Recent progress in direct laser writing of three‐dimensional (3D) polymer nanostructures for photonics is reviewed. This technology has reached a level of maturity at which it can be considered as the 3D analogue of planar electron‐beam lithography. Combined with atomic‐layer deposition and/or chemical‐vapor deposition of dielectrics—the 3D analogues of planar evaporation technologies, the 3D polymer templates can be converted or inverted into 3D high‐refractive‐index‐contrast nanostructures. Examples discussed in this review include positive and inverse 3D silicon‐based woodpile photonic crystals possessing complete photonic bandgaps, novel optical resonator designs within these structures, 3D chiral photonic crystals for polarization‐state manipulation, and 3D icosahedral photonic quasicrystals. The latter represent a particularly complex 3D nanostructure.

Q uasicrystals1-4 are a class of lattices characterized by a lack of translational symmetry. Nevertheless, the points of the lattice are deterministically arranged, obeying rotational symmetry. Thus, we expect properties that are different from both crystals and glasses. Indeed, naturally occurring electronic quasicrystals (for example, AlPdMn metal alloys) show peculiar electronic, vibrational and physico-chemical properties. Regarding artificial quasicrystals for electromagnetic waves, three-dimensional (3D) structures have recently been realized at GHz frequencies 5 and 2D structures have been reported for the near-infrared region 6-9 . Here, we report on the first fabrication and characterization of 3D quasicrystals for infrared frequencies. Using direct laser writing 10,11 combined with a silicon inversion procedure 12 , we achieve high-quality silicon inverse icosahedral structures. Both polymeric and silicon quasicrystals are characterized by means of electron microscopy and visible-light Laue diffraction. The diffraction patterns of structures with a local five-fold real-space symmetry axis reveal a ten-fold symmetry as required by theory for 3D structures.Quasicrystals are different from both crystals and glasses: crystals have long-range translational symmetry, whereas glasses show only short-range order. Quasicrystals show long-range order but not in a repeating fashion yielding periodicity [1][2][3][4] : although the local arrangements of atoms are fixed in a regular pattern, each atom has a different atom configuration surrounding it. The Laue diffraction pattern of quasicrystals can, for example, show peaks with a five-or ten-fold symmetry axis, whereas crystals can reveal only two-, three-, four-or six-fold symmetries. Quasicrystals can be viewed as a projection of a six-dimensional (6D) crystal to three dimensions 3,4 . Although nature provides us with 3D quasicrystals for electrons 1 , corresponding structures for light need to be fabricated artificially. Here, the projection procedure is not just a Gedanken experiment, but can rather be The 'central atom' is in the centre of the structure. b, The same as a, but the 'central atom' is outside the structure. c, Oblique-incidence overview of a. d, A focused-ion-beam cut of a structure corresponding to a, but oriented along a local two-fold symmetry axis, revealing an 3D structure.used for the actual fabrication. This was first realized in 2005 at microwave frequencies 5 . The subtle but important difference between real atoms in quasicrystals and the dielectric building blocks, 'photonic atoms' , in photonic quasicrystals is that real atoms can 'float' in vacuum via their binding potential. The

Silicon inverse woodpile photonic crystals are fabricated for the first time. Our approach, which is based on direct laser writing of polymeric templates and a novel silicon single‐inversion procedure, leads to high‐quality structures with gap/midgap ratios of 14.2 %, centered at a wavelength of 2.5 μm. It is shown that gap/midgap ratios as large as 20.5 %, centered at 1.55 μm, may become possible in the future.

The aesthetics of quasicrystals has fascinated mankind already for centuries. Numerous examples are known in one and two dimensions, yet in three dimensions only icosahedral quasicrystals have been realized and observed to date in any system, i.e., in man‐made, natural, photonic, and phononic quasicrystals. We rationally construct the novel class of three‐dimensional rhombicuboctahedral quasicrystals and realize it as polymer microstructure.

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