## 1 Introduction  
[PERSON] introduced the traditional short backfire antenna (SBF) with circular reflectors for the first time in 1962 at the Air Force Cambridge Research Centre in Bedford, Massachusetts, as an improved version of the backfire antenna. The short backfire antenna was initially published in 1965, and [PERSON] was awarded its first patent in 1969 [1, 2]. The SBF antenna can produce moderate gain values between 13 dBi to 20 dBi, with sidelobes of at least 10-15 dB and a cross-polarization of under 20 dB. The compact construction, radiation properties, and simplicity of the feed configuration make it particularly appealing for mobile/maritime satellite communications, remote sensing/tracking, telemetry, and wireless local-area network applications [3]. In [4, 5], we presented very low-mass SBF antennas with excellent performance, such as a high gain and wide bandwidth. In this work, our goal is to further enhance the SBF antenna's gain and bandwidth without sacrificing other crucial performance factors like the cross-polarization ratio. In doing this, we aim to make it more appealing for the targeted applications. Several gain-enhancing techniques for many antennas that have been presented in the literature can also be applied to the SBF antenna. The first technique involves the design of antenna arrays such as the horn antenna array [6, 7] and patch antenna array [8, 9]. Combining the performance of the individual elements results in overall increased gain and directivity. While this is a very effective way of achieving higher gain, some designs require a multilayer design [9] and a very sophisticated feed network, thereby increasing the cost and complexity of the antenna. This technique can be challenging for applications with limited antenna space, since multiple antennas increase the final size. Another common technique involves increasing aperture efficiency by manipulating the aperture phase. This has been done in the literature by employing metasurfaces [10; 11] such as electro bandgap (EBG) materials [12; 13], partially reflective surfaces (PRS), or a meta surface lens [14; 15] over the opening of the antenna's aperture. Although metamaterials have been effective in increasing horn antenna gain, their complex design and narrow bandwidth are downsides. The metasurface's resonant structure limits the bandwidth of the antenna, as it determines the band of operation which is usually very narrow. Increasing the antenna's physical aperture size [16; 17] is the third gain enhancement technique that has been widely used and can be applied to SBF antennas. The aperture size can be increased by flaring the opening of the antenna, like the design of a horn antenna, which is essentially a flared waveguide antenna [18]. Signals traveling through the waveguide experience an abrupt change in impedance from the waveguide to free space, which is approximately 377 \(\Omega\). As a result of this change, signals are reflected along the waveguide as standing waves, similar to having poor matches at the end of coaxial or other wire-based transmission lines. The waveguide is usually flared or tapered out to get around this problem. This has the effect of allowing the impedance of the waveguide to gradually change to that of free space. It functions as a progressive matching transformer, minimizing the reflected signal and thereby increasing the efficiency of the antenna. The flaring angle has a great effect on the antenna gain and directivity. As the flaring angle and the aperture size increase, the gain increases. However, there is an optimal angle, beyond which the gain starts to decrease with an increasing angle of flare. This is because of the increasing phase error (phase difference between the edges and center point), which cancels out the gain [19]. Because the flaring angle required to achieve higher gain and bandwidth is minimal, the increase in the size of the antenna is not very significant. This is in contrast to the metasurface technique, which makes the flaring technique appealing for the SBF antenna.