We fabricate three-dimensional photoresist templates by means of laser holography. In particular, fcc structures are achieved by placing a specially designed ''prism'' onto the photoresist surface. This solves the problem of previous work, in which the refraction at the air-photoresist interface made it impossible to obtain the required angles of the light wave vectors inside the photoresist. The photoresist templates are characterized by scanning electron microscopy as well as by optical transmission spectroscopy, which agree well with numerical band-structure calculations. © 2003 American Institute of Physics. ͓DOI: 10.1063/1.1557328͔Large-area, three-dimensional ͑3D͒ photonic crystals 1,2 incorporating cavities and waveguides would not only offer interesting perspectives in high-density integrated optics for telecommunications applications, but would also be interesting for fundamental studies, for instance on the quantum optical properties of nanoresonators. 3,4 Different approaches towards this goal are currently being followed, such as inverse opals, 5 stacked two-dimensional structures fabricated by electron-beam lithography, 6,7 and holographically generated photoresist templates [8][9][10][11] with the potential to be infiltrated by appropriate materials.In the latter holographic approach, N collimated coherent laser beams are sent onto a photoresist. The resulting multiple-beam interference pattern exposes the photoresist. In the developer, the more exposed and less exposed parts have different solubilities, leading to a porous photoresist structure. To obtain a 3D intensity pattern I(r), which exposes the photoresist, N needs to be four or larger ͓Fig. 1͑a͔͒. The light intensity for Nϭ4 can be written asHere, the reciprocal lattice vectors G nm ϭk n Ϫk m are determined by the differences of the wave vectors k n of the incident plane waves and the ͑generally complex͒ form factors a nm ϭE n 0•E m 0* , resulting from the relative amplitudes and polarizations of the incident laser beams. Three of the reciprocal lattice vectors G nm , for instance G 12 , G 13 , and G 14 , are linearly independent and form a basis of reciprocal space. The terms with nϭm lead to a constant background. Therefore, the reciprocal lattice vectors G nm determine the lattice of the crystal structure, whereas the form factors a nm determine the internal structure of the unit cell. While Ref. 8 used linear polarizations only, choosing different linear, circular, or generally elliptical polarizations results in more design freedom via the form factors a nm .In order to achieve a complete 3D photonic band gap, it is known that symmetric structures are advantageous as compared to more asymmetric structures. 12 An interesting candidate might be the fcc crystal structure ͑analogous to the inverse opals or diamond structures͒. In the pioneering work of Ref. 8, a bcc reciprocal lattice ͑equivalent to a fcc real-space lattice͒ was demonstrated in air.However, it is important to note that this fcc lattice in air translates into a non-fcc, st...

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The most interesting phenomena in photonic crystals stipulate the presence of omnidirectional band gap, i.e. overlapping of stop bands in all directions. Higher rotational symmetry and isotropy of quasicrystals in comparison with ordinary crystal give a hope to achieve a gap opening at lower dielectric contrasts. But nonperiodic nature of quasicrystals makes the size of stop bands lower than in the case of ordinary periodic crystal. We study transition from periodic structure to nonperiodic one by considering pseudoquasicrystals -quasicrystal approximants with growing period to weigh advantages and disadvantages of quasicrystals. We consider the structures that can be obtained by multiple exposure holographic lithography for the case of 2, 3, 4, and 6-fold exposure by two wave interference pattern, corresponding square, hexagonal, 8-fold and 12-fold symmetry lattice.

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