# Multi-Beam Circular Polarized Reflectarray on Parabolic Reflector by Variable Rotation Technique
## 1 Introduction  
The development of wireless communication systems has been widely demanded for many application areas, such as in car-to-car communications, car-to-direct-broadcast-satellite communications, and car-to-roadside-unit communications. For antennas in car-to-car communications applications, the use of several radiators is a prominent solution. However, placing several radiators within the small space of a vehicle is a daunting task [1]. Therefore, multiband [2; 3] and/or wideband antennas [4; 5; 6] of small size which provide broad beamwidth are desired. These properties make antennas form reliable links during the vehicle's mobility. For car-to-direct-broadcast-satellite communications, it is desirable to have high gain and circularly polarized (CP) antennas with wide beam scanning angles [7; 8; 9; 10; 11]. The wide beam scanning angles enable vehicles to keep track of the satellites so that they are always within the reception area of the satellite and do not fall within blind spots [9]. In the case of car-to-roadside-unit communications, the standard specifications require the uses of antennas with radiation patterns that provide roughly a half-power beamwidth of 20\({}^{\circ}\) to confine the main lobe and sidelobe level 15 dB lower than those of the boresight [12]. In other important application areas, such as direct broadcast satellite service, military communication satellite, and high-speed internet applications, the antenna system is hosted on the satellite. Multi-spot beam satellite antennas are promising to offer contiguous coverage over a specified field of view on Earth for dual-polarization transmit-receive applications [13; 14]. In order to avoid mutual interference between the spot beams, a four-color frequency and polarization reusescheme is usually employed [13; 14]. In this scheme, two different frequency sub-bands and two orthogonal polarizations are used such that each spot in two adjacent colors could differ in frequency, polarization, or both [15]. In a four-color configuration, the antenna system shown in [13; 14] employs one reflector aperture per color. Although there are system configurations which reduce the profile of four reflector antennas by means of linear or circular polarization selective surfaces [16], the mass reflector antennas and complex mechanical systems are unsuitable for satellites. Technology based on printed reflectarrays offers a reduction in the number of apertures in the satellite, keeping the stringent requirements of frequency band and cross-polarizations [17; 18]. Reflectarray elements with variable rotation are promising for the generation of a pencil beam in circular polarization with very low levels of cross-polarization [19]. In fact, in [19] it is shown that phase shifts with opposite signs are added to the co-polar components of the CP reflected fields when the co-polar reflection coefficients of the two orthogonal linear polarizations are of equal magnitude and opposite sign. These opposite phase shifts depend on twice the rotation angle of the rotating element. This is known as the variable rotation technique (VRT). In [15], these properties was exploited to tilt the dual CP focused beams in specular directions. In this work, we present analysis and design techniques of multi-beam parabolic reflectarrays in dual circular polarization exploiting properties associated with the variable rotation of reflectarray elements, similar to the work presented in [15] but with some important differences. First, we explore the usage of rotating elements that by themselves provide the reflection properties required by the VRT. In particular, we chose a conductive cross as the rotating element. Contrary to the single dipoles proposed in [15], these elements depend weakly on the thickness and other parameters of the reflectarray dielectric layers. Moreover, the conductive cross roughly offers the possibility of independent phase control on orthogonal field components for linear polarization.