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Abstract
Electromagnetic (EM) polarization control is a key issue in various studies on communication and imaging systems. Two-dimensional metasurfaces have been employed to realize polarization conversion based on chiral, anisotropic structures. Herein, we employ Huygens’ metasurfaces that utilize both electric and magnetic resonances when interacting with EM waves to realize polarization manipulation. Polarization conversion is achieved by introducing direct coupling between the equivalent electric and magnetic sources. A polarization conversion splitter as well as reflective and transmissive polarization convertors are designed and verified by simulations and experiments. The proposed polarization manipulation devices possess compact dimensions in the deep sub-wavelength regime and maintain good angular performance for oblique incidences up to 60°.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Huygens’ principle presents the relation between a radiating electromagnetic (EM) field and its electric or magnetic sources. Qualitatively, it states that each point on a wavefront acts as a secondary source for the outgoing waves. Love’s work in 1901 developed a rigorous form of Huygens’ principle by specifying the secondary sources in terms of well-defined fictitious electric and magnetic currents [1]. Later, Carson et al. extended Love’ s equivalence principle to allow for arbitrary field distributions on either side of a surface [2]. Recently, Huygens’ principle has been applied in several areas involving antennas [3–6], high efficiency metamaterials and metasurfaces [7–12], as well as EM wave imaging [13,14].
Polarization manipulation of EM waves is a key issue in EM wave studies. Among the various devices used for manipulation, a polarization convertor that rotates the EM wave’s polarization state to its cross-polarized state is widely used in microwave and optical research. It is applied in various polarization manipulating devices [15,16] as well as in circularly polarized antennas [17,18] or for radar cross section (RCS) reduction [19], among others. Further, it can also be used to construct complex EM waves using field transformation approaches [20,21].
The metamaterial concept and its two-dimensional case, the metasurface, have greatly facilitated research on polarization manipulation. In the present scenario, most reported works realizing polarization conversion are based on mechanisms employing anisotropic or chiral structures. For example, utilizing anisotropic metamaterials and through proper design of the phase responses along two mutually perpendicular directions, the polarization state of an incident wave can be rotated by 90° [22–25]. Several ultra-wideband and high-efficiency polarization convertors have been designed on the basis of this concept [24,25]. By employing the Jones matrix method [26] for theoretical analysis, the chiral structures can realize a polarization convertor [27–30]. However, in these designs the dimensions of the elements are usually not small compared to the operation wavelength, which in turn cannot guarantee good conversion performance for large oblique incidences.
Among all metasurface designs, the Huygens’ metasurfaces, which utilize Huygens’ principle in the metasurface element designs, are very useful examples, especially for high efficiency EM wave manipulations. However, most of the existing research on Huygens’ metasurfaces focus on manipulation of the EM wave’s magnitude and phase [10–12,31–34], especially for achieving high efficiency and reflectionless transmission designs. Meanwhile, the electric and magnetic fields are manipulated independently owing to the independent working of the fictitious magnetic and electric currents on the metasurface. In this study, we employ a Huygens’ metasurface to design EM wave polarization manipulation devices by introducing direct coupling between the induced electric and magnetic currents. We first investigate the detailed conversion mechanisms of the proposed devices by analyzing the coupling between the magnetic and electric resonances. To verify the design principle, a polarization conversion splitter, and one reflective and one transmissive polarization convertors are designed in microwave regime. The proposed devices possess compact element dimensions compared to the working wavelength, which enables good angular performance for wide incidence angles up to 60°.
2. Principle
Based on the Huygens’ principle, one can realize EM radiation control by manipulating the electric and magnetic secondary sources. For an electrically thin layer, based on Maxwell’s equations, the relation between incident/outgoing wave and the induced surface electric/magnetic current in the layer can be given as
where is the unit vector of the external normal direction of the layer, and indicate the induced electric and magnetic surface currents on the layer, and and represent the incident and outgoing waves’ electric/magnetic fields, respectively, as shown in Fig. 1(a).
Fig. 1 (a) Schematic of Huygens’ principle in the case of an electrically thin layer; (b) general equivalent electric and magnetic sources in the design of a Huygens’ metasurface; (c) schematic of the element of the polarization conversion device based on Huygens’ principle. When a y-polarized incident EM wave passes through the structure, currents will be induced in the loop. By guiding the induced current to the metallic wire pair along the x-axis, the formed electric dipole will radiate x-polarized waves secondary to both + z and –z directions.
