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Abstract
The polarizations of electromagnetic (EM) waves are very important for transceivers. We propose a broadband polarization-insensitive polarization rotator (PIPR), which can realize 90° polarization rotation for incident waves with an arbitrary azimuth angle. A unit of the PIPR is composed of two types of substrate integrated waveguide (SIW) units in a checkerboard pattern, which provides more than −0.2 dB transmission from 9.5 to 10.9 GHz. The electric field inside the cavity is analyzed to explain the working mechanism of the proposed rotator. A prototype is fabricated and measured to verify the proposed design, and satisfactory agreement between simulated and measured results is achieved, indicating that the converter has potential applications in imaging and communication systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The polarization of EM waves represents the trajectory of an electric field over time. A field might exhibit linear, circular, or elliptical polarization. Manipulating polarization at will is the foundation of many applications, such as radar cross-section reduction [1,2], wireless communications [3], and polarization imaging [4,5]. A polarization converter presents an effective means to modify polarization states due to the complicated feed system. In the optical frequency, traditional polarization converters such as waveplates [6,7] accomplish the polarization control because of the anisotropy. However, the anisotropy of regular materials is weak. The volume of a waveplate suffers from being bulky when it is applied in a microwave regime. Thus, it may be challenging to integrate wave plates into compact systems. In recent decades, a new avenue to manipulate EM waves based on metasurface has been opened. Furthermore, polarization converters based on metasurfaces exhibit unprecedented advantages, including low profiles and low losses. Therefore, the manipulation of polarization based on metasurfaces has attracted widespread attention.
To date, many researchers have studied and achieved various types of polarization conversion functions, such as linear-to-linear (LTL) [8–12], circular-to-circular [13,14], linear-to-circular [15–17], and combined polarization conversion functions [18–21]. The most widely used function is the LTL polarization converter, which can rotate the polarization direction of a linear polarization (LP) plane wave by a certain angle, such as 45° [22], 90° [10,12,23] or an arbitrary azimuth angle [24,25]. In particular, a 90° polarization rotation can also be called a cross-polarization conversion, which has a wide range of applications.
Various approaches have been investigated to realize cross-polarization conversion. For example, polarization converters based on the Fabry-Pérot resonant cavity theory have been intensively proposed due to their attractive advantages, including high efficiency and broadband [26–28]. Additionally, polarization conversions based on SIW structures have also been proposed. They have high efficiency and excellent performance in terms of polarization compatibility [9,29–31]. Recently, a polarization conversion method utilizing an antenna-coupler-antenna system [12] has been reported and implemented. The structure of the unit cell consists of a receiving element, nonradiating metal via holes, and an emitting element. The electric field direction of the output wave is changed by rotating the orientation of the radiating part, which has an excellent performance in terms of frequency selectivity.
The polarization conversion devices described above feature broadband or high efficiency. Whereas they are selective regarding the polarization direction of the incident wave, and their functions are feasible for an incident LP wave with one or two fixed polarization directions but not available for other polarization directions. For example, the cross-polarization converter [9] only responded to the y-polarized wave, while the x-polarized incident wave was blocked. For this reason, a cross-polarization converter was proposed, which could realize 90° polarization rotation under an LP plane wave with arbitrary azimuth excitation [32,33]. However, they can only operate on a single frequency, so their application is greatly limited in practice. To the best of our knowledge, few PIPRs have been reported in a wide frequency range.
In this paper, a broadband PIPR converter is presented based on combined SIW units, which is insensitive to arbitrary polarization directions in the azimuth plane at normal incidence. More importantly, the proposed design can achieve near perfect conversion efficiency and wide operating bandwidth, showing potential applications in wireless communication and radar systems.
