The Talbot effect is a self-imaging phenomenon of near-field diffraction. When a plane wave is incident on a periodic diffraction grating, the image of the grating is repeated at regular distances away from the grating plane. A Talbot array illuminator is a device that splits singular light beam into an array of beams with periodical optical intensity based on Talbot effect. LiNbO3 (LN) crystal is a kind of practicable material for a Talbot array illuminator due to its perfect optical characteristics. MgO-doped LiNbO3 (MgLN) crystal shows shorter absorption edge wavelength and higher resistance to photorefractive damage than LN. Up to now, the usefulness and simplicity of Talbot effect have still aroused the interest of many scholars. In the conventional method, a Talbot array illuminator is fabricated by using high external electric field to modulate the phase difference. However, essentially, high external electric field restricts the Talbot array illuminator to applications in optical integration and optical micro structure devices. Now we are looking forward to a new way which avoids using high external electric field. In this paper, we systematically study the two-dimensional (2D) hexagonal tunable array beam splitter, which is fabricated by domain-etching in MgLN crystal, and its fractional Talbot effect. The self-imaging phenomenon caused by Talbot effect in the Fresnel field for this phase array coherently illuminated is theoretically analyzed according to Fresnel diffraction theory. We numerically simulate the light intensity distributions of Talbot diffraction image under different values of Talbot coefficient β and different values of domain-etching depth. The simulation results show that β can change the array period and the structure distribution of the fractional Talbot diffraction image, and the domain-etching depth can modulate the light intensity distribution of diffraction image. Based on the numerical simulation results, the 2D hexagonal array beam splitters are fabricated with different values of domain-etching depth. The fractional Talbot diffraction images of array splitters are obtained at different values of β through the optical experiments. The results show that domain-etching depth can effectively modulate the intensity distribution of diffraction image, becoming a tunable array beam splitter successfully. The experimental results agree well with the simulation results. The theoretical and experimental results show that the optimal self-image visibility can be obtained at a Talbot coefficientβ of 0.5 and a domain-etching depth of 0.39 µm, while the duty cycle is 52%. Moreover, a good self-image pattern is also observed under thinner domain-etching depth, which is beneficial to optical integration and micro optical devices.
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