Generally, in the design of a Huygens’ metasurface, a metallic wire pair is introduced as an electric dipole that is oriented along the direction of the electric field and can be regarded as an electric source since it matches with the first formula in Eq. (1). The metallic loop arranged in the plane perpendicular to the magnetic field is usually introduced as a magnetic source since it matches with the second formula in Eq. (1), as shown in Fig. 1(b). Similarly, in the proposed Huygens’ devices, the metallic wire pair and loop structure are employed as the Huygens’ element generating both electric and magnetic currents.
In Eq. (1), the electric and magnetic fields are regulated independently by and respectively without coupling. However, by introducing a direct and coupling, i.e.,, the manipulation of the EM wave’s magnitude and phase can be enriched. In this work, we focus on polarization control through introducing direct coupling between the electric and magnetic currents.
By introducing coupling between the electric and magnetic currents in the Huygens’ element, we can construct a basic polarization conversion device, as shown in Fig. 1(c). We first employ a rectangular metallic loop in the YOZ plane as the magnetic resonance whereas a metallic wire pair along the x-axis acts as the electric resonance. By connecting these two elements, the whole structure can be regarded as one magnetic dipole that is connected directly to one electric dipole. In this case, the magnetic field of the y-polarized incident wave will interact with the loop and induce a current. After further guiding the induced current to the electric dipole along the x-axis, the dipole will produce x-polarized secondary EM radiation. Therefore, the y-polarized incident EM wave is converted to x-polarized secondary radiation through electric–magnetic resonance coupling. In this case, the relation between and can be given as
which represents an ideal complete coupling. is the wave impedance, which is equal to the free space impedance here. Both and are along the x-axis, as represented in the Fig. 1(c). Substituting Eq. (2) to Eq. (1), the results can be expressed asAs a result, the polarization of outgoing electric field is identical to the direction of the incident magnetic field, where E2 lies in a vertical direction with E1. Furthermore, the radiation from the equivalent secondary electric source is bi-directional, resulting in a polarization conversion splitter.
Based on the above analysis, we will show in the following session that three kinds of polarization conversion devices can be designed. (i) A polarization conversion splitter can divide the incident EM wave equally into cross-polarized reflective and transmissive waves. (ii) By adding a metallic background, this splitter can be converted to a polarization-independent reflective polarization convertor. (iii) By adding an x-oriented metallic grating in front of this convertor, the splitter can be repurposed into a polarization-dependent transmissive polarization convertor.
3. Design and analysis
3.1. Polarization conversion splitter
EM beam splitters [35–37] that can divide the EM waves into multiple parts are widely used in EM research. One typical design is to separate the incoming wave equally into two parts: reflective and transmissive. In conventional designs, the splitter usually does not possess the function of polarization conversion. Here, based on Huygens’ principle, we propose a polarization conversion splitter that generates the reflective and transmissive beams in the cross-polarized state.
Based on mechanism discussed in the previous section, we propose a splitter with improved element structure, as shown in Fig. 2(a). A single y-oriented metallic grating is employed on the bottom layer for preventing y-polarized incident EM waves from passing through the splitter. As shown in Fig. 2(a), there is also a metallic split loop, which consists of a y-oriented metallic wire on the top layer and two metallic vias connecting to the metallic grating on the bottom layer. The length of the entire loop is approximately half of the equivalent wavelength. The loop interacts with the incident wave and generates a loop current, which can be regarded as magnetic resonance. An x-oriented wire pair ending in short stubs which connects with the center of the y-oriented wire on the top layer can be regarded as electric resonance. The short stubs at the end of the wire pair introduce capacitive coupling between the elements so that the equivalent circuit model of the dipole is a series resonance circuit formed by this capacitive coupling and the lead inductance, thereby reducing the dimension of this equivalent electric source. Therefore, when y-polarized incoming EM wave passes through the splitter along the z-direction, the loop interacts with the incident magnetic field. Current is induced in the loop and extends to the x-oriented metallic wire pair on the top layer. As the secondary Huygens’ electric source, this wire pair will radiate x-polarized EM waves along both + z and -z directions equally. Therefore, when y-polarized wave impinges on the metasurface, it will generate equal reflective and transmissive beams, which are both cross-polarized. Thus, the whole structure can function as an EM wave splitter with polarization conversion.
Fig. 2 (a) Configuration and detailed dimensions of the element of the proposed splitter; (b) schematic functions of the splitter for x- (yellow shaded area) and y-polarized (blue shaded area) incidences, where the inset shows the fabricated sample with an enlarged view of the metasurface element.
