## 1 Introduction  
Commercial off-the-shelf cellular phones, or \"stock\" cellular phones, have a demand to establish connectivity directly with the satellite for voice, messaging, and basic web browsing services, especially outside the reach of traditional terrestrial mobile networks. Due to the limitation of terrestrial mobile terminals in gain and transmission power, a large aperture of phased array antenna for satellite payload is needed to improve the passive gain and realize direct-to-cellular communications. The space antenna with a large aperture should have the merits of a low-profile, shared aperture for RX/TX, be lightweight, and be deployable to meet the serious demands of limited space, weight, and power in a satellite platform. This work has selected the S-/C-band for direct-to-cellular communications services, specifically 1.9-2 GHz and 3.4-3.6 GHz for the downlink and uplink, respectively. However, it is costly to support two separate downlink and uplink phase arrays simultaneously, especially for a satellite with limited space and resources. The shared-aperture antenna is thus an attractive candidate due to its compact space and cost-effective manufacture [1]. Circularly polarized (CP) antennas have many advantages [2, 3] over linearly polarized antennas [4, 5, 6]. For example, due to its lower attenuation in complex climatic environments, the CP antenna could penetrate the ionosphere and overcome the Faraday Effect in the ionosphere between satellite and earth communications. Therefore, CP antennas have an important significance in direct-to-cellular communications. Recently, different antennas for space applications with dual-band and dual-CP operation have been reported. A simple way to achieve dual-band dual-CP operation is to use a reflector and feed horn with dual-frequency dual-CP characteristics [7; 8]. However, the reflector antenna is relatively too high and heavy for the application of the multi-satellite launch mode. Therefore, the planar phased array based on microstrip antenna technology is a better choice. In [9], this antenna is fed by microstrip lines with double orthogonal slits, and the circular-polarized radiation can be realized by tuning the quadrature slits with appropriate amplitude and phase. However, two orthogonal double-slit structures are too large and complicated to be arranged for dual-frequency dual-CP operation in the phased array normally with an elements space of half-wavelength. More commonly, dual-frequency, dual-CP performance is realized by multi-layer stacking [10; 11; 12] with two different elements for different frequencies, respectively. The multi-layer stacking structure can effectively improve the isolation between the two bands. However, the axial ratio (AR) and the gain of the lower frequency antenna are normally deteriorated due to the shielding of the upper layer. Moreover, multi-layer antennas are less stable than single-layer antennas and have the potential risk of delamination in the complex space environment, with alternate operation temperatures from \(-90^{\circ}\)C to \(90^{\circ}\)C in low earth orbit (LEO) as an example. Several antennas have also been proposed to achieve dual-frequency dual-CP through single-layer structures, such as monopole [13], slot [14], and patch [15]. However, these antennas have complex fed structures and are still difficult to form large arrays for the satellite payloads with direct-to-cellular communication capability. In design [13], two orthogonal E vectors with a 90-degree phase difference is excited in a planar monopole antenna for dual-CP operation. However, this monopole with a CPW ground is not suitable for working as a radiation element of a phased array. In design [14], a dual-CP, single-layer, full-metal slot array antenna in gap waveguide technology is proposed. However, this antenna has a complex fed structure and is too bulky to form a large direct-to-cellular communication payload, which is operated in the S-/C-band.