiates power into free space. The geometry of the proposed element, with key dimensions labeled, is shown in Fig. 1(d). The overall size of the element was kept small compared with the guide wavelength (</3.0) to ensure that the element can operate as a short dipole (such an element can be easily integrated into an aperture antenna). The current distribution on the element, as well as the tangential component of the electric fields formed on the element opening, are depicted in Figs. 1(b) and 1(c). As can be seen, strong electric fields are formed in the gaps (g1 and g3) of the element, which are responsible for radiating power. This resonance behavior occurs at the cost of the large electric currents formed on the central region (shown in Fig. 1 (c)). Such a high concentration of electric current on a narrow metallic trace contributes significantly to the ohmic losses. Furthermore, a closer look at the element's electric field distribution also reveals that the electric field formed in gaps g1 opposes the electric field formed on the edges, g3. In other words, they cancel each other’s radiation—a drawback that limits overall radiated power.
Having identified the primary mechanisms for radiation and losses in the rectangular cELC, we now propose the rounded cELC shown in Fig. 1(d). The uniform, circular gaps at either end act as capacitance while the narrowed section in the middle acts as inductance, together forming a series LC resonator. On resonance, the reactance of the element becomes zero, resulting in strong current flow along the structure, as can be seen in Fig. 1(f). To lower ohmic loss, the width of the inductive element is kept wide. The dielectric losses are reduced by curving the shape inwards to reduce capacitance (and thus the field concentration) between the element and the surrounding conductor (identified by d in Fig. 1(d)). This curvature is also intended to suppress the generation of the cross polarization component, which becomes more critical in two dimensional metasurfaces. Figure 1(e) also shows the distribution of the tangential component of the electric field. As can be seen, there is a high concentration of the electric field in the capacitive gaps at either end of the element (identified by g in Fig. 1 (d)), contributing dominantly to the radiation. It is worth emphasizing that the electric field components are parallel to each other, constructively interfering with each other in the far-field, in contrast to the rectangular cELC design.
The calculated radiated power, losses, and full-width at half-maximum (FWHM) of the radiated power curves for both elements are listed in Table 1. As expected, the rounded cELC produces higher radiated power (158 mW) compared to the rectangular cELC (130 mW), showing an enhancement of 21% (the input power in both cases is 500 mW). It is worth noting that electrical area of aperture of the round cELC is 64% of that of the rectangular cELC. More importantly, the increased radiated power is obtained while the ohmic and dielectric losses are both lower. For example, the ohmic losses for the curved cELC are more than twice lower, highlighting the importance of using a wide central conductor. All losses—from the entire structure, including the transmission line—are taken into account by the full-wave electromagnetic solver. In order to isolate the power dissipated by the metamaterial element as listed in Table 1, the losses computed without the metamaterial element are subtracted from the losses when the metamaterial element is included. Overall, the radiation efficiency of the curved cELC design is 90% compared to 77% for the rectangular cELC. The radiation efficiency in the table is calculated using the ratio of the radiated power and the accepted power, which can be expressed as , where and represent the radiated power and dissipated power, respectively .
It should be emphasized that neither designs have been optimized, except for the resonance frequency. While it may be possible to optimize each design to achieve a desired performance, the optimization process may be complicated or diverging, given the large number of geometrical parameters that govern each design's performance. Instead, in this paper we focused on identifying inherent loss and radiation mechanisms of two types of cELC design, and thereby revealed the advantages offered by the round cELC for efficiency-driven applications. We believe the identified mechanisms are not only useful to enhance the radiated power, but also clarify any optimization process by providing intuitive grounds. It is also worth noting that whenever these metamaterial elements are used as the building block of metasurfaces mutual coupling between elements should be taken into account. To do this, discrete dipole approximation methods have recently gained traction. These methods can accurately model the interactions between metamaterial elements and predict the overall performance [13,24–27]. Such an analysis can be applied to a metasurface composed of the proposed metamaterial element, a task which is beyond the scope of this paper.