When the incident wave is x-polarized, the reflective half will be y-polarized on the basis of the reciprocity theorem. This means that the x-polarized reflection in the case of y-polarized incidence is equal to y-polarized reflection in the case of x-polarized incidence. Such phenomena can be more clearly comprehended by assuming a simple model of a reflective test system composed of two ports: one port for y-polarization, named port 1, and the other for x-polarization, named port 2. If the incident wave comes from port 1, then S21, which denotes polarization conversion from y-polarization to x-polarization, will be equal to S12, which denotes polarization conversion from x-polarization to y-polarization for incidence from port 2, based on the reciprocity theorem. In consideration of the reflective polarization conversion feature of the proposed splitter for the y-polarized incidence discussed above, S21 is equal to , for half of the incident energy that is reflected as x-polarized wave. In such case, for x-polarized incidence, S12 should also be equal to , which implies that only half of the incident energy is adopted to the electric–magnetic coupling process resulting polarization-converted reflection as y-polarized wave. The remaining half will radiate via the dipole to both + z and -z directions equally. Both the reflective and transmissive waves are illustrated in Fig. 2(b) intuitively for x- or y-polarized incidences. Here, we can summarize the metasurface’s feature in terms of the electric field transmission matrix in the following form:
where the subscripts “o” and “i” denote the outgoing and incident waves, and “t” and “r” indicate the transmissive and reflective outgoing waves, respectively. The “x” and “y” subscripts express the corresponding polarization. The distance between the reference planes for phase probing and the top sheet of the metasurface are the same for reflection and transmission measurements. For y-polarized incidence, the phases of the cross-polarized transmitted and reflected waves are equal as both waves are generated by secondary radiations of the same electric source. The phases of the co-polarized transmitted and reflected waves for x-polarized incidence are also the same for this reason. Another criterion that should be noted here is the phase difference between the cross-polarized reflected wave and the co-polarized outgoing wave, which results from two distinct mechanisms: the cross-polarized wave is generated by electric–magnetic coupling, whereas the co-polarized wave is generated by the direct secondary radiation of the equivalent electric source.As a prototype example in the microwave frequency range, a metasurface is fabricated utilizing substrate material FR-4 with dielectric constant 4.3 and loss tangent 0.02 by standard printed circuit board (PCB) technique. The detailed dimensions of the metasurface element is shown in Fig. 2(a). The geometrical parameters were optimized based on the method mentioned in section 2 to guarantee predicted performance for the cross-polarized radiation. The splitter is designed to work at approximately 3.6 GHz, and the dimensions of the metasurface element are 5 mm, 10 mm, and 3 mm along the x, y, and z coordinates, which amount to working wavelengths of 0.06, 0.12, and 0.036, respectively. The single metasurface slab consists of 40 × 20 proposed elements of size 200 mm × 200 mm in the x-y plane, and the photo of the fabricated sample is shown in Fig. 2(b).
The measurement setup is schematically depicted in Fig. 3(a). The sample is placed in the middle of a planar screen surrounded by microwave absorbing material in a microwave anechoic chamber. The element is simulated using Ansoft high frequency structure simulator (HFSS) with a periodic boundary condition (PBC), which can be regarded as an equivalent model of an infinite metasurface with periodically arranged elements. The simulation and measurement results for normal y- and x-polarized incidence are compared in Figs. 3(b) and 3(c), where T and R respectively denote transmission and reflection, followed by polarization information; for example, XY corresponds to y-polarized incidence and x-polarized outgoing wave. In Figs. 3(b) and 3(c), both the operating frequency and performance at that frequency show good agreement between the simulated and measured data; these results are denoted in Table 1. As is known, compact elements cause small phase variations for oblique incidences, which can consequently keep its transmissive and reflective performance without much degradation for large oblique incident angles as what for normal incidence. We simulated and measured the performance of the proposed splitter under oblique incidence from 0° to 60° in steps of 20°. The measured results of T_XY and R_XY in the case of y-polarized incidence for different oblique angles along φ are presented in Figs. 3(d) and 3(e) respectively, as well as the results along θ in Figs. 3(f) and 3(g). φ and θ directions are as labeled in Fig. 2(b). The annotations are the same as those explained for the oblique angles labeled at the ends. We summarize these quantitative results in Table 1.
Fig. 3 (a) Measurement setup for polarization conversion metasurfaces. (b) and (c) simulated and measured performance of the splitter for normal y- and x-polarized incidences, respectively. (d) and (e) show the measurement results of T_XY and R_XY for the oblique incidence angle along φ direction respectively, while, (f) and (g) for the oblique incidence along θ direction. “T_XY” and “R_XY” represent the transmission and reflection of x-polarized outgoing wave in the case of y-polarized incidence, respectively.
