Broadband Single-Layered, Single-Sided Flexible Linear-to-Circular Polarizer Using Square Loop Array for S-Band Pico-Satellites

Two new flexible, single-sided linear-to-circular polarizers based on the square loop unit cells have been proposed in this work. The first uses a flexible Polydimethylsiloxane (PDMS) substrate, whereas the second polarizer is implemented on a felt textile substrate. Both polarizers uses the same ShieldIt textile to form their conducting elements. The proposed flexible single-layered structure potentially enables the implementation of the polarizer in a deployable format with improved performance consistency and reduced fabrication complexity for size- and weight-constrained applications such as in pico-satellites payloads. The textile-based design offered an improved performance and is advantageous in terms of weight compared to the PDMS-based polarizer. Besides discussing the operation principles and analyzing its surface currents, an equivalent circuit model is also proposed. Measurements of the textile-based polarizer showed satisfactory agreements with its simulated results, featuring a broad 3-dB axial ratio bandwidth of 33.57 %, operating from 1.71 GHz to 2.4 GHz. The bandwidth with at least 90 % of conversion efficiency for this structure is also improved to 47.3 % (from 1.55 GHz to 2.51 GHz), which is better than any other felt-based flexible polarizers in literature. Finally, the performance of the polarizer in different bending conditions is also assessed, indicating improved performance consistency relative to double-sided flexible polarizers.


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VOLUME XX, 2017 [6]. Different types of high gain antennas (HGAs) with CP characteristics have been reported for satellite applications. These include patch antennas, monopole/dipole antennas, reflector antennas, reflectarray antennas, spiral/ helical antennas etc. [1]. However, designing deployable versions of these antennas with accurate CP characteristics is challenging, especially in size-restricted CubeSats (smallest size is 10 cm × 10 cm × 10 cm for 1U). Placing a linear-tocircular polarizer over a linearly polarized (LP) antenna to achieve CP waves, is considered to be a versatile solution potentially for adoption in pico-satellite communication [7], [8], [12], [19], [21]. Different linear-to-circular polarizers have been reported in the literature, starting from the multilayered meander-line-based design proposed by Young et al. [9] in 1973. These linear-to-circular polarizers are formed by different combinations of frequency selective structures (FSS), including multi-layered meander line structures [9], combinations of square and metallic grids [10], periodic arrangement of slotted split rings [13], and multilayered metasurface-based structures [14]- [16]. These polarizers are designed on rigid structures, which does not enable their implementation on CubeSats in deployable formats. Moreover, there is very limited work available on the design of flexible polarizers for CubeSats application. Different multi-layered polarizers are presented in Table  I(A). It is evident that only one multi-layered polarizer has been designed in the S-band [7] from literature. The widest 3 dB axial ratio bandwidth ( 3 ) of 66.7 % achieved in [11] by implementing a patch array and complementary unit cell structure. However, its conversion efficiency was not assessed. Meanwhile, several other multi-layered polarizers featured 3 of between 20 % [8] and 40 % [9]. Nonetheless, the use of multi-layered structures is very challenging in applications such as CubeSats, as the consistent spacing requirement between the multiple layers is hard to maintain when implemented using flexible materials. Therefore, the choice of single-layered polarizers is more feasible. Next, several single-layered polarizers from literature are summarized in Table I(B). For instance, the work in [13] presented a single layered polarizer for Terahertz (THz) applications with a 3 of 11.75 %. Meanwhile, two metasurface-based polarizers were designed in [14] and [15] for WiFi/WiMAX applications, with the latter achieving a 3 of 9 %. From Table I(B) the highest   3 of 17 % was achieved by [16], which was designed using circular rings with inclined metal strip as its unit cell. The structures in Table I(A) and (B) (regardless of the number of layers) were designed on rigid surfaces, which are unsuitable when need to be implemented in a deployable format in a CubeSat due to its stringent size constraints. Moreover, the choice of its material based on its density will also determine whether these structures will result in additional payload weight in the CubeSats. Comparison among different materials indicated that felt ( [19] - [20]) featured the lowest density. Despite that, these polarizers were still designed with unit cells located on both sides of the substrate, adding complexity to the fabrication process. This is due to the need to accurately align patches on both sides of the substrate to guarantee performance consistency. Moreover, use of flexible materials and for these double-sided structures also potentially causes performance variation, especially when operated in bent conditions [19]- [21]. Among the recently designed flexible polarizers listed in Table I(C), the highest 3 of 32.64 % is exhibited by [21], with the double-sided polarizer implemented on a Polydimethylsiloxane (PDMS) substrate. On the other hand, the bandwidth with at least 90 % of conversion efficiency ( ) is 6.6 %, 23.88 % and 48.12 % from [19], [21] and [20], respectively. In this work, a new linear-to-circular polarizer based on a single-layered and single-sided topology is designed. Compared to literature, such structure avoids the aforementioned fabrication complexities, improve its performance consistency and implementation effectiveness when intended in a deployable format due its single-sided topology and compactness (sized at 0.38 0 ×0.36 0 ×0.02 0 per unit cell). Moreover, the proposed textile-based polarizer exhibited broader bandwidths ( 3 and ) in comparison to recently reported felt-based polarizers [19], [20]. Specifically, it features a 33.57 % (from 1.71 GHz to 2.4 GHz) of 3 and 47.3 % (from 1.55 GHz to 2.51 GHz) of . The paper is organized as follows. Section II introduces the theory and operation of liner-to-circular polarizers, including the assessment parameters. Section III outlines the design principles of the proposed polarizer, and proposes an equivalent circuit model based on the surface current analysis. Section IV presents and analyzes the results of the polarizer both in flat and bent conditions, besides a proposed deployment process, prior to the conclusions in Section V.

