Research Of Phase Characteristics In Nonlinear Talbot Effect

In 1785, David Rittenhouse became the first one to make the diffraction grating and observed diffraction effect. In 1836. H. F. Talbot found the self-imaging of grating in certain distance by extending the distance of observation from Fraunhofer diffraction region into Fresnel diffraction region, which was demonstrated by Lord Rayleigh in 1881. To commemorate H. F. Talbot, this non-lenses imaging method of periodical structures was named Talbot Effect after H. F. Talbot. For distinguishing from modern associated Talbot effect like nonlinear Talbot effect, X ray Talbot effect, electronic Talbot effect, quantum Talbot effect and so on, we call it conventional Talbot effect here.The conventional Talbot effect, in the long study history of more than 180 years, mainly focused on changing features of sources and structures of gratings, which showed its limitations. Whereas the nonlinear Talbot effect reported by Zhang’s research group in 2010, which referred to the second harmonic self-imaging phenomenon generated by periodically poled LiTaO3 (PPLT) crystal, broke through materials systems used by the conventional Talbot Effect and brought Talbot Effect into nonlinear optics. After the publication of the nonlinear Talbot effect. Zhang’s research group reported fractional nonlinear Talbot effect characterized by rotation and translation of images as well as period doubling. Soon afterwards, Zhang’s research group reported acousto-optic tunable nonlinear Talbot effect and quasi-phase-matched induced second-harmonic (SH) Talbot self-imaging by taking advantage of acousto-optic effect of nonlinear crystal and reciprocal lattice vector induced by ferroelectric domain engineeringoUp to now, study of the nonlinear Talbot effect has still concentrated on imaging effect in free space----the intensity patterns of the SH waves, while the phases of the generated SH waves in imaging process have not been explored. However, the phases of the generated SH waves are the key factor of nonlinear Talbot effect. When the laser beam focuses on the PPLT crystal, the antiparallel ferroelectric polarization between the positive and negative domains results in a π-phase shift in the generated SH waves. And the periodicity of structure leads to periodical phase distribution satisfying the sufficient condition of Talbot effect. So if we can figure out how phases interact with each other in self-imaging positions or other Fresnel imaging positions, it will help us to better understand SH self-imaging features and boost its applications. During researching propagation features of the π-phase-shift SH beams and their superposition, some conclusions are showed following:1. The cause of the π-phase-shift SH beams generated by PPLT crystal is that poling process changes the physical coordinate of nonlinear crystal, which change signs of relevant second nonlinear coefficients.2. The rotation operation can also changes signs of relevant second nonlinear coefficients, and then changes polarizations and phases of generated SH waves. Such simple method provides us a convenient way to fulfill interference between reference beam and signal beam.3. The π-phase-shift beams are separated successfully by introducing a reference beam to interfere with the signal beam from PPLT. Then their propagation features are studied independently, from which the self-imaging effect are found in the SH waves from positive domains or negative domains. Besides, their superposition restores the nonlinear Talbot effect.4. In the self-imaging planes, the SH waves from positive domains and negative domains are mutually complementary. It means the superposition can be seen as intensity addition. However, in other Fresnel imaging planes, complex amplitude superposition between SH waves from positive domains and negative domains generates special intensity images. Their interference produced focusing arrays and nested square arrays in different imaging planes.