Table 1. Quantitative results for the polarization conversion splitter
From the results in Table 1, it is seen that the test performance approximately coincides with the simulation. Under y-polarized incidence, the splitter can generate almost equal transmission and reflection (close to −3 dB) in the cross-polarized state. The transmissive power is a little larger than the reflective part, which is mainly caused by the slight difference between the impedances for the reflection and forward transmission. The phases of these two parts are almost the same as they are radiated by the same secondary Huygens’ source. The performance for oblique incidence is mostly retained as that for the normal incidence case.
To better understand the working mechanism, we investigate the surface current on the element’s metallic loop and wire pair at 3.6GHz for y- and x-polarized incidences, as shown in Figs. 4(a) and 4(b), respectively. Circulating current is formed in the loop and extends to the x-oriented wire pair resulting in a secondary source of electric dipole, as we predicted in the theoretical analysis. Figures 4(c) and 4(d) depict the magnetic field distributions on the YOZ plane for y- and x-polarized incidences. The magnetic field concentrates in the loop, which implies the structure’s good performance at harvesting the EM wave. In addition, we can easily observe that the current magnitude and magnetic field for y-polarized incidence is larger than that of x-polarized incidence, which implies a strong coupling between the electric and magnetic resonances.
Fig. 4 (a), (b) Surface currents on the element at 3.6GHz for y- and x-polarized incidences, respectively; (c), (d) magnetic field distributions on the YOZ plane at 3.6GHz for y- and x-polarized incidences, respectively.
3.2. Reflective polarization convertor
As mentioned before, by adding a metallic background, the proposed splitter can behave as a reflective polarization convertor. In the working scheme of the splitter, the secondary radiation by the x-oriented electric dipole is bidirectional along the ± z axis in the case of y-polarized incidence. If we replace the bottom grating layer with a metallic background, the forward radiation will be prohibited, thus resulting in a total reflection, and the outgoing wave is x-polarized. Based on this design scheme, the configuration parameters of the metasurface element are further optimized, as shown in Fig. 5(a). The dimensions of the element are approximately 5 mm, 6 mm, and 3 mm along x, y, and z coordinates, which amount to working wavelengths of 0.06, 0.08, and 0.04, respectively. The metasurface then consists of 40 × 30 proposed elements of size 200 mm × 180 mm each in the x-y plane; the fabricated sample is represented in Fig. 5(b). The schematic of the reflective polarization convertor is also shown in Fig. 5(b). Owing to reciprocity, the polarization conversion performance for both magnitude and phase are the same for either x-polarized or y-polarized incidences, i.e., the device works as a polarization-independent polarization convertor.
Fig. 5 (a) Configuration and detailed dimensions of the element for the reflective polarization convertor; (b) schematic of the function of the reflective polarization convertor, where the x-polarized incidence is represented as the yellow shaded areas, while y-polarized incidence as blue ones. The inset pictures show the fabricated sample and enlarged view of the element; (c) simulated and measured results of the co- and cross-polarized reflection coefficients for normal y-polarized incidence, while (d) for x-polarized incidence. The first and second letters represent the polarization of reflection and incidence, respectively. (e) and (f) measured cross-polarized reflection coefficients of the metasurface for y-polarized incidences in the case of oblique incidence along φ and θ directions, respectively.
The simulated and measured results in the case of normal incidence are presented in Figs. 5(c) and 5(d) for y- and x- polarized incidences, respectively. The center working frequency is approximately 4.3 GHz for both simulation and measurement. The simulated and measured cross-polarized reflection results are in good agreement. In Figs. 5(e) and 5(f), we provide the measured cross-polarized reflection coefficients for φ and θ direction oblique incidences respectively in the case of the y-polarized incidence. The annotations are similar to those in the previous section, and the quantitative results are summarized in Table 2. The performance of both normal and oblique incidences show good consensuses with the designs. Except for an insertion loss of approximately 1 dB due to the metallic and dielectric losses, the metasurface behaves as a polarization insensitive reflector with the property of polarization conversion. The ideal transmission matrix of the metasurface can be described as follows for a reflective polarization convertor.