II. THEORY AND OPERATION OF LINEAR-TO-CIRCULAR POLARIZERS
The electric field of a linearly polarized (LP) wave, , is assumed to be incident on one side of the polarizer along positive z-axis. This is aligned at an angle of 45° to the xaxis, and can be decomposed into two orthogonal field components along the x-and axes (denoted as and respectively). The polarization ellipse is calculated based on the ratio of the magnitudes of the orthogonal components of the transmitted electric field along and axes, and , expressed as (1) [18], [21], [22]: where , and is the transmission coefficient for and , respectively [6], [11], [20]. For an ideal circular polarization, the ratio in (1) should be unity, indicating an equal | | and | |. The other characterizing parameter for linear-to-circular polarization is the phase difference between and , which ideally must be 90°, calculated as follows [17], [18]: Assuming that and are equal in magnitude and phase, CP characteristics can be evaluated conditions (3) and (4) [18].
Besides these parameters, the CP performance can be further characterized on the basis of conversion efficiency expressed by . Others have defined ellipticity ( ) to determine the shape of the polarization ellipse. These parameters are expressed as follows [17], [18], [20], [23]- [25]: where − and + represents the circular conversion coefficient for right-handed CP wave and left handed CP wave, respectively [20].

A. PRINCIPLE OF OPERATION AND DESIGN
From literature on metamaterials and FSSs, it can be established that the metallic components typically act as the inductive component, whereas the gaps between constituent elements of the unit cells contribute to capacitance. The value of the inductance is directly proportional to the length of the corresponding metallic element, while the capacitance depends on the spacing of the gap and its surface area. The characteristics of the transmitted wave ( ) can be controlled by adjusting the values of inductance and capacitance interacting with one polarization to achieve the CP criteria. These principles are considered when designing the unit cell of the proposed linear-to-circular polarizer, which is based on a square-shaped loop tilted by 45° with respect to the −axis. To form the polarizer, the unit cells are connected at the −direction, and are located 2 mm apart from each other in the −direction. From a physical point of view, this polarizer is made to operate with broadband characteristic by first ensuring that a large transmission fractional bandwidth of the unit cell, , is produced by a small unit cell capacitance in the −direction, . This is so that = ( 0 0 ) ⁄ ; where 0 is the characteristic impedance of the substrate, is the normalized quality factor of the unit cell, 0 is the center frequency and 0 = 2 0 [26]. On the other hand, a high inductance in the orthogonal −direction is used to produce the required 90 o phase compensation. The structure's continuity in the −direction ensures this high inductance is produced onto the incident waves polarized in this direction. Once the level of capacitance is estimated, the phase delay in the −direction can be determined. This is done by optimizing the length of the unit cell and the gap between two consecutive unit cells in the −direction to result in the phase difference of 90° based on eqs. (3) and (4). Fig. 1 shows the proposed polarizer unit cell, with its parameters specified in Table II. The polarizer is designed on a flexible PDMS and felt substrate with a relative permittivity ( ) of 2.7 and 1.44, respectively. Meanwhile, the square loop is formed using ShieldIt conductive textile, with an electric conductivity of 1.18 x 10 5 S/m. CST Microwave Studio was used to design and optimize the dimension of structure. Note that this polarizer is single sided in contrast to the previous double-sided polarizers designed in [19], [20]. The advantage of the single sided design includes the simplicity in fabrication and reduced complexity of alignment on both sides for the polarizer for optimized performance.

