Periodic structures with higher symmetries and their applications in electromagnetic devices

Higher symmetries frequently amaze human beings because of the illusions and incredible landscapes such symmetries can produce. For example, imagine the unearthly pictures of the Dutch graphic artist M.C. Escher. He made use of glide symmetry and reflection to produce unbelievable transitions and transformations of objects and beings, as illustrated in Figure 1(a). However, the history of higher symmetries started much earlier. Escher was partially inspired by the Moorish tessellations in the Alhambra in Granada, Spain, such as the ones pictured in Figure 1(b). The authors would like to thank Oskar Zetterström for providing the photo in Figure 5(a). This work was partly funded by the Spanish Government, under grant TEC2016-79700-C2-2-R; the French Government, under National Research Agency (ANR) Modeling and De - sign of Holey Metasurfaces project grant ANR JCJC 2016, ANR-16-CE24-0030; the Vinnova project High-5 (grant 2018-01522), under the Strategic Program on Smart Electronic Systems; the Stiftelsen Åforsk project Higher-Symmetric Materials for 5G Communications (grant 18-302); and COST Action SyMat CA18223, supported by COST (European Cooperation in Science and Technology), www.cost.eu.