Table 2. Quantitative results for the reflective polarization convertor
3.3. Transmissive polarization convertor
Similar to the reflective polarization convertor, by adding an x-oriented metallic grating in front of the previously designed polarization conversion splitter, we can construct a polarization-dependent transmissive polarization convertor. The incident y-polarized EM waves pass through the grating and generate both reflective and transmissive x-polarized waves, and the x-polarized reflective wave from the splitter will be reflected to the + z direction. Thus, the EM wave transmit completely through the metasurface in the cross-polarized state and comprises two parts: one is generated by the splitter directly, and the other is reflected by the loaded grating layer. On the other hand, the x-polarized incident wave will be totally reflected by the grating without polarization conversion. The modified metasurface element is shown in Fig. 6(a). By adding the dielectric superstrate for the metallic grating, the effective dielectric constant of the metasurface is increased, and the working frequency is red-shifted to 2.4 GHz. The dimensions of the metasurface element are 5 mm, 10 mm, and 8 mm along x, y, and z coordinates, which amount to working wavelengths of 0.04, 0.08, and 0.06, respectively. The employed x-oriented metallic grating is fabricated using a FR-4 substrate of thickness 5 mm. The schematics of the proposed transmissive polarization convertor and the fabricated sample are shown in Fig. 6(b). The phase probing plane is set identical to that in the proposed splitter design. There exists a phase difference between the co-polarized reflection for x-polarized incidence and the cross-polarized transmission for y-polarized incidence because of different working mechanisms, as mentioned above. The ideal performance of such transmissive polarization convertors can be formulated by the following equation:
The simulation and measurement results in the case of normal y- and x- polarized incidence are shown in Figs. 6(c) and 6(d), respectively. The operating frequency of both simulation and measurement are similar, which is approximately 2.4 GHz. The measured performance is in agreement with the simulated one. We also depict the polarization conversion performance for y-polarized incidence along φ and θ directions in Figs. 6(e) and 6(f), respectively. The incident angle range from 0° to 60° in steps of 20°. The performance of polarization conversion in the case of oblique incidence is maintained similar to that in normal incidence. However, the level of cross-polarized transmission is a little low, which is approximately −3 dB and is mainly caused by losses from the loaded grating layer. To verify this phenomenon, the propagation loss of the grating layer is measured separately, which is approximately 1.5 dB owing to the rather large loss tangent and thickness of the layer over the band for the EM wave passing through the plate. To lower the total insertion loss, the grating can be replaced with a substrate having lower loss or even a freestanding metallic sheet. For comparison, by choosing a loss-free substrate for the grating layer, we re-simulate the structure; the insertion loss is observed to reduce to −0.5 dB at a lower frequency, as shown in Figs. 6(e) and 6(f). The quantitative results from Figs. 6(c)–6(f) are compared in Table 3.Fig. 6 (a) Configuration and detailed dimensions of the element of the transmissive polarization convertor; (b) schematic of the convertor, which is built by adding an x-oriented metallic grating in front of the previously designed splitter. The x- and y-polarized incidence are expressed as yellow and blue shaded areas, respectively. The fabricated sample with enlarged element view; (c) and (d) simulated and measured results for normal y- and x- polarized incidence, respectively. In the legends, “R” denotes the reflection, while “T” denotes transmission. The first and second letters behind underline represent the polarization of outgoing and incident wave, respectively. (e) and (f) measured cross-polarized transmissions of the metasurface for various oblique incidence angles of the y-polarized wave along φ and θ directions, respectively.
Table 3. Quantitative results for the transmissive polarization convertor
4. Conclusion
In this work, we propose the application of a Huygens’ metasurface for polarization manipulation. By introducing direct coupling between the electric and magnetic resonances in the Huygens’ element, the incident EM wave can be converted to its cross-polarized state. As examples, a single polarization conversion splitter as well as one reflective and one transmissive polarization convertors are designed to verify the mechanism. All three designs have the same feature of compact element size compared to the working wavelength; therefore, they have good angular performance at oblique incidence angles ranging from −60° to 60°. Both full-wave simulations and measurements were carried out on these three devices, which verify the proposed mechanism and polarization conversion performance. The proposed method may also be extended to design a polarization rotator with arbitrary rotation angle or for circular-polarized EM wave generation. Introducing coupling between the equivalent electric and magnetic sources enriches the research on Huygens’ metasurface. Using the ability of the Huygens’ metasurface ability for magnitude and phase control, we may envision further applications of integrated control of the EM wave’s magnitude, phase, and polarization state. This concept is also extendable to tunable devices by applying a tunable element in the polarization convertor.
Funding
National Natural Science Foundation of China (NSFC) (61571218, 61671231, and 61731010); National Key Research and Development Program of China (2017YFA0700201); China Postdoctoral Science Foundation (2017M620202); Natural Science Foundation of Jiangsu Province, China (BK20151393).
Acknowledgments
This work was partially supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Wave.
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