B. EQUIVALENT CIRCUIT MODEL
To simplify future design procedure of the polarizer, an equivalent circuit model is modelled. The circuit model is modeled based on the − and −polarized incident waves presented in Fig. 2. It can be seen that in the − polarization, the inductance ( ) is 8.4 nH, which is lower the value of 14.9 nH in the -directed polarization ( ). As aforementioned, the lower values of inductance can be attributed to the length discontinuities of the conductive elements in the unit cells in the − direction.

(c) comparison between circuit and EM simulations
On the other contrary, the connections between unit cells in the − direction resulted in the higher value of inductance, as also explained in Section II (A). Similarly, in the equivalent circuit model, the −polarized capacitance ( ) indicated a value of 0.2 pF, whereas a higher −polarized capacitance ( ) of 7 pF is produced. The higher capacitance in the − direction is due to the smaller gap area in proximity of the junction. On the other hand, the unit cells are 2 mm apart from each other in −direction, which then reduces its capacitance to 0.2 pF. A comparison between the simulated transmission characteristics from the modeled circuit and the full wave EM simulation is presented in Fig. 2(c), indicating good agreements in terms of transmission characteristics.
(a) (b)  The transmission characteristics of the − polarized waves is initially higher at lower frequencies and gradually decreases in value as frequency increases, with a -10 dB value at 3 GHz.
On the other hand, the − polarized transmission coefficient shows the opposite characteristics.
To obtain further insights of the operating principles of the polarizer, the surface current analysis of the unit cell in the -and − polarization are illustrated in Fig. 3. It is evident from Fig. 3(a) that the existence of the relatively large spacing of 2 mm in the − direction resulted in minimum surface currents at this direction. Relatively stronger surface currents are more concentrated on the inner sections of the top and bottom corners of the unit cells, and this level gradually degraded towards the outer perimeters of the loop structure. Meanwhile, the continuity of the unit cell structure in the −direction resulted in a more dense surface current in this direction compared to the −directed polarization. Moreover, it can be observed that the smaller gap at the junction of the two unit cells in the −direction resulted in the concentration of higher surface currents on the outer sections at the top and bottom corners of the unit cells, as seen in Fig. 3(b). The strength of the surface currents degraded towards the inner perimeters of the square loop, contrary to the previous observation for the transmission of the −directed polarized waves.

C. FABRICATION OF THE POLARIZER AND MEASUREMENT SETUP
As aforementioned, that the textile based design has been chosen for fabrication and further investigation assessment due to its better performance. The fabrication the conductive textile is performed using laser printing (dimensioned using a flat-bed fiber laser cutting machine (Glorystar GS-3015)) shown in Fig. 4(a), whereas the measurement setup is presented in Fig 4(b). The important steps in fabricating the polarizer can be summarized as follows:  The final optimized design is exported into a Gerber file format from the electromagnetic simulator.  The exported Gerber file is then imported into the flat-bed fiber laser cutting machine (model Glorystar GS-3015) as shown in Fig. 4(a).  Shieldit Super TM conductive textile from LessEMF Inc is inserted and dimensioned using the laser cutting machine.
 Completed samples of unit cells are checked for dimensional accuracies. If not satisfactory, refabrication will take place.  Dimensioned unit cells are then secured onto the felt substrate carefully using ironing. This can be performed easily as ShieldIt features a hot-melt adhesive on its reverse side.  Distance between adjacent unit cells are checked to ensure accuracy. If not satisfactory, re-fabrication will take place.
Next, the completed polarizer is experimentally assessed based on the method described in [27]- [29]. It is placed between a pair of transmitting and receiving horn antennas (A-INFOMW LB-8180-NF (0.8-18 GHz)) in the far field region, as depicted in Fig. 4(b).

