Harnessing nonlinear frequency upconversion of Talbot effect with flexible Talbot lengths

We report on a simple experimental scheme demonstrating nonlinear frequency upconversion of the Talbot effect with controllable Talbot lengths at high conversion efficiency. Using a microlens array (MLA) as an array illuminator at 1064 nm onto a 1.2-mm-thick BiBO crystal, we have observed the second harmonic Talbot effect in green at 532 nm with a Talbot length twice that of the pump Talbot length. However, the Talbot length is constant for fixed parameters of the periodic object and the laser wavelength. With the formulation of a suitable theoretical framework, we have implemented a generic experimental scheme based on the Fourier transformation technique to independently control the Talbot lengths of the MLA in both the pump and the second harmonic, overcoming the stringent dependence of MLA parameters on the self-images. Deploying the current technique, we have been able to tune the Talbot lengths from z_T = 26 cm to z_T = 62.4 cm in the pump and z_T = 12.4 cm to z_T = 30.8 cm in the second harmonic, respectively. The single pass conversion efficiency of the Talbot images is 2.91% W^-1, an enhancement of a factor of 10⁶ as compared to the previous reports. This generic experimental scheme can be used to generate long-range self-images of periodic structures and also to program desired Talbot planes at required positions at both pump and upconverted frequency to avoid any mechanical constraints of experiments.