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Abstract
The holographic technique is a promising way to manipulate light distribution and wave-front in the optical regime. In recent years, many researchers have extended this concept to microwave regime to manipulate phase, amplitude, and polarization of waves in a convenient way revealing diverse intriguing applications. Unlike the previous studies with optimization-based schemes, in this paper, we propose a simple route to design dual frequency dual-polarization holographic metasurfaces with negligible interference between the operating (lower and upper) frequencies. For this purpose, a Jerusalem-shape unit-cell is used to realize two distinct impedance distributions which yield two decoupled field profiles over the aperture of the metasurface at each frequency band. Consequently, the proposed metasurface radiator can operate in two frequency bands, independently. Each set of horizontal (vertical) cross-bars of the Jerusalem-shape unit-cell is illuminated by a vertical (horizontal) feeding network from one side of the metasurface. Side feeding has a null-free advantage, this undesired null emerges in central feeding metasurfaces and leads to an undesirable rabbit’s ears phenomenon. As the proof-of-concept, a prototype of the metasurface radiator for operating at 11.5 GHz and 14 GHz is fabricated and measured. The experimental results depict a good agreement with the full-wave simulations.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces are two-dimensional (2D) forms of metamaterials having all of the advantages of metamaterials. Also, by reducing the size, metasurfaces can be implemented in low-cost and low-profile manners. As a result, they are used in integrated structures while providing a wide range of applications in communication systems [1–11]. Besides, a challenging point for obtaining arbitrary radiation is the complexity of the design process . A promising approach to solve this problem is the Holography concept that originates from the optical frequency range [12]. In this theory, the information obtained from the interference of the reference wave and object wave may be used to reconstruct the desired object wave. In contrast with the conventional designs ([13,14]) of multi-frequency metasurfaces (any type, leaky or reflective metastructure), in Holographic metasurfaces, we do not use the multi-resonance method to tailor the phase matching for different frequencies. In holographic structure, the textures are not operating in resonance range but instead behave as the regular surface impedance. By reducing the size of pixels and employment of sub-wavelength pixels we enhance the resolution of the sampling process according to the Nyquist theorem and make a continuous impedance surface compared with the conventional structure. Besides, conventional Leaky wave metasurfaces suffer broadside stop-band that is omitted in Holographic metasurfaces. This concept has been adopted in a variety of applications in recent years at the microwave regime, by using isotropic unit-cells researchers can implement a radiator with a linear polarization. Also, the anisotropic unit-cell can be employed in order to create a circular polarization pattern [15,16]. This phenomenon has also been used for radar cross section reduction [17], wide-band antennas [18,19], implementation of multi-beam patterns [20,21] and beam shaping purposes [22,23] in both leaky-type [24,25] and reflector based metasurfaces [26,27]. Moreover, multi-band radiation structures and structures with polarization diversity ([28], [29]) are of great interest due to their wide range of applications such as satellite systems and remote sensing. In this Case, the metasurface can generate radiation beam for each band with individual specifications such as polarization. The dual-frequency application was already implemented by many groups in a variety of metasurface types. In the scattering-type metasurfaces (specially reflective metasurfaces illuminated by a horn feed antenna), for instance [30], the dual-band operation of the metasurfaces was realized, where a specific linear polarization can be observed at each band. However, due to their planar excitation, the leaky-type metasurfaces have many significant advantages compared with the reflective metasurfaces, such as convenient assembly and the possibility of integration with the other communication systems. Besides, the reflective meta-structures suffer from some destructive effects. To name a few, the shadow effect pertaining to the feeding assemblies and the required phase compensation on the aperture are examples of these degrading effects. Moreover, the leaky-wave (LW) metasurfaces are good candidates for realization of the dual-frequency applications. In [31], the authors utilized the half-mode microstrip substrate integrated waveguide (HMSIW) in a conventional method to design the a LW antenna. The major weakness of this approach is the fact that the main beam direction of their proposed antenna is not fixed when the operating frequency is swept between the two avaiable bands. In other words, their proposed leaky-wave antenna has an unwanted beam scanning property. Also, the employed HMSIW method leads to fan-shape