A. DEPLOYED CONDITION
In this work, two designs, one PDMS-based and the other textile-based are compared. In both cases, ShieldIt Super TM conductive textile from LessEMF Inc is used to build the square loop unit cells for both substrates. The transmission characteristics of both polarizers are shown in Fig. 5, indicating similarity at the -and − polarization. For the transmission coefficient in the − polarization, has equal value to that of the − polarized at 2.22 GHz for the case of PDMS-based design. This intersection is also observed at 2.18 GHz for the textile-based design (in simulations) and at 2.14 GHz (in measurements). Besides that, the phase difference between the -and −polarized transmission coefficient presented in Fig. 6 indicated that the phase criteria in (4) is fulfilled by the polarizer over the S-band. In broadband designs, a tolerance of ±° in the phase difference is typically considered. This effectively renders the operation of the polarizer from 1 GHz to 2.62 GHz (for the PDMS-based design) and from 1.67 GHz to 3 GHz (in simulations) and from 1.74 GHz to 3 GHz (in measurements) for the textile-based design. In Fig. 6, the purple-shaded zone represents the area with a phase difference of °±°, whereas the silver-shaded zone represents the frequency band with such phase difference. This indicated the fulfillment of the phase characteristics in the S-band. The conversion efficiency ( ), axial ratio (AR) and ellipticity ( ) of the proposed polarizer is presented in Fig.  7, Fig. 8 and Fig. 9 respectively. In these figures, the purpleshaded zones represent the target parameter ranges of the polarizer: > 90 % (in Fig. 7), AR < 3 dB (in Fig. 8) and 40° > >45° (in Fig. 9). On the other hand, the silver-shaded zone represents the achieved characteristics of these parameters and their frequency bands. The PDMS-based polarizer has shown a conversion efficiency higher than 90 % from 1.68 GHz to 2.62 GHz in simulations (see Fig. 7) which corresponds to bandwidth of 43.73 %. On the other hand, the textile-based polarizer has outperformed the PDMS-based polarizer with a bandwidth of 47.7 % (from 1.58 GHz to 2.57 GHz) in simulations and 47.3 % (from 1.55 GHz to 2.51 GHz) in measurements. Note that the values in Fig. 7 are not representative of the material losses, as the parameter are calculated based on the squared magnitude of the circular polarization conversion coefficients ( + and − ) based on eq. (5). These values, both in simulations or measurements results in relative values, which is then converted into percentage. In the case of the 3dB AR bandwidth, 3 is 32.3 % (from 1.82 GHz to 2.52 GHz) for PDMS-based design. Meanwhile, the textile-based design featured wider 3 relative to the PDMS-based design with 34.73 % (from 1.76 GHz to 2.5 GHz) in simulations and 33.57 % (from 1.71 GHz to 2.4 GHz) in measurements. Finally, the ellipticity of the polarizer (in degrees) is shown in Fig. 9(a). Fig. 9(b) shows the polarization azimuth characteristics whereas Fig. 9(c) shows polarization ellipses at different frequencies.
Measurements indicated an ellipticity of between 40° and 45° from 2 GHz to 2.4 GHz (18.18 %). On the other hand, for the PDMS-based design, this zone is observed to be from 2.05 GHz till 2.35 GHz (13.63 %) in simulations. In comparison, this band is observed to be from 2.02 GHz to 2.36 GHz (15.53 %) in the case the textile-based design in simulations. It is found that the measured results agreed very well with the simulations of the textile-based design. From Fig. 9(c), it can be seen that the polarizer featured a left handed polarization (considering wave propagation outwards from the viewing plane). Moreover, the main polarization axis is rotated towards the clockwise direction with the increase in frequency, as can be seen from the azimuth angles depicted by =82.6°, 76.7°, …, 38.77°. Furthermore, between 2 GHz and 2.4 GHz, the shape of the ellipse is quasi-circular due to the ellipticity value of between 40°and 45°. For example, the ellipticity is 41.36° at 2 GHz, whereas at 2.18 GHz it is 43.24°. This polarization ellipse is more elliptical in shape from 2.4 GHz onwards, as the ellipticity is reduced from 40° and less, as shown in Fig. 9.
The detailed performance of the polarizer is presented in Table III.   To ensure a fair comparison, the final operating bandwidth of the polarizer is determined based on the fulfillment of all four operational requirements: (a) the conversion efficiency, better than 90%, (b) phase difference of 90° with a tolerance of +10° or -10°, (c) ellipticity, varying from 40˚ to 45˚, and (d) axial ratio, AR less than 3 dB. It can be seen from Table III that the proposed textile-based polarizer featured improvement in performance compared to the PDMS-based version, with an operational bandwidth of 15.53 % in simulations and 14.77 % in measurements. At its optimal point (the intersection of the and ), the textilebased polarizer has shown a conversion efficiency, ellipticity and AR of 99.82 %, 43.27°, and 0.53 dB respectively. Meanwhile, whereas the PDMS-based polarizer has shown values of 99.5%, 42.13°, 0.87 dB, respectively at the same optimal operating point.

