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