Arrays of Gaussian vortex, Bessel and Airy beams by computer-generated hologram

•Simple and complex arrays are generated based on the fractional-Talbot effect.•Bessel and Airy arrays have pretty longer Rayleigh lengths.•Simple and complex photonic lattices are fabricated and far-field patterns are studied.•Our studies provide a simple way for the fabrication of photonic lattices.•The arrays are very practical in particle trapping to form desired particle arrays.

We generate various kinds of arrays of Gaussian vortex, Bessel and Airy beams, respectively, with digital phase holograms (DPH) based on the fractional-Talbot effect by using the phase-only spatial light modulator (SLM). The linear and nonlinear transmissions of these beam arrays in strontium barium niobate (SBN) crystal are investigated numerically and experimentally. Compared with Gaussian vortex arrays, Bessel and Airy beam arrays can keep their patterns unchanged in over 20 mm, realizing non-diffracting transmission. The Fourier spectra (far-field diffraction patterns) of the lattices are also studied. The experimental results are in good agreement with the numerical simulations.