B. ASSESSMENT IN BENT CONDITION AND DEPLOYMENT PROCESS
To analyze the possible changes in performance due to the use of flexible substrate, the textile-based polarizer is assessed when bent over a vacuum cylinder of 100 mm in radius in four different bending conditions. In each of − and −axis, the bending has been performed in two scenarios, inwards and outwards, as shown in Fig. 10. Generally, the two additional types of bending is each denoted as − or −axis bending, depending on the alignment of the vacuum cylinder towards these axes. For the case of inwards bending, the proposed polarizer is bent around the vacuum cylinder when it is placed on the reverse side of the polarizer. Conversely, outwards bending is realized when the vacuum cylinder is placed on the front face of the polarizer. Figs. 11, 12 and 13 present the performance of the polarizer in terms of AR, conversion efficiency( ), and ellipticity ( ). In general, the variation of these parameters can be attributed to the changes in capacitance and inductance in line with the physical modifications in spacing and coupling when bent. This then results in the deviation of the transmitted waves from the desired CP characteristics. From the results, it is observed that the two −axis bending conditions (inwards and outwards) performed better in comparison to when the polarizer is bent at the −axis. Specifically for the −axis bending, the polarizer starts to operate with an under 3dB AR at 1.78 GHz, as illustrated in Fig. 11. This indicated a 3 of 31.3 % and operation from 1.78 GHz to 2.44 GHz when bent inwards. Meanwhile when bent outwards, the operating bands with at least 3dB of AR is seen to be separated into two bands, from 1.7 GHz to On the contrary, when the polarizer is bent at the −axis in both inwards and outwards conditions, the 3 dB AR criteria is not met despite its AR improvement when approaching 1.9 GHz.This observation also serves as an indication of the better expected performance of the polarizer when bent at the −axis compared to bending at the −axis in terms of conversion efficiency and ellipticity. From Fig. 12, both cases of −axis bending resulted in an improving conversion efficiency for the polarizer. It started operating with 90 % of at 1.6 GHz. However, the when the polarizer is bent outwards (denoted by green dotted graph) did not follow the same trend as the of the polarizer bent inwards (denoted by blue dotted graph). The is 36.71 % (from 1.69 GHz to 2.45 GHz) when the polarizer is bent at the −axis inwards, whereas two of 28.12 % (from 1.62 GHz to 2.15 GHz) and 0.4 % (from 2.45 GHz to 2.46 GHz) are observed when bent outwards.   Fig. 13, it is seen that both inwards and outwards bending configurations of the polarizer at the −axis similarly improved ellipticity ( ) to an acceptable level at approximately 1.9 GHz. However, similar to the case of conversion efficiency, the outward bending of the polarizer (green dotted graph) did not perform as well as the inward bending (blue dotted graph) in terms of ellipticity. Therefore, the bandwidth with ellipticity of at least 40°is 16.59 % (from 1.88 GHz to 2.22 GHz) and 0.38 % (from 2.34 GHz to 2.43 GHz) when bent inwards at the −axis, while only 1.68 % of ellipticity (from 1.88 GHz to 1.912 GHz) is produced when the polarizer is bent outwards at the −axis. Despite being acceptable in terms of conversion efficiency, bending of the polarizer at the −axis, however, is unfavorable in terms of ellipticity and AR. This is attributed to the change of capacitance ( ), due to change of shape in the connecting junction of the polarizer unit cells when bent at the y-axis (see Fig. 3).To conclude, while the deployment process should ensure the flat operation of the polarizer, any fail-safe deployable mechanism must allow the bending inwards at the −axis for better operation.

V. CONCLUSION
A single sided linear-to-circular polarizer designed on flexible textile material has been proposed for S-band CubeSats application. The polarizer is designed using an array of squareshaped loop unit cells. Two different flexible material have been used as its substrate: PDMS and felt textile. A detailed description of its design principles and the proposal of an equivalent circuit model and surface current analysis is first presented. The performance of both polarizers are then assessed in terms of phase difference, axial ratio, conversion efficiency, ellipticity and polarization azimuth. The textilebased design was chosen for fabrication and further evaluation due to its better performance indicated in simulations. It is observed to operate from 1.74 GHz to 3 GHz with a phase difference between and of 90°±10°. The polarizer indicated a 3 dB axial ratio bandwidth of 33.57 % (from 1.71 GHz to 2.4 GHz), whereas the bandwidth with at least 90 % of conversion efficiency is 47.3 % (from 1.55 GHz to 2.51 GHz). Meanwhile, its bandwidth fulfilling the ellipticity of between 40° and 45° is observed to be from 2 GHz to 2.4 GHz (18.18 %). To ensure that the deployable polarizer can be used in a fail-safe condition on CubeSats, the polarizer is assessed further under different bending conditions. It is observed that the most favorable fail-safe deployment process should allow the polarizer to be bent inwards at the −axis compared to the other bending conditions, when studied in terms of axial ratio, conversion efficiency and ellipticity. Finally, it can be concluded that the performance exhibited by the proposed polarizer when assessed under different conditions meets the requirements for future integration in S-band CubeSats.