2. Theoretical analysis and design
It is well known that an LP wave polarized along an arbitrary direction can be decomposed into two orthogonal components. For convenience, it was assumed that the two orthogonal components were the x and y components. Furthermore, we assumed that the incident LP plane wave propagated along the -z direction, and its polarization direction was along the u-axis, which had φ degrees with respect to + x-axis. In this case, the electric field of the incident wave can be written as:
Fig. 1. Schematic of the LP incident wave with an arbitrary azimuth φ, whose polarization angle is deflected by 90° after passing through the PIPR.
Here, the first and second subscripts of matrix element T are the polarization directions of the output and incoming waves, respectively. It was assumed that the Jones matrix T met the requirement of a unique structure that could realize cross-polarization conversion for an incident LP wave with an arbitrary φ. Equation (3) is thus rewritten as:
Since Eq. (5) holds for an arbitrary azimuth φ, we chose some specific values (φ = 0° and 90°) and input them into Eq. (5). The Jones matrix T was calculated and expressed as:
We substituted the calculated result shown in Eq. (6) into Eq. (5), where Eq. (6) holds for an arbitrary azimuth φ. We found that Txy =−1 and Tyx =1 in the Jones matrix T in Eq. (6). This indicated that the x-polarized wave was converted into a y-polarized wave, and the y-polarized incident wave was converted into an x-polarized wave. Additionally, a 180° phase difference between Txy and Tyx was produced.
To satisfy the condition discussed above, two SIW units with 90° polarization rotations are designed and plotted in Figs. 2(a) and (b), which correspond to units 1 and 2, respectively. To show this more clearly, we separate some metal layers from the dielectric layers, where the blue dashed lines indicate that there is no distance between them. As shown in Fig. 2(a), the proposed SIW units have three layers of substrate dielectrics. The top and bottom layer substrate dielectrics are formed of the microwave composite material F4B, which has a relative permittivity ${\varepsilon _r}$ = 2.2 and a loss tangent tan δ = 0.001. This material is chosen because of its relatively low loss and parameter stability in the operating bandwidth. The middle layer substrate dielectric is a curing film with a thickness of 0.16 mm and a relative permittivity of 4.3, and it is utilized to glue the substrate dielectrics of the top and bottom layers together.
Fig. 2. Expanded views of (a) unit 1 and (b) unit 2, and the blue dashed lines indicate no distance between the associated layers. Under x- and y-polarized wave excitations. (c) The transmission amplitude responses of units 1 and 2. (d) The cross-polarization phase responses of units 1 and 2.
The top metal layer of unit 1 is etched in two parallel slots along the y-axis, which allow the x-polarized wave to couple into the upper cavity. The bottom metal layer is rotated by 90° along the z-axis, which allows the y-polarized wave to couple out the lower cavity. The middle double-arrow metal slot is oriented at 45° relative to the y direction. The metal is copper with a thickness of t = 0.02 mm. Additionally, periodic metalized via holes are located along the x- and y-directions around the unit structure, which are utilized to increase working bandwidth and conversion efficiency. Specifically, to form a cavity of vertical walls, the diameter of each metalized via hole and the distance between adjacent metalized via holes is chosen appropriately [30]. As illustrated in Fig. 2(b). Unit 2 is identical in size but orthogonal in direction to unit 1. Hence, the y-polarized incident wave can convert into an x-polarized transmitted wave for unit 2.
A numerical simulation of the proposed PIPR converter was carried out in the CST Microwave Studio 2019. The x and y directions followed the unit cell boundary. It was assumed that the incident wave propagated along the -z direction. Figures 2(c) and (d) shows the simulated results of units 1 and 2 under the excitations of x- and y-polarized waves. Here, the first and second subscripts of T are the polarization directions of the transmitted and incoming waves, respectively. As depicted in Figs. 2(c) and (d), Tyx for unit 1 and Txy for unit 2 are close to 0 dB at 10 GHz, while Txx, Tyy, and Txy for unit 1 and Tyy, Txx, and Tyx for unit 2 are below −30 dB. It is worth mentioning that the simulated curves of the magnitudes of Tyx for unit 1 and Txy for unit 2 overlap. Whereas the phase difference between Txy for unit 1 and Tyx for unit 2 remained at approximately 180° over the whole operating band because the directions of the middle metal slots in units 1 and 2 are orthogonal to each other. Hence, the above simulation results of units 1 and 2 cannot satisfy the transmission characteristic of the Jones matrix T shown in Eq. (6). To obtain a unit with the Jones matrix T, we attempted to combine units 1 and 2 into a new super unit cell in a checkerboard pattern. The permutation and combination results are shown in Fig. 3(a). This method of permutation was chosen because every metal layer was symmetrical about the centers of every layer. Hence, the four units can be seen as a super unit of the combined structure.
