Singular and nonsingular flat bands in a Sierpinski fractal‐like photonic lattice are reported. It is demonstrated that the lowest two bands, being isolated and degenerate due to geometrical frustration, are nonsingular and thus can be spanned by a complete set of compact localized states. These states are experimentally proven to propagate diffractionless in the photonic lattice. The results reveal the interplay between geometrical frustration, degenerate flat bands, and compact localized states in a single photonic lattice, and pave the way to photonic spin liquid ground states.
We explore a physical approach to invert ferroelectric domains in the volume of MgO-doped lithium niobate crystals without any external electric field. Permanent defect structures are created by focused infrared femtosecond laser pulses below the material surface along the polar axis followed by a thermal treatment. This procedure leads to an inversion of ferroelectric domains beneath and above the laser-induced filaments up to the surfaces of the crystal. All domain walls are straight and up to 800 μm long. We measure the domain width in dependence on the length of the filaments and the writing energy. The smallest achieved domain width and the domain spacing is 1 μm. We propose a model taking into account the temperature dependence of the pyroelectric field and thermally activated bulk charges to explain the mechanism of domain inversion. Our findings pave the way to all-optical printing of arbitrary ferroelectric domain structures for nonlinear photonic applications.
Engineered domain structures play an essential role in nonlinear optics for quasi-phase-matched parametric processes. Pyroelectric field-assisted domain inversion with focused femtosecond laser pulses is a promising approach to create arbitrary two-dimensional nonlinear photonic structures in a large volume without externally applied electrical fields. We fabricate lattices of ferroelectric domains by patterning lithium niobate crystals with femtosecond laser pulses and then heating them to elevated temperatures. After cooling to room temperature, domains form below and above the laser-induced seeds. We investigate the effect of temperature and seed spacing on the number and size of inverted domains. In a temperature range of 220 °C-300 °C all domains are inverted in a two-dimensional lattice with periods of 15 µm × 6.3 µm. Smaller lattice periods result in a smaller fraction of inverted domains. Measurements with conducting, nonconducting, and short-circuited crystal surfaces reveal the influence of surface charges during the domain formation process. From the obtained domain widths and spacings, we calculate the effective nonlinear coefficient of quasi-phase-matched second-harmonic generation in two-dimensional nonlinear photonic structures.
Photonic lattices have emerged as an ideal testbed for localizing light in space. Among others, the most promising approach is based on flat band systems and their related nondiffracting compact localized states. So far, only compact localized states arising from a single flat band have been found. Such states typically appear static, thus not allowing adaptive or evolutionary features of light localization. Here, we report on the first experimental realization of an oscillating compact localized state arising from multiple flat bands. We observe an oscillatory intensity beating during propagation in a two-dimensional photonic decorated Lieb lattice. The photonic system is realized by direct femtosecond laser writing and hosts most importantly multiple flat bands at different eigenenergies in its band structure. Our results open new avenues for evolution dynamics in the up to now static phenomenon of light localization in periodic waveguide structures and extend the current understanding of light localization in flat band systems.
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