Fabrication of two- and three-dimensional quasi-periodic structures with 12-fold symmetry by interference technique.

We demonstrate theoretically and experimentally a useful technique for fabrication of two- and three-dimensional (2D or 3D) quasi-periodic structures by a double-exposure of a periodic interference pattern. With three-beam and three-beam-plus-one interference techniques, one can fabricate a periodic 2D and 3D structure having six-fold symmetry, respectively. When this structure is duplicated in another orientation, its combination results in a quasi-periodic twelve-fold symmetry structure. Experimental results obtained by using two-exposure of three-beam and/or three-beam-plus-one interference pattern at 442 nm into a positive photoresist (AZ-4620) proved the theoretical predictions. This study is potentially useful for photonic researches and applications.