Study On Spatial Light Localization Of Flat-band Modes In Photonic Lattices

The localization of light and the propagation of non-diffracting images in photonic lattices have been studied for a long time. In recent years, such effects have been experimentally observed in photonic systems. Due to the presence of disorder, nonlinearity, some form of defects and analogous external fields, localization effects have been observed. However, there is another way of accomplishing this, in which the lattices remain perfectly periodic but is able to support localized states. In that case, one can find extremely localized entities that do not diffract at all, and that remain localized by virtue of the specific lattice geometries. Meanwhile, taking advantage of the superposition of localized flat-band states inherent can also remain localized states. We can exploit it to demonstrate distortion-free image transmission in such two-dimensional flat-band photonic structures. Those localized mode structures are more suitable for image transmission in optical communication.In this dissertation, we take the photonic lattices as transmission platform, particularly Kagome and Lieb photonic lattices, and study on the factors about affecting the existence of flat-band theoretically. We demonstrate the localization of flat-band modes by simulating the linear transmission in corresponding flat-band lattices. Experimentally, we fabricate Kagome, Lieb lattices by using the optical induction technique with amplitude and phase modulation, and show the localization of flat-band states and the distortion-free image transmission. Our experimental observations find good agreement with numerical simulations.Firstly, we derived the paraxial approximation schrodinger-like equation, which described the light propagation linearly in flat-band lattices.Secondly, we obtain the linear spectrum in the tight-binding models by considering the unit cell of Kagome and Lieb lattices. The band structures of these two lattices respectively both contain a flat band with zero diffraction. We explain the localization of flat-band modes for destructive wave interference. We give the range of lattice constant to remain flat band via step by step beam propagation method.Finally, we fabricate Kagome, Lieb lattices by using optical induction method with amplitude and phase modulation. To highlight the localization of flat-band states, we also excite the Kagome lattice by a single Gaussian beam and “ring” modes profile with uniform phase structure for comparison. We observe the nondestructive out pattern for the transmission of flat-band modes and linear combination of flat-band states. Our experimental observations find good agreement with numerical simulations. It is worth mentioning that this idea could find a direct application for all-optical applications.