far-field radiation pattern (has a wide beamwidth in one direction and narrow in orthogonal direction) and therefore yields low gain for the main beam. Recently, multi-wavelength holographic metasurfaces which can radiate in two distinct frequency bands have been studied [32,33]. In these studies, the radiating power has been guided to the azimuthal and elevational directions, very accurately. Consequently, they acquired a very high-gain pencil beam (in contrast with [31]), which had a narrow beamwidth in two orthogonal directions. Besides, as a solution for the prominent problem in the previous conventional methods for designing LW dual-frequency antennas, the beams with identical tilt-angles can be obtained in two distinct frequencies via the holographic method. Since the surface impedance modulation at both frequency bands was carried out through a single geometrical parameter, unwanted interference terms appeared in the holography formula, resulting in unintended radiation in the far field and degrading the side lobe level (SLL) of the metasurface radiator. Indeed, when only one physical dimension of the unit-cell varies to simultaneously satisfy the requirement of the impedance distribution in the same aperture and for both frequencies, just one holographic equation was employed which contains a superposition phenomenon. This equation consists of a few terms, some of these terms, causes the desired far-field pattern in one of the frequency bands. Consequently, when one excites the hologram interference at the first frequency, these terms will represent the response to the desired object wave at the first frequency. However, at the same time, the other terms also inevitably contribute to the radiation pattern as degrading factors and will disturb the performance of the metasurface in the far-field domain. So, these interference terms can be considered as unintended radiation in the far-field, which degrades the SLL. This drawback will be presented in more details in section 3. Due to lack of the analytical modeling techniques , this shortcoming was resolved 31,32 to some extent through applying some brute-force optimizations on the excitation positions of the two reference waves, by repeating the full-wave simulation for several times to obtain the lowest possible SLL. As known, their full structure consists of many thousand sub-wavelength pixels so that each run of the full-wave simulation may take several days with a normal PC (Core i7 CPU and 32GB RAM). More particularly, performing the iterative optimization procedure in the full-wave simulator takes a few weeks to acquire the best level of the sidelobe level. Moreover, when the separation between upper and downer frequencies becomes very large, it is obvious that, the impedance distribution cannot be met by only one set of impedance unit-cells employed in [32].
In this paper, we propose a straightforward route to design a dual-frequency dual-polarized impedance metasurface without resorting to any optimization-based steps. To aim this, the best solution is to use the dual-band unit-cells with uncorrelated impedance values in both bands. In doing so, the use of cross dipole or well-known Jerusalem configuration is the best choice, so that each arm of the dipole is dedicated for realizing the impedance value in the corresponding band. We employ a Jerusalem-cross unit-cell that includes two separate arms and can modulate the surface impedance distribution at each frequency separately (Fig. 1). It is obvious that by using this strategy a single holographic formula for each band is elaborately utilized and the superposition concept has not been employed in contrast with the previous works. Thus, we prevented the interference terms and as a result do not need any time consuming optimization process in the design process. The leaky-type meta-structures exhibit an frequency scanning behavior. Thus, using passive metasurfaces, it is difficult to realize multi-frequency with a fixed beam radiation due to its intrinsicly strong dispersion. However, we proposed a leaky-type metastructure with fix-broadside radiation at two separate frequencies. (braodside radiation was in stop-band in conventional LW antennas). Also, owing to the proposed pixel configuration, we have attained linearly-polarized beams with the orthogonal polarizations in the lower and upper bands. In contrast, [32,33] acquired the same polarization for both frequency bands. Finally, our proposed metasurface has the potential to be "Just dual-frequency" by mechanically 90$^{\circ }$ rotating in the higher band or to be "Just dual-polarization" by designing the metasurface and feeding networks in a single frequency. A prototype of the metasurface radiator for operating at 11.5 GHz and 14 GHz is fabricated and measured. The frequency and polarization multiplexing performances of the designed metasurface have been verified through both numerical and experimental results.
Fig. 1. General schematic of the proposed holographic metasurface. In each frequency a perfect flat wave-front as a reference wave excites the metasurface from one sides and then one sets of the modulated cross-bars radiate the power in the form of spatial wave for forming the desired object wave with specific polarization.
