Nonlinear Talbot Effect And Its Applications In Super-focusing

The conventional Talbot effect, also referred to as self-imaging or lensless imaging, was originally discovered in1836by H. F. Talbot. The Talbot effect is a near-field diffraction phenomenon in which self-imaging of a grating or other periodic structure replicates at certain imaging planes when illuminated by the incident light. Before2010, however, all the achievements in the Talbot effect are limited in studying properties of input fundamental signals. In2010, we demonstrate the first nonlinear Talbot effect, i.e., the formation of second-harmonic (SH) self-imaging instead of the fundamental one from periodically poled LiTaO3(PPLT) crystals. This demonstration not only maintains all characteristics of the conventional Talbot effect, but offers a new way to image objects with periodic structures with higher spatial resolution. In this thesis, we have studied the fractional Talbot effect in PPLT crystals tunable nonlinear Talbot effect by introducing acoustic standing waves or quasi-phase-matching. Interestingly, we also realized superfocusing in the nonlinear Talbot self-imaging, which could be applied in super-resolution imaging. The main results are listed as follows:1. Both integer and fractional nonlinear Talbot effects were experimentally investigated in PPLT crystals. We carefully recorded the SH Talbot images at1/2,1/3and1/4Talbot lengths, which are well matched the simulated images by using the modified Rayleigh-Sommerfeld diffraction formula. We found that the image at1/2 Talbot length should also be a hexagonal array but with one half of the input period. At1/3Talbot plane, the image shows that:(a) the SH image is a hexagonal array with a reduced period equal to√3/3of the original one; and (b) the basis vectors of the lattice of the image are rotated30°with respect to the input. At1/4Talbot length, the period of the image reduces to1/4of the object array.2. Based on the nonlinear Talbot effect, we theoretically propose an acousto-optic tunable second-harmonic (SH) array in a ID periodically-poled LiNbO3(PPLN) crystal. By introduce the standing wave in a ID PPLN, the refractive index in PPLN is periodically modulated by the acoustic wave, so is the phase of the light travelling through the crystal. Besides generating acoustic waves in the PPLN crystal, we can also induce an external acoustic wave from a transducer. By controlling the power and the frequency of the acoustic standing wave, the phase of the SH array can be continuously tuned. When increasing the acoustic power, the phases of the SH waves are modulated, and a series of gaps appear within each period of the patterns along the x-axis. If choosing appropriate parameters, the intensities of the gaps can be suppressed down to zero and the period of the pattern reduces to a half of the original one. When the power reaches a certain value, the SH wave is focused. If we apply an acoustic standing wave along z-axis, the two phase gratings are perpendicular to each other. If choosing appropriate power, the ID diffraction patterns can be tuned to2D.3. We demonstrate a quasi-phase-matched second-harmonic Talbot self-imaging in a squarely-poled LiTaO3crystal. The domain structure not only provides reciprocal vectors to satisfy the phase-matching condition for second-harmonic generation, but also composes a nonlinear optical grating which is necessary to realize nonlinear Talbot self-imaging. Besides the near-field images, we also experimentally observed the far-field SH patterns and found the wavelength which satisfied the quasi-phase-matched condition. The QPM SH Talbot self-imaging was experimentally observed by setting the fundamental wavelength at958nm. Quasi-phase-matching can greatly enhance the quality of the second-harmonic self-imaging.4. In nonlinear Talbot effect, we experimentally achieved sub-diffracted light spots by manipulating diffraction interference of generated second-harmonic (SH) fields. The essence of our observations can be considered as a combination of the Toraldo Di Francia’s proposalfor subdiffraction and super-resolution with superoscillations. It was hard to realize the specialized phase modulation in the incident light, so there was no related experiments before to prove the subdiffraction theory. Until now, we find that the poling inversions in the PPLT crystal make the SH waves generated in the negative domains possess a π phase shift relative to those in the positive domains. Because of phase matching, the generated SH signals are band-limited, which is a key ingredient for superoscillations. Experimentally, we have observed sub-diffracted SH spots with size to be less than λ/4at least, a factor of2over the Abbe-Rayleigh diffraction limit by using a squarely and hexagonally-poled LiTaO3(PPLT) crystal. The achievable sub-diffraction patterns depend on parameters such as the periodicity of domain structures, size of domain structures, and the propagation distance. In principle, there is no fundamental lower bound to limit the focusing ability in the current technique. From the practical point of view, the current scheme offers a much simpler way to squeeze light spots beyond the diffraction limit. We thus expect our imaging technique to provide a super-resolution alternative for photolithography, medical imaging, molecular imaging, as well as bioimaging.