In this paper, we consider the simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted THz communications with three-side beam split. Except for the beam split at the base station (BS), we analyze the double-side beam split at the STAR-RIS for the first time. To relieve the double-side beam split effect, we propose a time delayer (TD)-based fully-connected structure at the STAR-RIS. As a further advance, a low-hardware complexity and low-power consumption sub-connected structure is developed, where multiple STAR-RIS elements share one TD. Meanwhile, considering the practical scenario, we investigate a multi-STAR-RIS and multi-user communication system, and a sum rate maximization problem is formulated by jointly optimizing the hybrid analog/digital beamforming, time delays at the BS as well as the double-layer phase-shift coefficients, time delays and amplitude coefficients at the STAR-RISs. Based on this, we first allocate users for each STAR-RIS, and then derive the analog beamforming, time delays at the BS, and the double-layer phase-shift coefficients, time delays at each STAR-RIS. Next, we develop an alternative optimization algorithm to calculate the digital beamforming at the BS and amplitude coefficients at the STAR-RISs. Finally, the numerical results verify the effectiveness of the proposed schemes.

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