2. Principles and design process
2.1 Holographic theory and leaky-wave concepts
Many studies synthesized an arbitrary far-field pattern by using a metasurface. The majority of these approaches exploit Fast Fourier Transform (FFT) to manipulate the aperture field distribution to reach the desired pattern. Recently, a novel technique has been employed to simplify the synthesis of far-field patterns based on an optical principle named holography. Holography uses an interferogram for interaction between a reference incident wave and the object radiated wave in microwave region to record and control the electromagnetic features like shape, polarization, frequency and number of main beams. This technique utilizes the aperture field estimation in the general form for the synthesis of a metasurface with anisotropic pixels obeying the following formula.
Fig. 2. Concepts of leaky-type metasurface (a) Brillouin diagram and its specific regions,(b) Definition of rabbits ears phenomenon.
In addition, the far-field pattern can be obtained by taking the FFT from the aperture field as [35]
2.2 Unit-cell design
In order to have proper control over the local surface impedance, we need to place periodic patches on the grounded slabs (for TM case). The patch geometry and unit-cell dimensions should be chosen suitably to provide the required surface impedance range. In general, the dimensions of a unit-cell are usually chosen between $\lambda$/10 and $\lambda$/5 . In this situation, these pixels can effectively model the impedance surface. If the dimensions are larger than $\lambda$/5 (especially, when they approach $\lambda$/2), these patches act as local resonators. It is worth mentioning that for the case of half-wavelength unit-cell, the first-order dipolar resonance occurs, where patches radiate effectively. The dimensions of the lattice are selected as $4 \times 4 mm^2$, which is equal to $\lambda$/(6.5) at the lower frequency (11.5 GHz) and $\lambda$/(5.4) at the upper frequency (14 GHz). Note that, if the unit-cell becomes further miniaturized, its surface impedance range decreases and therefore the required range cannot be covered. Clearly, when the separation between the upper and lower frequencies becomes very large, the impedance distribution cannot be met by only one set of impedance unit-cells. In this state, the best solution is to use the dual-band unit-cells with uncorrelated impedance values in both bands. In doing so, the use of cross dipole or Jerusalem configuration is the best choice, so that each arm of the dipole is dedicated for realizing the impedance value in the corresponding band. Since there are many design parameters that potentially affect the admittance quantity, we can realize the required impedance or admittance value for each cell by only changing the length of the arms (vertical or horizontal) at each frequency band, while the other design parameters remain unchanged. Therefore, we obtain a set of single-layered Jerusalem cross-based artificial magnetic conductor (JC-AMC)(Figs. 3(a), 3(b)), in which the vertical and horizontal arms are modulated, so that they satisfy the impedance requirements of the upper and lower bands, respectively.
Fig. 3. Proposed JC-AMC pixel (a) Details of the pixel in 3D view,(b) Its dimensions (Dimensions are $p=4mm$, $d=1.44mm$, $W_{ind}=0.2mm$, $W_{cap}=0.2mm$. Also the substrate is Rogers 4003C with the 60mil thickness). (c) and (d) Show surface impedance distribution by sweeping length $L_1$ and $L_2$ of JC-AMC in lower and upper band, respectively. (e) Depicts the density of surface current distribution.
We should examine that whether the change in the parameters of one arm (corresponding to the lower or upper frequency band) affects the surface impedance at the other frequency band. For obtaining the surface impedance of an arbitrary pixel an approach that introduced in [16] was employed. Based on [16], in the first step, an incident incident plane wave illuminates the pixel and a full-wave software calculates the input impedance. Afterwards, set of relations are used to extract the surface impedance from the input impedance ([16]). Fig. 3(c) illustrates the impedance range for each particular length of horizontal arm ($L_1$). According to these figures by sweeping the length of the vertical arm ($L_2$) at the lower band ($f = 11.5GHz$), the surface impedance relatively remains unchanged for the fixed length of $L_1$. Same explanation can be applied in Fig. 3(d) for the upper band. Thus, the horizontal arm was used to modulate surface in the lower band ($f=11.5GHz$) and the vertical arm to modulate surface in the upper band ($f=14GHz$), independently. The achieved range of the surface impedance for unit-cell with the dimension shown in Fig. 3(b) is $249\Omega$ to $133\Omega$ for the lower band and $394\Omega$ to $198\Omega$ for the upper band.
