Here, for convenience, the vector in 2D is represented by a complex number: the real part represents the x-component and the imaginary part represents the y-component. How to get the Fourier transform is the key of this program. Here I used the analytical form for the circular cylinder and used the shift property to get the Fourier transform for more complicated system consisting of finite number of individual atoms.

Triangular lattice with air holes in Si or GaAs material.m

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