Fig. 3. (a) Permutation and combination of units 1 and 2. The inset shows of the unit cell unit of the final PIPR. (b) The top metal layer, (c) the bottom metal layer, (d) the middle metal layer. (e) The expanded view, where the blue dashed lines indicate no distance between the associated layers.
The simulated results of the combination of units 1 and 2 are shown in Fig. 4(a). Comparing Fig. 4(a) and Figs. 2(c) and (d), different simulated results were produced for the two kinds of unit structures, mainly because of the discrepancies in the boundary of unit structures. To broaden the bandwidth, some parameters, including gg, ww1, ss, ss1, ss2 and ss3, were scanned and optimized. The structural details of the final PIPR converter structure are plotted in Figs. 3(b)-(e). The digital geometrical parameters of the PIPR converter structure are as follows: ww1=2.5 mm, ss = 4.7 mm, ss1 =1.75 mm, ss2 =0.85 mm, gg =6.34, ss3 = 9 mm, w =17 mm, w1 =3 mm, l =16.1 mm, d =0.45 mm, p =1.7 mm, s =4.8 mm, g =6 mm, s1 =1.7 mm, s2 =0.7 mm, s3 = 9.2 mm, h1 =0.16 mm, h =4 mm,.
Fig. 4. Under the excitation of the x-polarized wave, (a) the simulated amplitudes of the combination of units 1 and 2, and (b) the simulated amplitudes of the final PIPR. Under excitations of x- and y-polarized waves, (c) transmitted magnitude responses, and (d) the phase responses of the cross-polarization conversion of the proposed final PIPR.
The reflected and transmitted results of the PIPR converter structure under x-polarized wave excitation are depicted in Fig. 4(b). The transmitted cross-polarization Tyx exceeded −0.2 dB from 9.5-10.9 GHz. It should be noted that the peak reached near 0 dB. Rxx and Ryx were below −14 dB and −70 dB, respectively, indicating low reflection loss. Simultaneously, Txx was below −20 dB across the corresponding operating frequency band, which meant that the co-polarization transmission was weak.
To verify whether the proposed design satisfied the Jones matrix described in Eq. (6), simulations under x- and y-polarized wave excitations were performed, and the simulated results are illustrated in Figs. 4(c) and (d). The curves of Txy and Tyx overlapped and were close to 0 dB, while the curves of Txx and Tyy overlapped and were below −20 dB. Additionally, the phase difference between φxy and φyx was 180° in the whole operating band. As a result, the proposed structure satisfied the properties of the Jones matrix T, which meant that the proposed design could realize cross-polarization conversion for incident LP waves with any arbitrary azimuth.
To demonstrate the proposed concept, the simulated results obtained under the excitation of LP waves with polarization azimuths at φ = 0°, 30°, 45°, and 90° at normal incidences are plotted in Fig. 5. It was clearly observed that the reflected and transmitted curves obtained under the excitation of the LP wave with different azimuths overlapped, demonstrating that the proposed polarization converter was immune to the polarization direction of a normal incident LP wave.
Fig. 5. (a) The cross-polarization transmission and co-polarization reflection of the proposed PIPR for incident LP waves with electric fields oscillating along azimuths at φ = 0°, 30°, 45°, and 90°. (b) Simulated PCR of the proposed PIPR converter.
