  Reconfigurable intelligent surface (RIS) has emerged as a promising
technology in both terrestrial and non-terrestrial networks (NTNs) due to its
ability to manipulate wireless environments for better connectivity.
Significant studies have been focused on conventional RIS with diagonal phase
response matrices. This simple RIS architecture, though less expensive, has
limited flexibility in engineering the wireless channels. As the latest member
of RIS technology, beyond diagonal RIS (BD-RIS) has recently been proposed in
terrestrial setups. Due to the interconnected phase response elements, BD-RIS
significantly enhances the control over the wireless environment. This work
proposes the potential and challenges of BD-RIS in NTNs. We begin with the
motivation and recent advances in BD-RIS. Subsequently, we discuss the
fundamentals of BD-RIS and NTNs. We then outline the application of BD-RIS in
NTNs, followed by a case study on BD-RIS enabled non-orthogonal multiple access
low earth orbit satellite communication. Finally, we highlight challenges and
research directions with concluding remarks.
