## 1 Introduction  
Satellites are attractive to both developed and developing countries because of their wide coverage. Low-earth orbit(LEO) satellite networks enable ubiquitous wireless coverage, which facilitates information access in rural areas of terrestrial networks. LEO satellites serve a wide range of audiences, including aircraft, ships, and automobiles, which in turn, placed a high demand on beam flexibility. According to the next-generation communication protocol [1; 2; 3], satellite internet is defined as a complement to the terrestrial internet. It benefits from LEO satellites' low orbital height, inexpensive launch, speedy transmission, and low path loss [4]. In the post-5G era, satellites are required to provide broadband services under large-scale constellations without interfering with other links, which requires flexible and controllable satellite beams in terms of directivity [5; 6]. Due to their outstanding dependability, low cost, and simplicity in implementing numerous beams, phased arrays have replaced classic mechanical scanning antennas [7; 8]. A number of phased-array antennas have been made available for satellite use in terms of beam forming, beam switching, and large beam-steering angle [9; 10; 11; 12; 13]. This high flexibility also makes the beam-hopping proposed in the DVB-S2X protocol possible [14]. For instance, each of the three active phased-array antennas on the US Iridium/NEXT constellation's LEO satellites can produce 16 beams when operating in the L-band [15]. The current major large LEO satellite constellation SpaceX also uses phased-array antennas as well as OneWeb and Telesat. Each SpaceX satellite is outfitted with a sophisticated digital payload that contains a phased array, allowing for the independent steering and shaping of each beam. Each of the 16 very elliptical beams that OneWeb produces, which correspond to the satellite's flight path, leaves an imprint on Earth. With individually formable and programmable beams that may be sparsely deployed and precoded to serve customers, Telesat and SpaceX are comparable [16; 17]. It is generally known that huge LEO satellites' constellations can interact directly via laser links, making the compatibility of phased array systems for LEO satellites with optical links all the more crucial [18]. First, in 1995 [PERSON] et al. used optical techniques to solve various approaches to the fundamental problem of broadband phased arrays, namely the most critical beam strabismus [19]. [PERSON] et al. proposed an optical true-time delayed (OTTD) beamforming system using dispersion-compensating fiber and multi-wavelength lasers for phased-array antennas in 2011 [20]. Starlink is an existing electronically controlled phased-array antenna system that is extremely scalable and aircraft independent. They designed and manufactured a new all-optical driven passive phase shifter in the X-band, based on a nematic phase liquid crystal mesocrystal azo dye hybrid in 2020 [21]. Due to the recent rapid advancement of photonic integration technology, some integrated OTTD has undergone several modifications and iterations with noticeable performance increases [22; 23; 24], especially optical true delay lines based on the array waveguide grating router(AWGR) structure [25; 26; 27; 28; 29; 30]. [PERSON] built and characterized an array waveguide grating feedback loop-based remotely controllable integrated OTTD (AWG loop). Since AWGs are employed as wavelength multiplexers (MUXs) and de-multiplexers (de-MUXs), AWG loops can offer an integrated OTDL solution that is small, fabrication-resistant, and scalable [31]. [PERSON] et al. reported an AWGR integrated chip with doubled delay resolution and experimentally verified its use in a 38-GHz fiber-optic wireless beam-steering system with 186\({}^{\circ}\) angular steering [32]. In a multi-hop bent-pipe LEO satellite network, a flexible beam-management system especially created to include an optical switching network is essential.