Polarization conversion rate (PCR) was utilized to depict the efficiency of cross-polarization conversion, and this metric is calculated as follows:
PCR of the PICP converter is plotted in Fig. 5(b). It was clearly seen that the PCR exceeded 99.3% over the whole operating range, indicating that a very high cross-polarization purity was achieved for the output wave.The electric field distribution inside the cavity at a frequency of 10.2 GHz was assessed to investigate the physical mechanism of the proposed PICP converter. Figure 6 depicts the electric fields inside the upper and lower cavities under the excitations of LP waves with electric fields aligned at φ = 0°, 30°, 45°, and 90°. When the LP wave polarized along the + x direction (φ = 0°) irradiates the proposed sample, as shown in Fig. 6(a), the directions of the electric field inside the upper and lower cavities in the red frame are oriented in x- and y-directions, respectively, indicating the direction of the electric field is rotated 90° when passing through the double-arrow slots. Finally, the y-polarized wave is coupled out from the x-directed slots of the backside. In this way, an x-polarized incident wave is converted into a y-polarized transmitted wave. Comparing the intensities of the electric fields inside the cavity in the red and blue frames, we clearly observe that there was a strong electric field density inside the cavity in the red frame, while there is almost no electric field inside the cavity in the blue frame. This reveals that only the cavity in the red frame responded to the x-polarized incident wave.
Fig. 6. Electric field distributions inside the upper and lower cavities of a PIPR cell for incident waves with different polarization azimuths: (a) φ = 0°, (b) φ = 30°, (c) φ =45°, and (d) φ = 90°.
The electric fields inside the upper and lower cavities of the proposed structure are plotted in Fig. 6(d) for the y-polarized (φ=90°) incident wave. Obviously, the directions of the electric fields in the upper and lower cavities in the blue frame are orthogonal to each other. Accordingly, the x-polarization wave is achieved under the excitation of the y-polarized wave. We compare the intensities of the electric fields inside the cavity in the red and blue frames. It is clearly observed that a strong electric field density is produced inside the cavity in the red frame, while almost no electric field inside the cavity in the red frame is excited. This reveals that only the cavity in the blue frame responded to the y-polarized incident wave. Based on the analysis of the electric fields, it is concluded that the cavity in the red frame responded to the x-polarized incident wave and converted it into a y-polarized wave. In contrast, the cavity in the blue frame responds to the y-polarized incident wave and can transform it into an x-polarized wave.
As shown in Figs. 6(b) and (c), when the waves with their electrical field vectors aligned at other azimuths (φ = 30° and 45°) irradiated in the array, they can always be resolved into Eix (Eiu*cosφ) and Eiy (Eiu*sinφ) components, which respond to units 1 and 2, respectively. According to the conversion principle mentioned above, the Eix (Eiu*cosφ) component of the incident wave is converted into the Eiy (Eiu*cosφ) component. In contrast, the Eiy (Eiu*sinφ) component of the incident wave is converted into the -Eix (-Eiu*sinφ) component. The synthetic electric field of the final transmitted wave will be rotated anticlockwise by 90°.
Comparing the electric field intensities inside the cavities of units 1 and 2 under the excitations of EM waves with various azimuths φ, it can be concluded that the ratio of the intensities of the electric fields inside the cavities in the red and blue frames is approximately expressed by cosφ/sinφ. Without loss of generality, LP plane waves with arbitrary azimuths are applied to the above discussion.
3. Experimental verification
As a proof of principle, a prototype consisting of 12 × 12 unit cells was fabricated. The overall size of this fabricated sample was 420 mm × 420 mm. The fabricated sample are shown in Figs. 7(a) and (b). Subsequently, experiments were carried out using the free-space method. Figure 7 shows a schematic of the experimental setup. To minimize the interference induced by undesired edge diffraction of the fabricated sample with a finite size, the surrounding region of the fabricated sample was surrounded with microwave absorbing materials. Additionally, the time domain gate on the Agilent (N5230C) vector network analyzer (VNA) was also adjusted to perform spatial filtering, which might have lessened the unwanted interferences from multipath echoes.
