Theoretical investigation on a general class of 2D quasicrystals with the rectangular projection method

We take a theoretical investigation on the reciprocal property of a class of 2D nonlinear photonic quasicrystal proposed by Lifshitz et al. in PRL 95, 133901 (2005). Using the rectangular projection method, the analytical expression for the Fourier spectrum of the quasicrystal structure is obtained explicitly. It is interesting to find that the result has a similar form to the corresponding expression of the well-known 1D Fibonacci lattice. In addition, we predict a further extension of the result to higher dimensions. This work is of practical importance for the photonic device design in nonlinear optical conversion progresses.