Professor Satoshi Iwamoto, Visiting Associate Professor Yasutomo Ota (Associate Professor at Keio University), and their international research team have succeeded for the first time in generating periodic three-dimensional topological structures within propagating electromagnetic waves. In recent years, three-dimensional topological structures known as hopfions, which had been theoretically predicted, have been observed in several physical systems such as solids and electromagnetic waves. These structures have garnered attention as media capable of storing and transmitting data with high density and stability. However, the creation of hopfion crystal states was essential for engineering applications. In this study, by appropriately designing the polarisation state and spatial intensity distribution of electromagnetic waves propagating in free space for two frequencies and creating their superposition, the team succeeded in periodically generating the three-dimensional structure of hopfions in four-dimensional spacetime, where the polarisation state changes temporally and spatially. This achievement is expected to significantly enhance transmission capacity and error tolerance when applied to optical communication and wireless communication. Additionally, it paves the way for the development of technologies to create and manipulate topological three-dimensional structures within materials. This international collaborative research team includes Assistant Professor Wenbo LIN from the Institute of Advanced Science at Tokyo University of Science and researchers from Nanyang Technological University in Singapore.This research paper was published in the 21 August online edition of Physical Review Letters.