Also, for proving the decoupling characteristic of the JC-AMC pixels, 4 adjacent unit-cells are excited by an electric field in the vertical-direction. (Fig. 3(e)) depicts the surface current density distribution on these unit-cells. According to the nature of the unit-cell (grounded dielectric slab), the dominant propagation mode of this structure is TM mode. Consequently, horizontal-directed magnetic field is existed. This magnetic field induces a surface current density in the vertical direction owing to the Maxwell equation($\nabla \times \textrm {H} = \textrm {J}$) (parallel direction with electric field). As Fig. 3(e) depicts, the electric field makes a close path through the upper small strip in the top of the vertical-directed arm, the joint of the two arms in the middle of unit-cell and the vertical-directed arm. Same circumstance occurs in the lower half of the unit-cell. It should be noted that two small strips at the end of the horizontal-directed arm also have the same direction as the electric field but the electric field that induces in these strips closes its path by the same small patches in the above and below unit- cells. Besides, the distance between the same small strips located at the end of the horizontal-directed arms in two adjacent unit-cells is very long. Therefore, the surface current is not induced in these strips. Thus, the vertical electric field induces the current just on the vertical cross-bars. in the same manner, if a horizontal electric field is applied to the structure, the current is induced just on the horizontal cross-bar. Consequently, the Jerusalem-cross unit-cell has decoupled nature for each of its arms.
3. Discussion and simulations
In this section, a dual-frequency dual-polarization metasurface is introduced. A recent study [32] was implemented a dual-frequency metasurface by utilizing square unit-cells for modulating the surface impedance of metasurface in two distinct frequency bands by varying the size of the square patch (single parameter). Thus, authors shared the surface impedance range for both frequency bands and used superposition concept in Eq. (2) to achieve the following statement.
Let us consider a reference electric wave in the form of a flat wave-front that propagates along the metasurface toward the $\hat {x}$ direction ( ($\psi _{ref}@f_1=e^{-jk_t x}$)) for the lower frequency band. Furthermore, assume another flat wave-front that propagates along the metasurface in $\hat {y}$ direction (($\psi _{ref}@f_2=e^{-jk_t y}$)) for the upper frequency band. Meanwhile, assume that the desired far-field radiation is describe in the form $\psi _{obj}@f_1,f_2=e^{-jk_0(xcos(\phi _0)sin(\theta _0)+ysin(\phi _0)sin(\theta _0))}$.) in which $\theta _0$=0 (broadside direction). In order to span all the realizable admittance values by the hologram, we select $X = (max X_s + min X_s) /2$ and $M = (max X_s - min X_s) /2$. By referring to these ranges, we choose the M and X parameters for the lower frequency band ($X_{low}=191\Omega$ , $M_{low}=0.30$) and for the upper frequency band ($X_{up}=296\Omega$ , $M_{up}=0.33$), respectively. By substituting all aforementioned parameters to Eq. (10) and Eq. (11) the surface impedance distribution is calculated in both frequency bands. The contours of the required impedance distributions are plotted in Figs. 4(a), 4(b). Moreover, by using the FFT relations introduced in Section.(2), the far-field pattern at each frequency bands can be computed. the corresponding results are plotted in Figs. 4(b), 4(d).
Fig. 4. (a) and (c) show the surface impedance distribution needed for broadside direction in lower and upper band respectively, Also (b) and (d) depict predicted far-field pattern for the lower and upper band respectively.
