Fabrication of highly rotational symmetric quasi-periodic structures by multiexposure of a three-beam interference technique

A simple and efficient interference method for fabricating highly symmetric two-dimensional (2-D) quasi-periodic structures (QPSs) is theoretically and experimentally demonstrated. With a three-beam interference technique, one can fabricate a periodic 2-D structure having sixfold symmetry. When this structure is multiduplicated into other specific orientations its combination results in a QPS with multifold symmetry. By use of n exposures with a rotation angle of 60 degrees /n, one can create a 2-D QPS with six n-fold symmetry. The QPS with a super high symmetry level, as high as 60-fold, is demonstrated for the first time to the best of our knowledge. The diffraction pattern of a QPS is consistent with the Fourier transform calculation. The fabricated structures should be useful for many applications, such as isotropic bandgap materials and extraction enhancement of light-emitting diodes.