3. Performance in two-dimensional configuration
In this section, we investigate the performance of the proposed element in two dimensional radiative platforms, desirable in various applications [5–14,16]. The element is etched in the top conductor of a dielectric-filled parallel plate waveguide, as shown in Fig. 2(a). The same substrate thickness and dielectric constant was used as in Section II. All side boundaries of the waveguide were terminated in “open boundaries” to absorb the guided wave. A coaxial connector is used to excite the waveguide. The inner conductor of the coaxial cable is connected to the top plate and the outer conductor is connected to the bottom plate to excite the parallel plate waveguide. An annular gap (diameter of 8 mm) is etched around the center conductor of the coaxial feed to improve the impedance match. Due to the annular gap, the is kept below ~10 dB over the entire range of K-band. The metamaterial element is placed 30 mm away from the coaxial feed.
In contrast to the 1D waveguide examined in the previous section, where a quasi-TEM with phase-planes perpendicular to the element was exciting the element, the coaxial connector generates a TEM cylindrical wave. This change has two implications for the designed elements: First, the effective dielectric constant in the parallel plate waveguide is different from the one in microstrip line. As a result, the resonance frequencies of the elements designed in 1D are slightly different in 2D (this slight shift is seen in Table 1). The second consequence is that the cylindrical wave may be incident on the element from different angles. In reality, both cELC designs consist of two orthogonal LC resonators with different resonant frequencies. As a result, the metamaterial element response is dependent on the incidence angle of the excitation wave.
To better contrast the curved and rectilinear cELC, both elements have been simulated as shown in Fig. 2(a). Figure 2(b) shows the surface current distribution along the curved element at the resonant frequency. Unlike the surface current distribution in the one dimensional case in the previous section, strong concentration is observed in the middle of the inductive element as well as near the edges. Therefore, the width of the inductive element becomes more crucial with respect to reducing ohmic loss. The radiated power is 4.87 mW and the fractional bandwidth is calculated by measuring the FWHM of the radiated power—it is found to be 7.14%. The antenna parameters in this case are summarized in Table 1. For comparison, the same parameters for the rectangular cELC used in the previous section are also presented. While the losses are similar in the two elements, the curved cELC radiates almost 75% more power, indicating much higher radiation efficiency.
In single-polarized metasurface radiating platforms [6,7], the radiated power in the cross polarization is unwanted and contributes to losses. As mentioned earlier, the cylindrical wave may excite the cross-polarized LC resonator in both elements. However, the inwardly curved shape of the inductive element in the proposed design can provide a means to suppress the radiation of the component. It reduces capacitance in the cross-direction to make the resonant frequency substantially different from the main polarization, effectively suppressing the cross polarization radiation. In this way, the element not only reduces the resulting dielectric loss, but also prevents radiation of the cross polarization component over the frequency band of operation. To confirm the suppression, the dependence of the radiated power on the different angles of incidence is calculated and plotted in Fig. 2(c). As shown, the rounded element shows high suppression in the radiated power over the entire K-band and the ratio of power at resonant frequency is measured to be ~49.7(~17.0 dB). In contrast, the rectangular cELC has high cross polarization radiation in the given setup (~4.56 dB), as can be seen in Fig. 2(c). This suppression of cross polarization component is especially crucial in computational imaging and wireless communication systems. In both cases, unwanted radiation of such component leads to decrease in the signal-to-noise ratio (SNR) as it can be regarded as loss.
In this paper, we presented a rounded metamaterial element design aimed at low-loss, high radiation power, and low cross polarization radiation suitable for 1D and 2D waveguide-fed metasurfaces. For the design of the element, the primary mechanisms of radiation and power dissipation were identified. Based on this analysis, simple design steps were introduced to enhance the desired performance. The efficient performance was demonstrated through full-wave simulations in both 1D and 2D metasurfaces. Especially, it was shown that the proposed design can significantly increase the radiated power, while keeping losses minimal. The suppression of unwanted cross-polarized radiation was also demonstrated in 2D configuration. Given these advantages, this elements poses as a promising building block for metasurface structures for computational microwave imaging, wireless communication, SAR antenna platforms, and many other exciting applications.
Air Force Office of Scientific Research (AFOSR) (FA9550-12-1-0491).
Insang Yoo also acknowledges scholarship support from the Fulbright program.
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