After mapping this surface impedance distribution to the length of orthogonal arms by using the curves in Figs. 3(c), 3(d), the full structure of the metasurface can be constructed. The structure and the 3-dimensional simulation radiation pattern are illustrated in Figs. 5(a), 5(b). Dimensions of the metasurface radiator are $14:8\textrm {cm} \times 14:8\textrm {cm}$ and consist of 1369 pixels. Also, the distribution of the unit-cells is shown in the inset of Fig. 5(a). By referring to this figure, in the lower band, the wave illuminates the holographic metasurface from left and the metasurface leaks the surface wave in the form of spatial wave along the broadside direction. At the other band, the feeding network excites the structure from the bottom and this leads to the same radiation in the broadside direction. The Cartesian far-field patterns are sketched in Figs. 5(c), 5(d) for both lower and upper bands. It is obvious that the main lobe of the pattern is oriented along the broadside direction at $\theta _0$=0. In addition, the SLL is low enough about -13.8dB and -12.1dB for the lower and upper band, respectively which are better than the result presented in [32] where after a time-consuming optimization process for minimizing the SLL, the value of -10dB was obtained. However, by the proposed method, a lower SLL level without accomplishing any optimization-based steps is obtained. The lower SLL is due to the issue that the proposed pixel separates the design process for two band. In fact, in this approach, the coupling is eliminated between the two bands. The beam-width of the main lobe for the lower and upper band is about 7.8 and 9.4 degrees, respectively, which confirms that the emitting beams are very high-quality pencil beams. In Table 1 the performance of the proposed leaky-type hologram is compared with other structure in the literature. All the works realized a dual-frequency band metasurface, however, some of works do not have the dual-polarization characteristic like [32,33]. Besides [31] implemented a low-gain antenna with fan-shape beam. This beam scan in each of bands which is undesired in dual-frequency application. [30] used reflect-array method for designing his hologram which has integration problem with other planar communication system referred to employing the unplanar horn feed and also has other disadvantages like shadow effect of horn feed and required phase compensation on the horn aperture as mentioned in introduction.
Fig. 5. (a) and (b) depict the full structure configuration, excitation direction and the 3D far-field pattern for lower and upper band, respectively. (c) and (d) show Cartesian normalized pattern in lower and upper bands respectively.
Table 1. Performance comparison between the proposed metasurfce with same works
4. Implementation and fabrication results
4.1 Feeding network
4.1.1 Power splitter
The proposed structure requires two orthogonal feeding systems that illuminate our structure from the side at each frequency band and also provide a perfect flat wave-front to excite the holographic metasurface as the reference wave in the holography formula.
A promising solution for these requirements is to use a power splitter structure for feeding network and attach this power splitter to the arrays of surface wave launchers which provide flat wave-front in wide area. One of the best technologies for this application is SIW (Substrate Integrated Waveguide). This technology acts like an ideal waveguide, avoiding the power leakage, and providing a confined wave on the surface while benefiting from a simple implementation process. Therefore, based on [37,38], we design an 8-way power splitter network by means of SIW technology. Fig. 6(a) illustrates the 8-way SIW power splitter and for which the dimensions were obtained by using a comprehensive parameter study for each band. Besides, the diameter of vias and the space between them determine so as satisfy the SIW limitations. The inner vias were adjusted to have good matching condition and minimize the power reflected to the input port of the structure. The corresponding scattering parameters are shown in Figs. 6(b), 6(c). As can be noticed for the the designed frequencies, i.e., $f_1 = 11.5GHz$ and $f_2 = 14GHz$, the scattering parameters show promising results for both reflection and transition parameters in each bands. The return loss level of $S_{11}$ is low that represents the small amount of the power reflected to the input port( $S_{11} < -10dB$). Also, the transmission coefficients show that power received by each output ports is near the ideal value(-9 dB for 8 ways power splitter). Overall the power is guided to the output ports by minimum reflection and spatial radiation. In addition, the same power reaches each output port due to the symmetric nature of the structure.
Fig. 6. (a) SIW power splitter in the feeding network configuration and its dimensions($L_1=16mm$, $L_2=6.89mm$, $W_1=W_2=W_3=W_4=W_5=W_6=W_7=9mm$, $W_8=6.38mm$, $W_9=4.93mm$, $W_{10}=5.26mm$, $W_{11}=36mm$, $W_{12}=18mm$ ) for the lower band. All dimensions are same for upper band except $W_8=3.62mm$, $W_9=2.60mm$, $W_{10}=2.69mm$. Also, scattering parameters results of the power splitter in (b) lower band,(c) upper band, respectively.
