Periodic Structures With Higher Symmetries: 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).