The effect of lattice shapes of Thue-Morse crystals on the diffraction pattern

According to the principle of Fourier optics, the effect of the lattice shape of two-dimensional Thue-Morse quasicrystais (2D TM QC) on the diffraction patterns is analyzed. The shapes of lattices have a considerable influence on the diffraction pattern of the lower order 2D TM QC, but do not affect that of the higher order 2D TM QC, excepting a little change on the intensity distribution. And the above numerical results are demonstrated by the diffraction experiments of samples of 2D TM QC with the circle and square lattices, which are fabricated on the substrate of Poly Methyl Methacrylate (PMMA) by the Electron Beam Lithography (EBL). It is shown that the experimental results are consistent with the theoretic simulations very well.