4.1.2 SIW horn launcher
At the end of each output ports of the power splitter, we need surface wave launchers to excite the surface wave on the dielectric slab and provide a flat wave-front for the metasurface. [39] was proposed an SIW horn launcher and connect this launcher to the microstrip line by an SIW to microstrip transition and feed this horn by a microstrip line. Here we omitted this transition network and connect the horn to the SIW divider directly (Fig. 7(a)). An SIW horn launcher should expose a proper matching condition and reflect a very small amount of input power (<-10dB). As a result, most of the power should transmit to the the horn aperture. To confirm these conditions two horn launchers should be placed in a back-to-back configuration. The inset of Fig. 7(b) depicts a structure that consists of back-to-back horns and its dimensions. Also, this figure exhibits the related scattering parameters of this structure. It is obvious that the launcher has an ideal insertion loss ($S_{21}$ is about 0dB). Furthermore, the reflection coefficient $S_{11}$ is less than -10dB in the entire frequency band. Finally, Figs. 7(c), 7(d) present the electric field distribution inside and in front of the SIW horn arrays at each frequencies. According to these figures, a flat wave-front electric field which is needed to excite our metasurface as a reference wave is successfully provided by using the SIW horn arrays in both frequencies.
Fig. 7. (a) Proposed SIW horn structure in 3D perspective, (b) scattering parameters result. The inset picture shows the back-to-back configuration for the calculation of scattering parameters ($W_1=9mm$ and $W_2=17mm$). (c) and (d ) show the electric field distribution inside and in front of the horn arrays which is provided for exciting the metasurface.
4.2 Fabrication results
For the design of the holographic antenna, it is very hard to realize the radiation at the same angle under dual or multi-wavelength only using passive structures due to the intrinsical performance of the frequency scanning in leaky wave antenna [32]. In this article, our proposed method can realize broadside radiation at two different frequencies using isotropic passive structures. In the last step, we fabricate a sample of the proposed metasurface radiator and validate our simulation result with some measurements. The prototype is located at the distance longer than the Fraunhofer distance($(2D^2)/\lambda$) from reference horn antennas that covering X and Ku frequency bands, which utilized to measure the far-field radiation patterns at the both operating bands. As shown in Fig. 8(a). Thus the far-field approximation is satisfied and the prototype was tested in $f_1=11.5 GHz$ and $f_2=14 GHz$. dimension of the whole structure is about $23\textrm {cm} \times 23\textrm {cm}$. Co component of the far-field pattern is sketched in the horizontal ($\phi =0$) and vertical ($\phi =90$) planes for the lower and upper frequency, respectively compared with the simulation results in polar coordination Figs. 8(b), 8(c). According to these figures, the simulation result and measurement pattern are in a good agreement. In both states, the SLL is lower than -11dB for the lower band and -12.5dB for the upper band. Also, the main beam direction for both frequency bands (both simulation and measurement) is very close to the broadside direction. . The small deviation may be caused by the fabrication variations of the sample and the measurement noise in the anechoic chamber.
Fig. 8. Psrototype located in anechoic chamber. Also, the insets show the zoom picture of components of the structure. (b) and (c) clarify the normalized measurement far-field pattern and compare it with the simulation result in lower and upper band, respectively, in the polar coordination.
5. Conclusion
In this paper, a novel dual-band dual-orthogonal polarization leaky-type holographic metasurface was presented. In this work, we utilized a dual-band suited pixel i.e. JC-AMC to realize a dual-frequency metasurface without any disturbing coupling between its frequency bands. This feature was obtained by two orthogonal arms in this pixel that allows us to modulate each arm at its corresponding frequency separately by means of the well-known holography theory. For feeding the engineered metasurface, two orthogonal feeding systems were utilized to illuminate each set of cross bars from the metasurface sides. Side feeding omit the destructive "rabbit ears" phenomenon that happening in the center feed leaky-type structures. Flat wave-front reference wave was obtained by these feeding networks. By this approach, in contrast to the previous works, we achieve a free coupling structure, which enhances the metasurface performance and reduced some negative factors such as the SLL and coupling between the lower and upper frequency bands. According to the leaky wave phenomenon, this surface wave was converted into the spatial wave if the structure was designed to operate in the fast-wave region due to the Brillouin diagram. through a proper distribution of subwavelength pixels, we could synthesis our desired far-field pattern in arbitrary direction and shape. We simulated our structure with a full-wave commercial software and confirmed non-decoupling behaviour of the proposed structure. Eventually,a sample prototype was fabricated and tested. A good agreement between the simulation and fabrication results were acquired. This work can be easily extended to the millimeter wave range or even higher bands. Multi-band radiation structures are of interest due to their wide range of applications such as satellite systems, remote sensing, multi-band communication and radar systems.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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