Fig. 7. Photographs of the fabricated sample from the (a) top view and (b) bottom view. (c) Schematic of the experimental setup. (d) Simulated and measured results of the co-polarization reflection and cross-polarization transmission magnitudes for incident waves with different polarization azimuths.
Ports 1 and 2 of the VNA were connected to the ports of the two identical LP horn antennas marked 1# and 2#, which were employed to transmit and receive the EM wave signal, respectively. The two horn antennas were placed face to face on two sides of the fabricated sample and were orthogonal to each other in the polarization direction. In other words, they were rotationally symmetric about the fabricated sample. It should be mentioned that the distance between the fabricated model and the horn antenna was larger than the far-field distance from the horn antenna, which ensured that the incident wave was a plane wave.
Through the abovementioned experimental setup, the co-polarized reflection coefficient rxx and the cross-polarized transmission coefficient tyx were measured. To obtain normalized values, the reference values were measured in the cross-polarized transmission measurement case. The fabricated sample was removed simultaneously, and the received horn antenna was rotated by 90° along the z-axis. The two horn antennas had the same polarization direction. Subsequently, the co-polarized transmission coefficient produced without the fabricated sample tair was measured, and this coefficient was employed as the reference value. Following this, the normalized cross-polarized transmission coefficient was obtained from Tyx = tyx/tair. For the reference values of the co-polarized reflection measurements, a metal plate of the same size as the fabricated sample was used to replace the fabricated sample. Then, the co-polarized reflection efficient rmetal was measured. Similarly, the normalized co-polarized reflection coefficient was calculated from Rxx = rxx/rmetal.
Horn antennas 1 and 2 were both rotated by φ anticlockwise along the direction of the LP wave propagation. It should be mentioned that antennas 1 and 2 were always orthogonal in the polarization direction during rotation. Following the above measurement process, the corresponding experiments were carried out under the excitations of LP waves with different azimuths (φ=30°, 45°, and 90°). The simulated and experimental results of Tvu and Ruu for LP incident waves with different azimuths at φ = 0°, 30°, 45°, and 90° are plotted in Fig. 7. Tvu and Ruu curves obtained under the excitations of LP waves with different azimuths at φ = 0°, 30°, 45°, and 90° were almost identical, which verified the feasibility of polarization-insensitive cross-conversion. Moreover, close agreement between the experimental results and the simulated results was observed. The tolerances in the production and measuring processes are to blame for the disparity between the measured and simulated results.
4. Conclusion
In summary, we propose a broadband cross-polarization converter composed of two types of SIW units in a checkerboard pattern. In this design, LP waves with arbitrary azimuth angles can be rotated by 90°. A −0.2 dB cross-polarization conversion efficiency is obtained from 9.5 to 11.9 GHz with a 13.7% relative wideband, and a PCR of more than 99.3% is also produced over the entire bandwidth, indicating high polarization purity. Furthermore, a theoretical analysis of the proposed PIPR converter is conducted. In addition, the electric field inside the SIW cavity is used to explain its physical mechanisms. Here, the designed sample is fabricated and measured. The consistency between simulations and experiments demonstrates the feasibility of the proposed design. Although the proposed design is verified in the microwave frequency, it may be applied to the terahertz and optical regime by using the same concept, presenting a new opportunity for wideband PIPR conversion. Hence, the proposed approach has wide applications in many fields, such as imaging and wireless communication systems.
Funding
National Key Research and Development Program of China (2017YFA0700201, 2017YFA0700202, 2017YFA0700203); National Natural Science Foundation of China (11227904, 61138001, 61371035, 61571117, 61631007, 61722106, 61731010); 111 Project (111-2-05); Natural Science Foundation of Jiangsu Province (BK20212002).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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