A light intensity distribution generated by an electro-optic tunable multiphase array based on the Talbot effect under lower external electric field was demonstrated. This 2-D distribution is mapped as a 2D hexagonal tunable phase array based on the periodically poled MgO-doped LiNbO<sub>3</sub> crystal (PPMgLN). Applying a lower external electric field through the Indium Tin Oxide (ITO) electrodes coated on the +z and –z surfaces of PPMgLN crystal, a tunable PTAI was fabricated. The self-imaging phenomenon of Talbot effect in the Fresnel field for this phase array coherently illuminated is theoretically analyzed according to Fresnel diffraction theory. The experimental and theoretical results show that the self-images visibility depends on array duty cycle and external electric field for a fixed diffraction distance. The optimal self-images visibility can be obtained at array duty cycle of 52%, phase difference of 0.75π for diffraction position of 0.33 times Talbot distance. Moreover, a preferable self-image pattern can be observed under an unprecedented lowest external voltage of 0.461kV correspond to phase difference of 0.35π，which is beneficial to optical integration and micro optical devices.
Electro-optically tunable two-dimensional hexagonal Talbot phase array which are based on congruent Lithium
Niobate crystal and MgO doped Lithium Niobate crystals are investigated, respectively. Experimental results show that a
variety of pattern can be generated under different voltage bias and fractional distance. Numerical simulation was studied,
and the experimental results agreed with simulation.